%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW388+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n011.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 18:09:05 EDT 2024 % Result : Theorem 165.14s 165.03s % Output : CNFRefutation 165.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWW388+1 : TPTP v8.2.0. Released v5.2.0. % 0.12/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n011.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Jun 19 05:51:54 EDT 2024 % 0.12/0.33 % CPUTime : % 0.20/0.56 start to proof:theBenchmark % 164.75/164.87 %------------------------------------------- % 164.75/164.87 % File :CSE---1.7 % 164.75/164.87 % Problem :theBenchmark % 164.75/164.87 % Transform :cnf % 164.75/164.87 % Format :tptp:raw % 164.75/164.87 % Command :java -jar mcs_scs.jar %d %s % 164.75/164.87 % 164.75/164.87 % Result :Theorem 150.940000s % 164.75/164.87 % Output :CNFRefutation 150.940000s % 164.75/164.87 %------------------------------------------- % 164.75/164.88 %------------------------------------------------------------------------------ % 164.75/164.88 % File : SWW388+1 : TPTP v8.2.0. Released v5.2.0. % 164.75/164.88 % Domain : Software Verification % 164.75/164.88 % Problem : Hoare's Logic with Procedures 435670, 5000 axioms selected % 164.75/164.88 % Version : Especial. % 164.75/164.88 % English : % 164.75/164.88 % 164.75/164.88 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 164.75/164.88 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 164.75/164.88 % Source : [Bla11] % 164.75/164.88 % Names : hoare_435670.5000.p [Bla11] % 164.75/164.88 % 164.75/164.88 % Status : ContradictoryAxioms % 164.75/164.88 % Rating : 0.75 v8.2.0, 0.72 v8.1.0, 0.78 v7.4.0, 0.87 v7.3.0, 0.83 v7.1.0, 0.78 v7.0.0, 0.83 v6.4.0, 0.81 v6.3.0, 0.79 v6.2.0, 0.88 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.93 v5.4.0, 1.00 v5.2.0 % 164.75/164.88 % Syntax : Number of formulae : 5248 (1762 unt; 0 def) % 164.75/164.88 % Number of atoms : 12558 (4565 equ) % 164.75/164.88 % Maximal formula atoms : 13 ( 2 avg) % 164.75/164.88 % Number of connectives : 8316 (1006 ~; 149 |; 706 &) % 164.75/164.88 % ( 886 <=>;5569 =>; 0 <=; 0 <~>) % 164.75/164.88 % Maximal formula depth : 22 ( 6 avg) % 164.75/164.88 % Maximal term depth : 19 ( 2 avg) % 164.75/164.88 % Number of predicates : 145 ( 144 usr; 2 prp; 0-6 aty) % 164.75/164.88 % Number of functors : 393 ( 393 usr; 57 con; 0-7 aty) % 164.75/164.88 % Number of variables : 16629 (16492 !; 137 ?) % 164.75/164.89 % SPC : FOF_CAX_RFO_SEQ % 164.75/164.89 % 164.75/164.89 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 164.75/164.89 % 2011-03-01 13:03:12 % 164.75/164.89 %------------------------------------------------------------------------------ % 164.75/164.89 %----Relevant facts (4986) % 164.75/164.89 fof(fact_ext,axiom, % 164.75/164.89 ! [V_g_2,V_f_2] : % 164.75/164.89 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 164.75/164.89 => V_f_2 = V_g_2 ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_empty,axiom, % 164.75/164.89 ! [V_G_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ). % 164.75/164.89 % 164.75/164.89 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 164.75/164.89 ! [V_a_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool))) ). % 164.75/164.89 % 164.75/164.89 fof(fact_cut,axiom, % 164.75/164.89 ! [V_G_2,V_ts_2,V_G_H_2,T_a] : % 164.75/164.89 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 164.75/164.89 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_G_H_2) % 164.75/164.89 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_WT__bodiesD,axiom, % 164.75/164.89 ! [V_b,V_pn] : % 164.75/164.89 ( c_Com_OWT__bodies % 164.75/164.89 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) % 164.75/164.89 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_WT_Oequations_I7_J,axiom, % 164.75/164.89 ! [V_a_2] : % 164.75/164.89 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) % 164.75/164.89 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_bot__fun__def,axiom, % 164.75/164.89 ! [V_x_2,T_b,T_a] : % 164.75/164.89 ( class_Orderings_Obot(T_a) % 164.75/164.89 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_MGF,axiom, % 164.75/164.89 ! [V_ca_2] : % 164.75/164.89 ( c_Hoare__Mirabelle_Ostate__not__singleton % 164.75/164.89 => ( c_Com_OWT__bodies % 164.75/164.89 => ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 164.75/164.89 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_empty__is__image,axiom, % 164.75/164.89 ! [V_A_2,V_f_2,T_b,T_a] : % 164.75/164.89 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) % 164.75/164.89 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_image__empty,axiom, % 164.75/164.89 ! [V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.75/164.89 % 164.75/164.89 fof(fact_image__is__empty,axiom, % 164.75/164.89 ! [V_A_2,V_f_2,T_a,T_b] : % 164.75/164.89 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.89 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_bot__apply,axiom, % 164.75/164.89 ! [V_x_2,T_b,T_a] : % 164.75/164.89 ( class_Orderings_Obot(T_a) % 164.75/164.89 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_MGF__lemma2__simult,axiom, % 164.75/164.89 ! [V_F_2] : % 164.75/164.89 ( c_Hoare__Mirabelle_Ostate__not__singleton % 164.75/164.89 => ( c_Com_OWT__bodies % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),V_F_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)))) % 164.75/164.89 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody)),V_F_2) ) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_MGF__lemma1,axiom, % 164.75/164.89 ! [V_ca_2,V_G_2] : % 164.75/164.89 ( c_Hoare__Mirabelle_Ostate__not__singleton % 164.75/164.89 => ( ! [B_x] : % 164.75/164.89 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) % 164.75/164.89 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,B_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) % 164.75/164.89 => ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 164.75/164.89 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_WTs__elim__cases_I7_J,axiom, % 164.75/164.89 ! [V_P] : % 164.75/164.89 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P))) % 164.75/164.89 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_image__image,axiom, % 164.75/164.89 ! [V_A_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_c,T_a,hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_f_2),V_g_2)),V_A_2) ). % 164.75/164.89 % 164.75/164.89 fof(fact_order__refl,axiom, % 164.75/164.89 ! [V_x,T_a] : % 164.75/164.89 ( class_Orderings_Opreorder(T_a) % 164.75/164.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_equalityI,axiom, % 164.75/164.89 ! [V_B_2,V_A_2,T_a] : % 164.75/164.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 164.75/164.89 => V_A_2 = V_B_2 ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_empty__subsetI,axiom, % 164.75/164.89 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 164.75/164.89 % 164.75/164.89 fof(fact_subset__refl,axiom, % 164.75/164.89 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2)) ). % 164.75/164.89 % 164.75/164.89 fof(fact_subset__insertI,axiom, % 164.75/164.89 ! [V_a_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ). % 164.75/164.89 % 164.75/164.89 fof(fact_le__fun__def,axiom, % 164.75/164.89 ! [V_g_2,V_f_2,T_a,T_b] : % 164.75/164.89 ( class_Orderings_Oord(T_b) % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 164.75/164.89 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_linorder__linear,axiom, % 164.75/164.89 ! [V_y,V_x,T_a] : % 164.75/164.89 ( class_Orderings_Olinorder(T_a) % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.75/164.89 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_set__eq__subset,axiom, % 164.75/164.89 ! [T_a,V_B_2,V_A_2] : % 164.75/164.89 ( V_A_2 = V_B_2 % 164.75/164.89 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.89 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_order__eq__iff,axiom, % 164.75/164.89 ! [V_y_2,V_x_2,T_a] : % 164.75/164.89 ( class_Orderings_Oorder(T_a) % 164.75/164.89 => ( V_x_2 = V_y_2 % 164.75/164.89 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 164.75/164.89 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_insert__absorb2,axiom, % 164.75/164.89 ! [V_A_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) ). % 164.75/164.89 % 164.75/164.89 fof(fact_insert__commute,axiom, % 164.75/164.89 ! [V_A_2,V_y_2,V_x_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) ). % 164.75/164.89 % 164.75/164.89 fof(fact_insert__code,axiom, % 164.75/164.89 ! [V_x_2,V_A_2,V_y_2,T_a] : % 164.75/164.89 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2)) % 164.75/164.89 <=> ( V_y_2 = V_x_2 % 164.75/164.89 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_equalityD1,axiom, % 164.75/164.89 ! [T_a,V_B_2,V_A_2] : % 164.75/164.89 ( V_A_2 = V_B_2 % 164.75/164.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_equalityD2,axiom, % 164.75/164.89 ! [T_a,V_B_2,V_A_2] : % 164.75/164.89 ( V_A_2 = V_B_2 % 164.75/164.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_order__eq__refl,axiom, % 164.75/164.89 ! [V_y,V_x,T_a] : % 164.75/164.89 ( class_Orderings_Opreorder(T_a) % 164.75/164.89 => ( V_x = V_y % 164.75/164.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_subset__insertI2,axiom, % 164.75/164.89 ! [V_b_2,V_B_2,V_A_2,T_a] : % 164.75/164.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_le__funD,axiom, % 164.75/164.89 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 164.75/164.89 ( class_Orderings_Oord(T_b) % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 164.75/164.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_insert__mono,axiom, % 164.75/164.89 ! [V_a_2,V_D_2,V_C_2,T_a] : % 164.75/164.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)) % 164.75/164.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_D_2))) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_order__antisym__conv,axiom, % 164.75/164.89 ! [V_x_2,V_y_2,T_a] : % 164.75/164.89 ( class_Orderings_Oorder(T_a) % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 164.75/164.89 <=> V_x_2 = V_y_2 ) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_ord__eq__le__trans,axiom, % 164.75/164.89 ! [V_c,V_b,V_a,T_a] : % 164.75/164.89 ( class_Orderings_Oord(T_a) % 164.75/164.89 => ( V_a = V_b % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 164.75/164.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_xt1_I3_J,axiom, % 164.75/164.89 ! [V_c,V_b,V_a,T_a] : % 164.75/164.89 ( class_Orderings_Oorder(T_a) % 164.75/164.89 => ( V_a = V_b % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 164.75/164.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_subset__trans,axiom, % 164.75/164.89 ! [V_C_2,V_B_2,V_A_2,T_a] : % 164.75/164.89 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 164.75/164.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_ord__le__eq__trans,axiom, % 164.75/164.89 ! [V_c,V_b,V_a,T_a] : % 164.75/164.89 ( class_Orderings_Oord(T_a) % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.75/164.89 => ( V_b = V_c % 164.75/164.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_xt1_I4_J,axiom, % 164.75/164.89 ! [V_c,V_a,V_b,T_a] : % 164.75/164.89 ( class_Orderings_Oorder(T_a) % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 164.75/164.89 => ( V_b = V_c % 164.75/164.89 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_order__antisym,axiom, % 164.75/164.89 ! [V_y,V_x,T_a] : % 164.75/164.89 ( class_Orderings_Oorder(T_a) % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 164.75/164.89 => V_x = V_y ) ) ) ). % 164.75/164.89 % 164.75/164.89 fof(fact_order__trans,axiom, % 164.75/164.89 ! [V_z,V_y,V_x,T_a] : % 164.75/164.89 ( class_Orderings_Opreorder(T_a) % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.75/164.89 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_xt1_I5_J,axiom, % 164.75/164.90 ! [V_x,V_y,T_a] : % 164.75/164.90 ( class_Orderings_Oorder(T_a) % 164.75/164.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 164.75/164.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.75/164.90 => V_x = V_y ) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_xt1_I6_J,axiom, % 164.75/164.90 ! [V_z,V_x,V_y,T_a] : % 164.75/164.90 ( class_Orderings_Oorder(T_a) % 164.75/164.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 164.75/164.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_equalityE,axiom, % 164.75/164.90 ! [T_a,V_B_2,V_A_2] : % 164.75/164.90 ( V_A_2 = V_B_2 % 164.75/164.90 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.90 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_le__funE,axiom, % 164.75/164.90 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 164.75/164.90 ( class_Orderings_Oord(T_b) % 164.75/164.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_subset__singletonD,axiom, % 164.75/164.90 ! [V_x_2,V_A_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 164.75/164.90 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.90 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_linorder__le__cases,axiom, % 164.75/164.90 ! [V_y,V_x,T_a] : % 164.75/164.90 ( class_Orderings_Olinorder(T_a) % 164.75/164.90 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_singleton__inject,axiom, % 164.75/164.90 ! [V_b_2,V_a_2,T_a] : % 164.75/164.90 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 164.75/164.90 => V_a_2 = V_b_2 ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_doubleton__eq__iff,axiom, % 164.75/164.90 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 164.75/164.90 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 164.75/164.90 <=> ( ( V_a_2 = V_ca_2 % 164.75/164.90 & V_b_2 = V_d_2 ) % 164.75/164.90 | ( V_a_2 = V_d_2 % 164.75/164.90 & V_b_2 = V_ca_2 ) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_insert__not__empty,axiom, % 164.75/164.90 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.75/164.90 % 164.75/164.90 fof(fact_empty__not__insert,axiom, % 164.75/164.90 ! [V_A_2,V_a_2,T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ). % 164.75/164.90 % 164.75/164.90 fof(fact_bot__least,axiom, % 164.75/164.90 ! [V_x,T_a] : % 164.75/164.90 ( class_Orderings_Obot(T_a) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_image__insert,axiom, % 164.75/164.90 ! [V_B_2,V_a_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ). % 164.75/164.90 % 164.75/164.90 fof(fact_subset__empty,axiom, % 164.75/164.90 ! [V_A_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 164.75/164.90 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_image__mono,axiom, % 164.75/164.90 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_subset__image__iff,axiom, % 164.75/164.90 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 164.75/164.90 <=> ? [B_AA] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2)) % 164.75/164.90 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_thin,axiom, % 164.75/164.90 ! [V_G_2,V_ts_2,V_G_H_2,T_a] : % 164.75/164.90 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 164.75/164.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_H_2),V_G_2)) % 164.75/164.90 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_weaken,axiom, % 164.75/164.90 ! [V_ts_2,V_ts_H_2,V_G_2,T_a] : % 164.75/164.90 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_H_2) % 164.75/164.90 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_ts_H_2)) % 164.75/164.90 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_asm,axiom, % 164.75/164.90 ! [V_G_2,V_ts_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_ts_2),V_G_2)) % 164.75/164.90 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_image__constant__conv,axiom, % 164.75/164.90 ! [V_ca_2,T_b,T_a,V_A_2] : % 164.75/164.90 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.90 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 164.75/164.90 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.90 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_derivs__insertD,axiom, % 164.75/164.90 ! [V_ts_2,V_t_2,V_G_2,T_a] : % 164.75/164.90 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) % 164.75/164.90 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 164.75/164.90 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_hoare__derivs_Oinsert,axiom, % 164.75/164.90 ! [V_ts_2,V_t_2,V_G_2,T_a] : % 164.75/164.90 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 164.75/164.90 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) % 164.75/164.90 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),V_t_2),V_ts_2)) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_MGT__BodyN,axiom, % 164.75/164.90 ! [V_G_2,V_pn_2] : % 164.75/164.90 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,V_pn_2))),V_G_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 164.75/164.90 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_com_Osimps_I6_J,axiom, % 164.75/164.90 ! [V_pname_H_2,V_pname_2] : % 164.75/164.90 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 164.75/164.90 <=> V_pname_2 = V_pname_H_2 ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_insert__dom,axiom, % 164.75/164.90 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] : % 164.75/164.90 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 164.75/164.90 => hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) = c_Map_Odom(T_b,T_a,V_f_2) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_the__elem__eq,axiom, % 164.75/164.90 ! [V_x_2,T_a] : c_Set_Othe__elem(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ). % 164.75/164.90 % 164.75/164.90 fof(fact_the_Osimps,axiom, % 164.75/164.90 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 164.75/164.90 % 164.75/164.90 fof(fact_BodyN,axiom, % 164.75/164.90 ! [V_G_2,V_Q_2,V_pn_2,V_P_2,T_a] : % 164.75/164.90 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),V_G_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 164.75/164.90 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_weak__Body,axiom, % 164.75/164.90 ! [V_Q_2,V_pn_2,V_P_2,V_G_2,T_a] : % 164.75/164.90 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 164.75/164.90 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_image__ident,axiom, % 164.75/164.90 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 164.75/164.90 % 164.75/164.90 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 164.75/164.90 ! [V_x_2,T_a] : c_Option_Oset(T_a,hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 164.75/164.90 % 164.75/164.90 fof(fact_MGT__Body,axiom, % 164.75/164.90 ! [V_Procs_2,V_G_2] : % 164.75/164.90 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Procs_2)) % 164.75/164.90 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),V_Procs_2)) % 164.75/164.90 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_G_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),V_Procs_2)) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_option_Oinject,axiom, % 164.75/164.90 ! [V_a_H_2,V_a_2,T_a] : % 164.75/164.90 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2) % 164.75/164.90 <=> V_a_2 = V_a_H_2 ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_image__constant,axiom, % 164.75/164.90 ! [V_ca_2,T_b,V_A_2,V_x_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.90 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_WTs__elim__cases_I8_J,axiom, % 164.75/164.90 ! [V_a_2,V_P_2,V_X_2] : % 164.75/164.90 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2))) % 164.75/164.90 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_WT_OBody,axiom, % 164.75/164.90 ! [V_pn] : % 164.75/164.90 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) % 164.75/164.90 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_equalityCE,axiom, % 164.75/164.90 ! [V_ca_2,T_a,V_B_2,V_A_2] : % 164.75/164.90 ( V_A_2 = V_B_2 % 164.75/164.90 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.90 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) % 164.75/164.90 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_emptyE,axiom, % 164.75/164.90 ! [V_a_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 164.75/164.90 % 164.75/164.90 fof(fact_insertCI,axiom, % 164.75/164.90 ! [V_b_2,V_B_2,V_a_2,T_a] : % 164.75/164.90 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 164.75/164.90 => V_a_2 = V_b_2 ) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_insertE,axiom, % 164.75/164.90 ! [V_A_2,V_b_2,V_a_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 164.75/164.90 => ( V_a_2 != V_b_2 % 164.75/164.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_subsetD,axiom, % 164.75/164.90 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.90 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_image__eqI,axiom, % 164.75/164.90 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] : % 164.75/164.90 ( V_b_2 = hAPP(V_f_2,V_x_2) % 164.75/164.90 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_UnE,axiom, % 164.75/164.90 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.90 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_UnCI,axiom, % 164.75/164.90 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 164.75/164.90 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_Un__absorb,axiom, % 164.75/164.90 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 164.75/164.90 % 164.75/164.90 fof(fact_mem__def,axiom, % 164.75/164.90 ! [V_A_2,V_x_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.90 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_Un__commute,axiom, % 164.75/164.90 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 164.75/164.90 % 164.75/164.90 fof(fact_Un__left__absorb,axiom, % 164.75/164.90 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 164.75/164.90 % 164.75/164.90 fof(fact_Un__left__commute,axiom, % 164.75/164.90 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 164.75/164.90 % 164.75/164.90 fof(fact_Un__iff,axiom, % 164.75/164.90 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.90 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.90 | hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_Un__assoc,axiom, % 164.75/164.90 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 164.75/164.90 % 164.75/164.90 fof(fact_bex__Un,axiom, % 164.75/164.90 ! [V_P_2,V_B_2,V_A_2,T_a] : % 164.75/164.90 ( ? [B_x] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.90 & hBOOL(hAPP(V_P_2,B_x)) ) % 164.75/164.90 <=> ( ? [B_x] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.75/164.90 & hBOOL(hAPP(V_P_2,B_x)) ) % 164.75/164.90 | ? [B_x] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 164.75/164.90 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_ball__Un,axiom, % 164.75/164.90 ! [V_P_2,V_B_2,V_A_2,T_a] : % 164.75/164.90 ( ! [B_x] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.90 => hBOOL(hAPP(V_P_2,B_x)) ) % 164.75/164.90 <=> ( ! [B_x] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.75/164.90 => hBOOL(hAPP(V_P_2,B_x)) ) % 164.75/164.90 & ! [B_x] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 164.75/164.90 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_com_Osimps_I7_J,axiom, % 164.75/164.90 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] : % 164.75/164.90 ( c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2) = c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) % 164.75/164.90 <=> ( V_vname_2 = V_vname_H_2 % 164.75/164.90 & V_pname_2 = V_pname_H_2 % 164.75/164.90 & V_fun_2 = V_fun_H_2 ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_UnI1,axiom, % 164.75/164.90 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_UnI2,axiom, % 164.75/164.90 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_eqset__imp__iff,axiom, % 164.75/164.90 ! [V_x_2,T_a,V_B_2,V_A_2] : % 164.75/164.90 ( V_A_2 = V_B_2 % 164.75/164.90 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.90 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_eqelem__imp__iff,axiom, % 164.75/164.90 ! [V_A_2,T_a,V_y_2,V_x_2] : % 164.75/164.90 ( V_x_2 = V_y_2 % 164.75/164.90 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.90 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_eq__mem__trans,axiom, % 164.75/164.90 ! [V_A_2,T_a,V_b_2,V_a_2] : % 164.75/164.90 ( V_a_2 = V_b_2 % 164.75/164.90 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 164.75/164.90 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_set__empty__eq,axiom, % 164.75/164.90 ! [V_xo_2,T_a] : % 164.75/164.90 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.90 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 164.75/164.90 ! [T_a] : c_Option_Oset(T_a,c_Option_Ooption_ONone(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.75/164.90 % 164.75/164.90 fof(fact_triple_Oinject,axiom, % 164.75/164.90 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] : % 164.75/164.90 ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H_2),V_com_H_2),V_fun2_H_2) % 164.75/164.90 <=> ( V_fun1_2 = V_fun1_H_2 % 164.75/164.90 & V_com_2 = V_com_H_2 % 164.75/164.90 & V_fun2_2 = V_fun2_H_2 ) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_domIff,axiom, % 164.75/164.90 ! [V_m_2,T_b,V_a_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) % 164.75/164.90 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_elem__set,axiom, % 164.75/164.90 ! [V_xo_2,V_x_2,T_a] : % 164.75/164.90 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2))) % 164.75/164.90 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ). % 164.75/164.90 % 164.75/164.90 fof(fact_option_Osimps_I2_J,axiom, % 164.75/164.90 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 164.75/164.90 % 164.75/164.90 fof(fact_option_Osimps_I3_J,axiom, % 164.75/164.90 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 164.75/164.90 % 164.75/164.90 fof(fact_not__Some__eq,axiom, % 164.75/164.90 ! [T_a,V_x_2] : % 164.75/164.91 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y) % 164.75/164.91 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_not__None__eq,axiom, % 164.75/164.91 ! [T_a,V_x_2] : % 164.75/164.91 ( V_x_2 != c_Option_Ooption_ONone(T_a) % 164.75/164.91 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_Un__empty__left,axiom, % 164.75/164.91 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 164.75/164.91 % 164.75/164.91 fof(fact_Un__empty__right,axiom, % 164.75/164.91 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 164.75/164.91 % 164.75/164.91 fof(fact_Un__empty,axiom, % 164.75/164.91 ! [V_B_2,V_A_2,T_a] : % 164.75/164.91 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.91 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.91 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_Un__insert__left,axiom, % 164.75/164.91 ! [V_C_2,V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 164.75/164.91 % 164.75/164.91 fof(fact_Un__insert__right,axiom, % 164.75/164.91 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 164.75/164.91 % 164.75/164.91 fof(fact_Un__mono,axiom, % 164.75/164.91 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 164.75/164.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_Un__least,axiom, % 164.75/164.91 ! [V_B_2,V_C_2,V_A_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 164.75/164.91 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_Un__absorb2,axiom, % 164.75/164.91 ! [V_A_2,V_B_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 164.75/164.91 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_Un__absorb1,axiom, % 164.75/164.91 ! [V_B_2,V_A_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.91 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_subset__Un__eq,axiom, % 164.75/164.91 ! [V_B_2,V_A_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.91 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_Un__upper2,axiom, % 164.75/164.91 ! [V_A_2,V_B_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 164.75/164.91 % 164.75/164.91 fof(fact_Un__upper1,axiom, % 164.75/164.91 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ). % 164.75/164.91 % 164.75/164.91 fof(fact_image__Un,axiom, % 164.75/164.91 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)) ). % 164.75/164.91 % 164.75/164.91 fof(fact_all__not__in__conv,axiom, % 164.75/164.91 ! [V_A_2,T_a] : % 164.75/164.91 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.75/164.91 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_ex__in__conv,axiom, % 164.75/164.91 ! [V_A_2,T_a] : % 164.75/164.91 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.75/164.91 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_empty__iff,axiom, % 164.75/164.91 ! [V_ca_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 164.75/164.91 % 164.75/164.91 fof(fact_equals0D,axiom, % 164.75/164.91 ! [V_a_2,T_a,V_A_2] : % 164.75/164.91 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.91 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_insert__absorb,axiom, % 164.75/164.91 ! [V_A_2,V_a_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.75/164.91 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_insertI2,axiom, % 164.75/164.91 ! [V_b_2,V_B_2,V_a_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 164.75/164.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_insert__ident,axiom, % 164.75/164.91 ! [V_B_2,V_A_2,V_x_2,T_a] : % 164.75/164.91 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.91 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 164.75/164.91 => ( hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2) % 164.75/164.91 <=> V_A_2 = V_B_2 ) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_insert__iff,axiom, % 164.75/164.91 ! [V_A_2,V_b_2,V_a_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 164.75/164.91 <=> ( V_a_2 = V_b_2 % 164.75/164.91 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_insertI1,axiom, % 164.75/164.91 ! [V_B_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) ). % 164.75/164.91 % 164.75/164.91 fof(fact_set__mp,axiom, % 164.75/164.91 ! [V_x_2,V_B_2,V_A_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_set__rev__mp,axiom, % 164.75/164.91 ! [V_B_2,V_A_2,V_x_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_in__mono,axiom, % 164.75/164.91 ! [V_x_2,V_B_2,V_A_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.91 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_image__iff,axiom, % 164.75/164.91 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 164.75/164.91 <=> ? [B_x] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 164.75/164.91 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_imageI,axiom, % 164.75/164.91 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.91 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_rev__image__eqI,axiom, % 164.75/164.91 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.91 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 164.75/164.91 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_com_Osimps_I62_J,axiom, % 164.75/164.91 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_pname_2] : hAPP(c_Com_Ocom_OBODY,V_pname_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 164.75/164.91 % 164.75/164.91 fof(fact_com_Osimps_I63_J,axiom, % 164.75/164.91 ! [V_pname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != hAPP(c_Com_Ocom_OBODY,V_pname_2) ). % 164.75/164.91 % 164.75/164.91 fof(fact_domI,axiom, % 164.75/164.91 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 164.75/164.91 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 164.75/164.91 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_dom__empty,axiom, % 164.75/164.91 ! [T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.75/164.91 % 164.75/164.91 fof(fact_dom__eq__empty__conv,axiom, % 164.75/164.91 ! [V_f_2,T_b,T_a] : % 164.75/164.91 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.91 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_insert__is__Un,axiom, % 164.75/164.91 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_A_2) ). % 164.75/164.91 % 164.75/164.91 fof(fact_singletonE,axiom, % 164.75/164.91 ! [V_a_2,V_b_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 164.75/164.91 => V_b_2 = V_a_2 ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_singleton__iff,axiom, % 164.75/164.91 ! [V_a_2,V_b_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 164.75/164.91 <=> V_b_2 = V_a_2 ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_subset__insert,axiom, % 164.75/164.91 ! [V_B_2,V_A_2,V_x_2,T_a] : % 164.75/164.91 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 164.75/164.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_insert__subset,axiom, % 164.75/164.91 ! [V_B_2,V_A_2,V_x_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2)) % 164.75/164.91 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 164.75/164.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_insert__image,axiom, % 164.75/164.91 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.91 => hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_Body1,axiom, % 164.75/164.91 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 164.75/164.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2)) % 164.75/164.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(V_P_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Q_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_WT_Oequations_I8_J,axiom, % 164.75/164.91 ! [V_a3_2,V_a1_2,V_a2_2] : % 164.75/164.91 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2))) % 164.75/164.91 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_WT_OCall,axiom, % 164.75/164.91 ! [V_a_2,V_X_2,V_pn_2] : % 164.75/164.91 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2))) % 164.75/164.91 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_hoare__derivs_OBody,axiom, % 164.75/164.91 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 164.75/164.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2)) % 164.75/164.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite__dom__body,axiom, % 164.75/164.91 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 164.75/164.91 % 164.75/164.91 fof(fact_Body__sound__lemma,axiom, % 164.75/164.91 ! [V_Procs_2,V_Q_2,V_P_2,V_G_2,T_a] : % 164.75/164.91 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)),V_G_2),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),V_Q_2)),V_Procs_2)) % 164.75/164.91 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(T_a)),V_P_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite__imageI,axiom, % 164.75/164.91 ! [V_h_2,T_b,V_F_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 164.75/164.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite_OinsertI,axiom, % 164.75/164.91 ! [V_a_2,V_A_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite_OemptyI,axiom, % 164.75/164.91 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 164.75/164.91 % 164.75/164.91 fof(fact_MGF__complete,axiom, % 164.75/164.91 ! [V_Q_2,V_P_2,V_ca_2] : % 164.75/164.91 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 164.75/164.91 => ( c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 164.75/164.91 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite__surj,axiom, % 164.75/164.91 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 164.75/164.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup1CI,axiom, % 164.75/164.91 ! [T_a,V_A_2,V_x_2,V_B_2] : % 164.75/164.91 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 164.75/164.91 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 164.75/164.91 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup1E,axiom, % 164.75/164.91 ! [V_x_2,V_B_2,V_A_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 164.75/164.91 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 164.75/164.91 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite__pointwise,axiom, % 164.75/164.91 ! [V_Q_2,V_P_2,V_Q_H_2,V_c0_2,V_P_H_2,V_G_2,T_b,V_U_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2)) % 164.75/164.91 => ( ! [B_p] : % 164.75/164.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_H_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_H_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) % 164.75/164.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(V_P_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) % 164.75/164.91 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_H_2)),V_c0_2)),V_Q_H_2)),V_U_2)) % 164.75/164.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(c_Set_Oimage(T_a,tc_Hoare__Mirabelle_Otriple(T_b),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_b))),T_a),c_Hoare__Mirabelle_Otriple_Otriple(T_b)),V_P_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__fun__def,axiom, % 164.75/164.91 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 164.75/164.91 ( class_Lattices_Olattice(T_a) % 164.75/164.91 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__Un__eq,axiom, % 164.75/164.91 ! [V_x_2,V_S_2,V_R_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2)) % 164.75/164.91 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_pred__subset__eq,axiom, % 164.75/164.91 ! [V_S_2,V_R_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))) % 164.75/164.91 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_hoare__sound,axiom, % 164.75/164.91 ! [V_ts_2,V_G_2,T_a] : % 164.75/164.91 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,V_ts_2) % 164.75/164.91 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_eq__mem,axiom, % 164.75/164.91 ! [V_y_2,V_x_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 164.75/164.91 <=> V_x_2 = V_y_2 ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite,axiom, % 164.75/164.91 ! [V_A_2,T_a] : % 164.75/164.91 ( class_Finite__Set_Ofinite(T_a) % 164.75/164.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite__code,axiom, % 164.75/164.91 ! [V_A_2,T_a] : % 164.75/164.91 ( class_Finite__Set_Ofinite(T_a) % 164.75/164.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup_Oidem,axiom, % 164.75/164.91 ! [V_a,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__idem,axiom, % 164.75/164.91 ! [V_x,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup_Ocommute,axiom, % 164.75/164.91 ! [V_b,V_a,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => 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) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_inf__sup__aci_I5_J,axiom, % 164.75/164.91 ! [V_y,V_x,T_a] : % 164.75/164.91 ( class_Lattices_Olattice(T_a) % 164.75/164.91 => 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) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__commute,axiom, % 164.75/164.91 ! [V_y,V_x,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => 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) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup_Oleft__idem,axiom, % 164.75/164.91 ! [V_b,V_a,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => 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) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_inf__sup__aci_I8_J,axiom, % 164.75/164.91 ! [V_y,V_x,T_a] : % 164.75/164.91 ( class_Lattices_Olattice(T_a) % 164.75/164.91 => 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) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__left__idem,axiom, % 164.75/164.91 ! [V_y,V_x,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => 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) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup_Oleft__commute,axiom, % 164.75/164.91 ! [V_c,V_a,V_b,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => 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)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_inf__sup__aci_I7_J,axiom, % 164.75/164.91 ! [V_z,V_y,V_x,T_a] : % 164.75/164.91 ( class_Lattices_Olattice(T_a) % 164.75/164.91 => 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)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__left__commute,axiom, % 164.75/164.91 ! [V_z,V_y,V_x,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => 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)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup_Oassoc,axiom, % 164.75/164.91 ! [V_c,V_b,V_a,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => 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)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_inf__sup__aci_I6_J,axiom, % 164.75/164.91 ! [V_z,V_y,V_x,T_a] : % 164.75/164.91 ( class_Lattices_Olattice(T_a) % 164.75/164.91 => 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)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__assoc,axiom, % 164.75/164.91 ! [V_z,V_y,V_x,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => 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)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_rev__predicate1D,axiom, % 164.75/164.91 ! [V_Q_2,T_a,V_x_2,V_P_2] : % 164.75/164.91 ( hBOOL(hAPP(V_P_2,V_x_2)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 164.75/164.91 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_predicate1D,axiom, % 164.75/164.91 ! [V_x_2,V_Q_2,V_P_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 164.75/164.91 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 164.75/164.91 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup1I1,axiom, % 164.75/164.91 ! [V_B_2,T_a,V_x_2,V_A_2] : % 164.75/164.91 ( hBOOL(hAPP(V_A_2,V_x_2)) % 164.75/164.91 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup1I2,axiom, % 164.75/164.91 ! [V_A_2,T_a,V_x_2,V_B_2] : % 164.75/164.91 ( hBOOL(hAPP(V_B_2,V_x_2)) % 164.75/164.91 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_pred__equals__eq,axiom, % 164.75/164.91 ! [V_S_2,V_R_2,T_a] : % 164.75/164.91 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2) % 164.75/164.91 <=> V_R_2 = V_S_2 ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_inf__sup__ord_I3_J,axiom, % 164.75/164.91 ! [V_y,V_x,T_a] : % 164.75/164.91 ( class_Lattices_Olattice(T_a) % 164.75/164.91 => 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))) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__ge1,axiom, % 164.75/164.91 ! [V_y,V_x,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => 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))) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_inf__sup__ord_I4_J,axiom, % 164.75/164.91 ! [V_x,V_y,T_a] : % 164.75/164.91 ( class_Lattices_Olattice(T_a) % 164.75/164.91 => 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))) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__ge2,axiom, % 164.75/164.91 ! [V_x,V_y,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => 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))) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_le__iff__sup,axiom, % 164.75/164.91 ! [V_y_2,V_x_2,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 164.75/164.91 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_le__sup__iff,axiom, % 164.75/164.91 ! [V_z_2,V_y_2,V_x_2,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2)),V_z_2)) % 164.75/164.91 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 164.75/164.91 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_le__supI1,axiom, % 164.75/164.91 ! [V_b,V_a,V_x,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 164.75/164.91 => 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))) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_le__supI2,axiom, % 164.75/164.91 ! [V_a,V_b,V_x,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 164.75/164.91 => 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))) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__absorb2,axiom, % 164.75/164.91 ! [V_y,V_x,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.75/164.91 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__absorb1,axiom, % 164.75/164.91 ! [V_x,V_y,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 164.75/164.91 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_le__supI,axiom, % 164.75/164.91 ! [V_b,V_x,V_a,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 164.75/164.91 => 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)) ) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__least,axiom, % 164.75/164.91 ! [V_z,V_x,V_y,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 164.75/164.91 => 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)) ) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__mono,axiom, % 164.75/164.91 ! [V_d,V_b,V_c,V_a,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 164.75/164.91 => 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))) ) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_le__supE,axiom, % 164.75/164.91 ! [V_x,V_b,V_a,T_a] : % 164.75/164.91 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.91 => ( 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)) % 164.75/164.91 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 164.75/164.91 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite_Oequations_I1_J,axiom, % 164.75/164.91 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__eq__bot__iff,axiom, % 164.75/164.91 ! [V_y_2,V_x_2,T_a] : % 164.75/164.91 ( class_Lattices_Obounded__lattice__bot(T_a) % 164.75/164.91 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a) % 164.75/164.91 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a) % 164.75/164.91 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__bot__right,axiom, % 164.75/164.91 ! [V_x,T_a] : % 164.75/164.91 ( class_Lattices_Obounded__lattice__bot(T_a) % 164.75/164.91 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__bot__left,axiom, % 164.75/164.91 ! [V_x,T_a] : % 164.75/164.91 ( class_Lattices_Obounded__lattice__bot(T_a) % 164.75/164.91 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite__insert,axiom, % 164.75/164.91 ! [V_A_2,V_a_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) % 164.75/164.91 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_rev__finite__subset,axiom, % 164.75/164.91 ! [V_A_2,V_B_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite__subset,axiom, % 164.75/164.91 ! [V_B_2,V_A_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite__Un,axiom, % 164.75/164.91 ! [V_G_2,V_F_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_G_2))) % 164.75/164.91 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 164.75/164.91 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite__UnI,axiom, % 164.75/164.91 ! [V_G_2,V_F_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 164.75/164.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) % 164.75/164.91 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_G_2))) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_sup__apply,axiom, % 164.75/164.91 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 164.75/164.91 ( class_Lattices_Olattice(T_a) % 164.75/164.91 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_bot__empty__eq,axiom, % 164.75/164.91 ! [V_x_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) % 164.75/164.91 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_triple_Orecs,axiom, % 164.75/164.91 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 164.75/164.91 % 164.75/164.91 fof(fact_triple_Osimps_I2_J,axiom, % 164.75/164.91 ! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_a,T_b] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_b,T_a,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2) ). % 164.75/164.91 % 164.75/164.91 fof(fact_folding__one_Oinsert,axiom, % 164.75/164.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 164.75/164.91 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 164.75/164.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.91 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.91 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_folding__one__idem_Ounion__idem,axiom, % 164.75/164.91 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 164.75/164.91 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 164.75/164.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.91 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.91 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.91 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_folding__one__idem_Osubset__idem,axiom, % 164.75/164.91 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 164.75/164.91 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 164.75/164.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.91 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 164.75/164.91 => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_finite__subset__induct,axiom, % 164.75/164.91 ! [V_P_2,V_A_2,V_F_2,T_a] : % 164.75/164.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2)) % 164.75/164.91 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 164.75/164.91 => ( ! [B_a,B_F] : % 164.75/164.91 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 164.75/164.91 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 164.75/164.91 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F)) % 164.75/164.91 => ( hBOOL(hAPP(V_P_2,B_F)) % 164.75/164.91 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) ) % 164.75/164.91 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 164.75/164.91 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 164.75/164.91 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 164.75/164.91 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.91 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.91 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ). % 164.75/164.91 % 164.75/164.91 fof(fact_escape,axiom, % 164.75/164.91 ! [V_Q_2,V_ca_2,V_G_2,T_a,V_P_2] : % 164.75/164.91 ( ! [B_Z,B_s] : % 164.75/164.91 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 164.75/164.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_ca_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) % 164.75/164.91 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 164.75/164.91 % 164.75/164.92 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 164.75/164.92 ! [V_a2_2,V_a1_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 164.75/164.92 % 164.75/164.92 fof(fact_hoare__derivs_OSkip,axiom, % 164.75/164.92 ! [V_P_2,V_G_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSKIP),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 164.75/164.92 % 164.75/164.92 fof(fact_the__elem__def,axiom, % 164.75/164.92 ! [V_X_2,T_a] : c_Set_Othe__elem(T_a,V_X_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__one__idem_Oidem,axiom, % 164.75/164.92 ! [V_x_2,V_F_2,V_f_2,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 164.75/164.92 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I18_J,axiom, % 164.75/164.92 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I19_J,axiom, % 164.75/164.92 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 164.75/164.92 % 164.75/164.92 fof(fact_WT_OSkip,axiom, % 164.75/164.92 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 164.75/164.92 % 164.75/164.92 fof(fact_WT_Oequations_I1_J,axiom, % 164.75/164.92 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I20_J,axiom, % 164.75/164.92 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I21_J,axiom, % 164.75/164.92 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__one_Osingleton,axiom, % 164.75/164.92 ! [V_x_2,V_F_2,V_f_2,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 164.75/164.92 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__one__idem_Oin__idem,axiom, % 164.75/164.92 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 164.75/164.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__one_Oclosed,axiom, % 164.75/164.92 ! [V_A_2,V_F_2,V_f_2,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 164.75/164.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.92 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.92 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_conseq2,axiom, % 164.75/164.92 ! [V_Q_2,V_Q_H_2,V_ca_2,V_P_2,V_G_2,T_a] : % 164.75/164.92 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 164.75/164.92 => ( ! [B_Z,B_s] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 164.75/164.92 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 164.75/164.92 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_conseq1,axiom, % 164.75/164.92 ! [V_P_2,V_Q_2,V_ca_2,V_P_H_2,V_G_2,T_a] : % 164.75/164.92 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 164.75/164.92 => ( ! [B_Z,B_s] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 164.75/164.92 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 164.75/164.92 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__one__idem_Ohom__commute,axiom, % 164.75/164.92 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 164.75/164.92 => ( ! [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)) % 164.75/164.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 164.75/164.92 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.92 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Comp,axiom, % 164.75/164.92 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_P_2,V_G_2,T_a] : % 164.75/164.92 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 164.75/164.92 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_Q_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 164.75/164.92 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSemi(V_ca_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_dom__eq__singleton__conv,axiom, % 164.75/164.92 ! [V_x_2,V_f_2,T_b,T_a] : % 164.75/164.92 ( c_Map_Odom(T_a,T_b,V_f_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 164.75/164.92 <=> ? [B_v] : V_f_2 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),B_v)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__image__simple_Oinsert,axiom, % 164.75/164.92 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 164.75/164.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.75/164.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 164.75/164.92 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_the__eq__trivial,axiom, % 164.75/164.92 ! [V_a_2,T_a] : c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ). % 164.75/164.92 % 164.75/164.92 fof(fact_the__sym__eq__trivial,axiom, % 164.75/164.92 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 164.75/164.92 % 164.75/164.92 fof(fact_LoopF,axiom, % 164.75/164.92 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__one_Oremove,axiom, % 164.75/164.92 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 164.75/164.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.92 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 164.75/164.92 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.92 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__upd__triv,axiom, % 164.75/164.92 ! [V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),hAPP(V_f_2,V_x_2)) = V_f_2 ). % 164.75/164.92 % 164.75/164.92 fof(fact_DiffE,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.92 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_DiffI,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.92 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_finite__Diff,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.92 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_WTs__elim__cases_I6_J,axiom, % 164.75/164.92 ! [V_ca_2,V_b_2] : % 164.75/164.92 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) % 164.75/164.92 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_WTs__elim__cases_I4_J,axiom, % 164.75/164.92 ! [V_c2,V_c1] : % 164.75/164.92 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2))) % 164.75/164.92 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 164.75/164.92 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__upd__idem,axiom, % 164.75/164.92 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] : % 164.75/164.92 ( hAPP(V_f_2,V_x_2) = V_y_2 % 164.75/164.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__upd__other,axiom, % 164.75/164.92 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 164.75/164.92 ( V_z_2 != V_x_2 % 164.75/164.92 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__upd__twist,axiom, % 164.75/164.92 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_ca_2,V_a_2] : % 164.75/164.92 ( V_a_2 != V_ca_2 % 164.75/164.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_a_2),V_b_2)),V_ca_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_ca_2),V_d_2)),V_a_2),V_b_2) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__upd__apply,axiom, % 164.75/164.92 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 164.75/164.92 ( ( V_z_2 = V_x_2 % 164.75/164.92 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 ) % 164.75/164.92 & ( V_z_2 != V_x_2 % 164.75/164.92 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__upd__same,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2 ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__upd__upd,axiom, % 164.75/164.92 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_z_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__upd__idem__iff,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 164.75/164.92 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 % 164.75/164.92 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I5_J,axiom, % 164.75/164.92 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 164.75/164.92 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 164.75/164.92 <=> ( V_fun_2 = V_fun_H_2 % 164.75/164.92 & V_com_2 = V_com_H_2 ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I3_J,axiom, % 164.75/164.92 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 164.75/164.92 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 164.75/164.92 <=> ( V_com1_2 = V_com1_H_2 % 164.75/164.92 & V_com2_2 = V_com2_H_2 ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Diff__idemp,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I47_J,axiom, % 164.75/164.92 ! [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) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I46_J,axiom, % 164.75/164.92 ! [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) ). % 164.75/164.92 % 164.75/164.92 fof(fact_minus__apply,axiom, % 164.75/164.92 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 164.75/164.92 ( class_Groups_Ominus(T_a) % 164.75/164.92 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__diff__def,axiom, % 164.75/164.92 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 164.75/164.92 ( class_Groups_Ominus(T_a) % 164.75/164.92 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__upd__def,axiom, % 164.75/164.92 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] : % 164.75/164.92 ( ( V_x_2 = V_a_2 % 164.75/164.92 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = V_b_2 ) % 164.75/164.92 & ( V_x_2 != V_a_2 % 164.75/164.92 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_a_2),V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_DiffD2,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.92 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_DiffD1,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Diff__iff,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.92 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.92 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Diff__cancel,axiom, % 164.75/164.92 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Diff__empty,axiom, % 164.75/164.92 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 164.75/164.92 % 164.75/164.92 fof(fact_empty__Diff,axiom, % 164.75/164.92 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.75/164.92 % 164.75/164.92 fof(fact_finite__Diff2,axiom, % 164.75/164.92 ! [V_A_2,V_B_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.92 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Diff__subset,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Diff__mono,axiom, % 164.75/164.92 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_double__diff,axiom, % 164.75/164.92 ! [V_C_2,V_B_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 164.75/164.92 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Un__Diff,axiom, % 164.75/164.92 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Un__Diff__cancel2,axiom, % 164.75/164.92 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Un__Diff__cancel,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_map__upd__eqD1,axiom, % 164.75/164.92 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] : % 164.75/164.92 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) % 164.75/164.92 => V_x_2 = V_y_2 ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_map__upd__triv,axiom, % 164.75/164.92 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] : % 164.75/164.92 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 164.75/164.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_a),V_x_2)) = V_t_2 ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_map__upd__Some__unfold,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] : % 164.75/164.92 ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 164.75/164.92 <=> ( ( V_x_2 = V_a_2 % 164.75/164.92 & V_b_2 = V_y_2 ) % 164.75/164.92 | ( V_x_2 != V_a_2 % 164.75/164.92 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I58_J,axiom, % 164.75/164.92 ! [V_pname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I59_J,axiom, % 164.75/164.92 ! [V_com_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_While,axiom, % 164.75/164.92 ! [V_b_2,V_ca_2] : % 164.75/164.92 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 164.75/164.92 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_ca_2))) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_WT_Oequations_I6_J,axiom, % 164.75/164.92 ! [V_a1_2,V_a2_2] : % 164.75/164.92 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2))) % 164.75/164.92 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I61_J,axiom, % 164.75/164.92 ! [V_com_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I60_J,axiom, % 164.75/164.92 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I17_J,axiom, % 164.75/164.92 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I16_J,axiom, % 164.75/164.92 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_empty__upd__none,axiom, % 164.75/164.92 ! [V_xa_2,V_x_2,T_a,T_b] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))),V_x_2),c_Option_Ooption_ONone(T_a)),V_xa_2) = c_Option_Ooption_ONone(T_a) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I48_J,axiom, % 164.75/164.92 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I49_J,axiom, % 164.75/164.92 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_WT_OSemi,axiom, % 164.75/164.92 ! [V_c1,V_c0] : % 164.75/164.92 ( hBOOL(hAPP(c_Com_OWT,V_c0)) % 164.75/164.92 => ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 164.75/164.92 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_WT_Oequations_I4_J,axiom, % 164.75/164.92 ! [V_a2_2,V_a1_2] : % 164.75/164.92 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2))) % 164.75/164.92 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 164.75/164.92 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I51_J,axiom, % 164.75/164.92 ! [V_com2_2,V_com1_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I50_J,axiom, % 164.75/164.92 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I13_J,axiom, % 164.75/164.92 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 164.75/164.92 % 164.75/164.92 fof(fact_com_Osimps_I12_J,axiom, % 164.75/164.92 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 164.75/164.92 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 164.75/164.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.75/164.92 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_dom__fun__upd,axiom, % 164.75/164.92 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] : % 164.75/164.92 ( ( V_y_2 = c_Option_Ooption_ONone(T_a) % 164.75/164.92 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) % 164.75/164.92 & ( V_y_2 != c_Option_Ooption_ONone(T_a) % 164.75/164.92 => c_Map_Odom(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Map_Odom(T_b,T_a,V_f_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_insert__Diff__if,axiom, % 164.75/164.92 ! [V_A_2,V_B_2,V_x_2,T_a] : % 164.75/164.92 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 164.75/164.92 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) % 164.75/164.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 164.75/164.92 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_insert__Diff1,axiom, % 164.75/164.92 ! [V_A_2,V_B_2,V_x_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 164.75/164.92 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Diff__insert,axiom, % 164.75/164.92 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Diff__insert2,axiom, % 164.75/164.92 ! [V_B_2,V_a_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_insert__Diff__single,axiom, % 164.75/164.92 ! [V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_finite__Diff__insert,axiom, % 164.75/164.92 ! [V_B_2,V_a_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)))) % 164.75/164.92 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_image__map__upd,axiom, % 164.75/164.92 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] : % 164.75/164.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))),V_A_2) = hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_b),V_m_2),V_A_2) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_image__diff__subset,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Diff__subset__conv,axiom, % 164.75/164.92 ! [V_C_2,V_B_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) % 164.75/164.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Diff__partition,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.92 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__image__simple_Oempty,axiom, % 164.75/164.92 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 164.75/164.92 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__upd__image,axiom, % 164.75/164.92 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 164.75/164.92 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) % 164.75/164.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__image__simple_Oremove,axiom, % 164.75/164.92 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 164.75/164.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 164.75/164.92 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_map__upd__nonempty,axiom, % 164.75/164.92 ! [V_x_2,V_k_2,V_t_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) != hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Diff__insert__absorb,axiom, % 164.75/164.92 ! [V_A_2,V_x_2,T_a] : % 164.75/164.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_insert__Diff,axiom, % 164.75/164.92 ! [V_A_2,V_a_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.75/164.92 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = V_A_2 ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_dom__minus,axiom, % 164.75/164.92 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] : % 164.75/164.92 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a) % 164.75/164.92 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_a,V_f_2)),V_A_2) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_subset__insert__iff,axiom, % 164.75/164.92 ! [V_B_2,V_x_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 164.75/164.92 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ) % 164.75/164.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_diff__single__insert,axiom, % 164.75/164.92 ! [V_B_2,V_x_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__one_Oinsert__remove,axiom, % 164.75/164.92 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 164.75/164.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.92 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.92 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 164.75/164.92 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.92 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_ran__map__upd,axiom, % 164.75/164.92 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] : % 164.75/164.92 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a) % 164.75/164.92 => c_Map_Oran(T_b,T_a,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_flat__lub__def,axiom, % 164.75/164.92 ! [V_b_2,V_A_2,T_a] : % 164.75/164.92 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 164.75/164.92 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 ) % 164.75/164.92 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) % 164.75/164.92 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__upd__None__restrict,axiom, % 164.75/164.92 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] : % 164.75/164.92 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 164.75/164.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) % 164.75/164.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 164.75/164.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),c_Option_Ooption_ONone(T_b)) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_diff__eq__diff__less__eq,axiom, % 164.75/164.92 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 164.75/164.92 ( class_Groups_Oordered__ab__group__add(T_a) % 164.75/164.92 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 164.75/164.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__upd__restrict__conv,axiom, % 164.75/164.92 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 164.75/164.92 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_restrict__fun__upd,axiom, % 164.75/164.92 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 164.75/164.92 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 164.75/164.92 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ) % 164.75/164.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 164.75/164.92 => c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),V_y_2),V_D_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_finite__empty__induct,axiom, % 164.75/164.92 ! [V_P_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.92 => ( hBOOL(hAPP(V_P_2,V_A_2)) % 164.75/164.92 => ( ! [B_a,B_A] : % 164.75/164.92 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) % 164.75/164.92 => ( hBOOL(hAPP(V_P_2,B_A)) % 164.75/164.92 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_a),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) % 164.75/164.92 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__left__comm__idem__remove,axiom, % 164.75/164.92 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 164.75/164.92 % 164.75/164.92 fof(fact_ran__empty,axiom, % 164.75/164.92 ! [T_a,T_b] : c_Map_Oran(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__upd__restrict,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,V_D_2,V_m_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,V_D_2)),V_x_2),V_y_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2),V_y_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_psubset__insert__iff,axiom, % 164.75/164.92 ! [V_B_2,V_x_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_B_2))) % 164.75/164.92 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 164.75/164.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 164.75/164.92 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2)) ) % 164.75/164.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 164.75/164.92 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 164.75/164.92 => 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) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__less__irrefl,axiom, % 164.75/164.92 ! [V_x,T_a] : % 164.75/164.92 ( class_Orderings_Opreorder(T_a) % 164.75/164.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_linorder__neq__iff,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( V_x_2 != V_y_2 % 164.75/164.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 164.75/164.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_not__less__iff__gr__or__eq,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 164.75/164.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 164.75/164.92 | V_x_2 = V_y_2 ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_linorder__less__linear,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 | V_x = V_y % 164.75/164.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_linorder__antisym__conv3,axiom, % 164.75/164.92 ! [V_x_2,V_y_2,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 164.75/164.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 164.75/164.92 <=> V_x_2 = V_y_2 ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_linorder__neqE,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( V_x != V_y % 164.75/164.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_less__imp__neq,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 => V_x != V_y ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__less__not__sym,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Opreorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__less__imp__not__less,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Opreorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__less__imp__not__eq,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 => V_x != V_y ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__less__imp__not__eq2,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 => V_y != V_x ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__less__asym_H,axiom, % 164.75/164.92 ! [V_b,V_a,T_a] : % 164.75/164.92 ( class_Orderings_Opreorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.75/164.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_xt1_I9_J,axiom, % 164.75/164.92 ! [V_a,V_b,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 164.75/164.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_ord__eq__less__trans,axiom, % 164.75/164.92 ! [V_c,V_b,V_a,T_a] : % 164.75/164.92 ( class_Orderings_Oord(T_a) % 164.75/164.92 => ( V_a = V_b % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_xt1_I1_J,axiom, % 164.75/164.92 ! [V_c,V_b,V_a,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( V_a = V_b % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_psubset__trans,axiom, % 164.75/164.92 ! [V_C_2,V_B_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_ord__less__eq__trans,axiom, % 164.75/164.92 ! [V_c,V_b,V_a,T_a] : % 164.75/164.92 ( class_Orderings_Oord(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.75/164.92 => ( V_b = V_c % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_xt1_I2_J,axiom, % 164.75/164.92 ! [V_c,V_a,V_b,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 164.75/164.92 => ( V_b = V_c % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__less__trans,axiom, % 164.75/164.92 ! [V_z,V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Opreorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_xt1_I10_J,axiom, % 164.75/164.92 ! [V_z,V_x,V_y,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__less__asym,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Opreorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_linorder__cases,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 => ( V_x != V_y % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_diff__eq__diff__less,axiom, % 164.75/164.92 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 164.75/164.92 ( class_Groups_Oordered__ab__group__add(T_a) % 164.75/164.92 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 164.75/164.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 164.75/164.92 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 164.75/164.92 => c_Finite__Set_Ofun__left__comm__idem(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_less__fun__def,axiom, % 164.75/164.92 ! [V_g_2,V_f_2,T_a,T_b] : % 164.75/164.92 ( class_Orderings_Oord(T_b) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 164.75/164.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 164.75/164.92 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_xt1_I8_J,axiom, % 164.75/164.92 ! [V_z,V_x,V_y,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__le__less__trans,axiom, % 164.75/164.92 ! [V_z,V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Opreorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_xt1_I7_J,axiom, % 164.75/164.92 ! [V_z,V_x,V_y,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__less__le__trans,axiom, % 164.75/164.92 ! [V_z,V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Opreorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_xt1_I11_J,axiom, % 164.75/164.92 ! [V_a,V_b,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 164.75/164.92 => ( V_a != V_b % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__le__neq__trans,axiom, % 164.75/164.92 ! [V_b,V_a,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.75/164.92 => ( V_a != V_b % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__le__imp__less__or__eq,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 | V_x = V_y ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_linorder__antisym__conv2,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 164.75/164.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 164.75/164.92 <=> V_x_2 = V_y_2 ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__less__imp__le,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Opreorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_leD,axiom, % 164.75/164.92 ! [V_x,V_y,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 164.75/164.92 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_xt1_I12_J,axiom, % 164.75/164.92 ! [V_b,V_a,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( V_a != V_b % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__neq__le__trans,axiom, % 164.75/164.92 ! [V_b,V_a,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( V_a != V_b % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_linorder__antisym__conv1,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 164.75/164.92 <=> V_x_2 = V_y_2 ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_not__leE,axiom, % 164.75/164.92 ! [V_x,V_y,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_leI,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__le__less,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 164.75/164.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 164.75/164.92 | V_x_2 = V_y_2 ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_less__le__not__le,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,T_a] : % 164.75/164.92 ( class_Orderings_Opreorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 164.75/164.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 164.75/164.92 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_order__less__le,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,T_a] : % 164.75/164.92 ( class_Orderings_Oorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 164.75/164.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 164.75/164.92 & V_x_2 != V_y_2 ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_linorder__le__less__linear,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.75/164.92 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_linorder__not__le,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 164.75/164.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_linorder__not__less,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,T_a] : % 164.75/164.92 ( class_Orderings_Olinorder(T_a) % 164.75/164.92 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 164.75/164.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_psubsetD,axiom, % 164.75/164.92 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_not__psubset__empty,axiom, % 164.75/164.92 ! [V_A_2,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 164.75/164.92 % 164.75/164.92 fof(fact_less__supI2,axiom, % 164.75/164.92 ! [V_a,V_b,V_x,T_a] : % 164.75/164.92 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 164.75/164.92 => 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))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_less__supI1,axiom, % 164.75/164.92 ! [V_b,V_a,V_x,T_a] : % 164.75/164.92 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 164.75/164.92 => 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))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_subset__psubset__trans,axiom, % 164.75/164.92 ! [V_C_2,V_B_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_psubset__subset__trans,axiom, % 164.75/164.92 ! [V_C_2,V_B_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_psubset__imp__subset,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_subset__iff__psubset__eq,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.92 | V_A_2 = V_B_2 ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_psubset__eq,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.92 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.92 & V_A_2 != V_B_2 ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_restrict__in,axiom, % 164.75/164.92 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__left__comm__idem__insert,axiom, % 164.75/164.92 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ). % 164.75/164.92 % 164.75/164.92 fof(fact_restrict__map__empty,axiom, % 164.75/164.92 ! [V_x_2,V_D_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_D_2),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__left__comm__idem__sup,axiom, % 164.75/164.92 ! [T_a] : % 164.75/164.92 ( class_Lattices_Osemilattice__sup(T_a) % 164.75/164.92 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_restrict__out,axiom, % 164.75/164.92 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 164.75/164.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_restrict__map__insert,axiom, % 164.75/164.92 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Orestrict__map(T_a,T_b,V_f_2,V_A_2)),V_a_2),hAPP(V_f_2,V_a_2)) ). % 164.75/164.92 % 164.75/164.92 fof(fact_restrict__map__def,axiom, % 164.75/164.92 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 164.75/164.92 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = hAPP(V_m_2,V_x_2) ) % 164.75/164.92 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.92 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_restrict__map__to__empty,axiom, % 164.75/164.92 ! [V_x_2,V_m_2,T_a,T_b] : hAPP(c_Map_Orestrict__map(T_b,T_a,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 164.75/164.92 % 164.75/164.92 fof(fact_diff__eq__diff__eq,axiom, % 164.75/164.92 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 164.75/164.92 ( class_Groups_Oab__group__add(T_a) % 164.75/164.92 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2) % 164.75/164.92 => ( V_a_2 = V_b_2 % 164.75/164.92 <=> V_ca_2 = V_d_2 ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_ranI,axiom, % 164.75/164.92 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 164.75/164.92 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_ran__restrictD,axiom, % 164.75/164.92 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Map_Oran(T_b,T_a,c_Map_Orestrict__map(T_b,T_a,V_m_2,V_A_2)))) % 164.75/164.92 => ? [B_x] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 164.75/164.92 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_restrict__upd__same,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ). % 164.75/164.92 % 164.75/164.92 fof(fact_restrict__complement__singleton__eq,axiom, % 164.75/164.92 ! [V_x_2,V_f_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,V_f_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),c_Option_Ooption_ONone(T_b)) ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 164.75/164.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.75/164.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 164.75/164.92 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_option_Orecs_I2_J,axiom, % 164.75/164.92 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_option_Osimps_I5_J,axiom, % 164.75/164.92 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 164.75/164.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 164.75/164.92 => 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) ) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_option_Osimps_I4_J,axiom, % 164.75/164.92 ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),c_Option_Ooption_ONone(T_b)) = V_f1_2 ). % 164.75/164.92 % 164.75/164.92 fof(fact_option_Orecs_I1_J,axiom, % 164.75/164.92 ! [V_f2_2,V_f1_2,T_b,T_a] : c_Option_Ooption_Ooption__rec(T_a,T_b,V_f1_2,V_f2_2,c_Option_Ooption_ONone(T_b)) = V_f1_2 ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 164.75/164.92 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 164.75/164.92 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.75/164.92 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_ComplI,axiom, % 164.75/164.92 ! [V_A_2,V_ca_2,T_a] : % 164.75/164.92 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.92 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_neg__equal__iff__equal,axiom, % 164.75/164.92 ! [V_b_2,V_a_2,T_a] : % 164.75/164.92 ( class_Groups_Ogroup__add(T_a) % 164.75/164.92 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 164.75/164.92 <=> V_a_2 = V_b_2 ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_minus__equation__iff,axiom, % 164.75/164.92 ! [V_b_2,V_a_2,T_a] : % 164.75/164.92 ( class_Groups_Ogroup__add(T_a) % 164.75/164.92 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2 % 164.75/164.92 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_equation__minus__iff,axiom, % 164.75/164.92 ! [V_b_2,V_a_2,T_a] : % 164.75/164.92 ( class_Groups_Ogroup__add(T_a) % 164.75/164.92 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 164.75/164.92 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_minus__minus,axiom, % 164.75/164.92 ! [V_a,T_a] : % 164.75/164.92 ( class_Groups_Ogroup__add(T_a) % 164.75/164.92 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Compl__eq__Compl__iff,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,T_a] : % 164.75/164.92 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2) % 164.75/164.92 <=> V_A_2 = V_B_2 ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_double__complement,axiom, % 164.75/164.92 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = V_A_2 ). % 164.75/164.92 % 164.75/164.92 fof(fact_compl__eq__compl__iff,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,T_a] : % 164.75/164.92 ( class_Lattices_Oboolean__algebra(T_a) % 164.75/164.92 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2) % 164.75/164.92 <=> V_x_2 = V_y_2 ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_uminus__apply,axiom, % 164.75/164.92 ! [V_x_2,V_A_2,T_b,T_a] : % 164.75/164.92 ( class_Groups_Ouminus(T_a) % 164.75/164.92 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_double__compl,axiom, % 164.75/164.92 ! [V_x,T_a] : % 164.75/164.92 ( class_Lattices_Oboolean__algebra(T_a) % 164.75/164.92 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_fun__Compl__def,axiom, % 164.75/164.92 ! [V_x_2,V_A_2,T_b,T_a] : % 164.75/164.92 ( class_Groups_Ouminus(T_a) % 164.75/164.92 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(V_A_2,V_x_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_folding__image__simple__idem_Oidem,axiom, % 164.75/164.92 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.92 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 164.75/164.92 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_compl__le__compl__iff,axiom, % 164.75/164.92 ! [V_y_2,V_x_2,T_a] : % 164.75/164.92 ( class_Lattices_Oboolean__algebra(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2))) % 164.75/164.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_compl__mono,axiom, % 164.75/164.92 ! [V_y,V_x,T_a] : % 164.75/164.92 ( class_Lattices_Oboolean__algebra(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.75/164.92 => 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))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_le__minus__iff,axiom, % 164.75/164.92 ! [V_b_2,V_a_2,T_a] : % 164.75/164.92 ( class_Groups_Oordered__ab__group__add(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 164.75/164.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_minus__le__iff,axiom, % 164.75/164.92 ! [V_b_2,V_a_2,T_a] : % 164.75/164.92 ( class_Groups_Oordered__ab__group__add(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 164.75/164.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_neg__le__iff__le,axiom, % 164.75/164.92 ! [V_a_2,V_b_2,T_a] : % 164.75/164.92 ( class_Groups_Oordered__ab__group__add(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 164.75/164.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_le__imp__neg__le,axiom, % 164.75/164.92 ! [V_b,V_a,T_a] : % 164.75/164.92 ( class_Groups_Oordered__ab__group__add(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.75/164.92 => 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))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_less__minus__iff,axiom, % 164.75/164.92 ! [V_b_2,V_a_2,T_a] : % 164.75/164.92 ( class_Groups_Oordered__ab__group__add(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 164.75/164.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_minus__less__iff,axiom, % 164.75/164.92 ! [V_b_2,V_a_2,T_a] : % 164.75/164.92 ( class_Groups_Oordered__ab__group__add(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 164.75/164.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_neg__less__iff__less,axiom, % 164.75/164.92 ! [V_a_2,V_b_2,T_a] : % 164.75/164.92 ( class_Groups_Oordered__ab__group__add(T_a) % 164.75/164.92 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 164.75/164.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_ComplE,axiom, % 164.75/164.92 ! [V_A_2,V_ca_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 164.75/164.92 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_ComplD,axiom, % 164.75/164.92 ! [V_A_2,V_ca_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 164.75/164.92 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Compl__iff,axiom, % 164.75/164.92 ! [V_A_2,V_ca_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 164.75/164.92 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_minus__diff__eq,axiom, % 164.75/164.92 ! [V_b,V_a,T_a] : % 164.75/164.92 ( class_Groups_Oab__group__add(T_a) % 164.75/164.92 => 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) ) ). % 164.75/164.92 % 164.75/164.92 fof(fact_Compl__subset__Compl__iff,axiom, % 164.75/164.92 ! [V_B_2,V_A_2,T_a] : % 164.75/164.92 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) % 164.75/164.92 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 164.75/164.92 % 164.75/164.93 fof(fact_Compl__anti__mono,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_subset__Compl__self__eq,axiom, % 164.75/164.93 ! [V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 164.75/164.93 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Compl__Diff__eq,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2) ). % 164.75/164.93 % 164.75/164.93 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 164.75/164.93 => 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) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__add__upd__left,axiom, % 164.75/164.93 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] : % 164.75/164.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2))) % 164.75/164.93 => c_Map_Omap__add(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_e1_2),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)),V_e2_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_e1_2,V_e2_2)),V_m_2),hAPP(c_Option_Ooption_OSome(T_b),V_u1_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_finite__induct,axiom, % 164.75/164.93 ! [V_P_2,V_F_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 164.75/164.93 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 164.75/164.93 => ( ! [B_x,B_F] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 164.75/164.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F)) % 164.75/164.93 => ( hBOOL(hAPP(V_P_2,B_F)) % 164.75/164.93 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) ) % 164.75/164.93 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 164.75/164.93 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2) % 164.75/164.93 => c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Sup__fin_Oremove,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 ) % 164.75/164.93 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Diff1__fold__graph,axiom, % 164.75/164.93 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_y_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__Diff2__less,axiom, % 164.75/164.93 ! [V_y_2,V_x_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__Diff1__less,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__comp__None__iff,axiom, % 164.75/164.93 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 164.75/164.93 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 164.75/164.93 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 164.75/164.93 | ? [B_k_H] : % 164.75/164.93 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 164.75/164.93 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__insert,axiom, % 164.75/164.93 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) % 164.75/164.93 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 & ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 164.75/164.93 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 164.75/164.93 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf1I,axiom, % 164.75/164.93 ! [T_a,V_B_2,V_x_2,V_A_2] : % 164.75/164.93 ( hBOOL(hAPP(V_A_2,V_x_2)) % 164.75/164.93 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf1E,axiom, % 164.75/164.93 ! [V_x_2,V_B_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 164.75/164.93 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 164.75/164.93 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_IntI,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_IntE,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.93 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.93 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_finite__Int,axiom, % 164.75/164.93 ! [V_G_2,V_F_2,T_a] : % 164.75/164.93 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 164.75/164.93 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_G_2)) ) % 164.75/164.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_G_2))) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__empty,axiom, % 164.75/164.93 ! [V_f_2,T_b,T_a] : c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__uminus,axiom, % 164.75/164.93 ! [V_A_2,T_a] : % 164.75/164.93 ( class_Groups_Oordered__ab__group__add(T_a) % 164.75/164.93 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_pigeonhole,axiom, % 164.75/164.93 ! [V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) % 164.75/164.93 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf_Oidem,axiom, % 164.75/164.93 ! [V_a,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__idem,axiom, % 164.75/164.93 ! [V_x,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__fun__def,axiom, % 164.75/164.93 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf_Ocommute,axiom, % 164.75/164.93 ! [V_b,V_a,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => 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) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__sup__aci_I1_J,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => 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) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__commute,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => 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) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf_Oleft__idem,axiom, % 164.75/164.93 ! [V_b,V_a,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => 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) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__sup__aci_I4_J,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => 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) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__left__idem,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => 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) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf_Oleft__commute,axiom, % 164.75/164.93 ! [V_c,V_a,V_b,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__sup__aci_I3_J,axiom, % 164.75/164.93 ! [V_z,V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__left__commute,axiom, % 164.75/164.93 ! [V_z,V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf_Oassoc,axiom, % 164.75/164.93 ! [V_c,V_b,V_a,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__sup__aci_I2_J,axiom, % 164.75/164.93 ! [V_z,V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__assoc,axiom, % 164.75/164.93 ! [V_z,V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__apply,axiom, % 164.75/164.93 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf1D1,axiom, % 164.75/164.93 ! [V_x_2,V_B_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 164.75/164.93 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf1D2,axiom, % 164.75/164.93 ! [V_x_2,V_B_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) % 164.75/164.93 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__absorb,axiom, % 164.75/164.93 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__commute,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__left__absorb,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__left__commute,axiom, % 164.75/164.93 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__assoc,axiom, % 164.75/164.93 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Inf__fin_Oidem,axiom, % 164.75/164.93 ! [V_x,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__def,axiom, % 164.75/164.93 ! [V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 <=> ! [B_x] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.75/164.93 => ! [B_xa] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 164.75/164.93 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 164.75/164.93 => B_x = B_xa ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__add__assoc,axiom, % 164.75/164.93 ! [V_m3_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__add(T_a,T_b,V_m2_2,V_m3_2)) = c_Map_Omap__add(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_m3_2) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__Int,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 164.75/164.93 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__id2,axiom, % 164.75/164.93 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__image,axiom, % 164.75/164.93 ! [V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__map__add__dom,axiom, % 164.75/164.93 ! [V_m_H_2,V_m_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),c_Map_Omap__add(T_a,T_b,V_m_2,V_m_H_2),c_Map_Odom(T_a,T_b,V_m_H_2)) % 164.75/164.93 <=> c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_b),V_m_H_2,c_Map_Odom(T_a,T_b,V_m_H_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__Sup__absorb,axiom, % 164.75/164.93 ! [V_a_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = V_a_2 ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__iff__eq__card,axiom, % 164.75/164.93 ! [V_f_2,T_b,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 <=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_eq__card__imp__inj__on,axiom, % 164.75/164.93 ! [V_f_2,T_b,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) % 164.75/164.93 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__image__Int,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 164.75/164.93 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__Diff__subset__Int,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.93 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__onD,axiom, % 164.75/164.93 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 164.75/164.93 => V_x_2 = V_y_2 ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__iff,axiom, % 164.75/164.93 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 164.75/164.93 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 164.75/164.93 <=> V_x_2 = V_y_2 ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__contraD,axiom, % 164.75/164.93 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => ( V_x_2 != V_y_2 % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 164.75/164.93 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_subset__inj__on,axiom, % 164.75/164.93 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.93 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_le__infE,axiom, % 164.75/164.93 ! [V_b,V_a,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => ( 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))) % 164.75/164.93 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 164.75/164.93 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__mono,axiom, % 164.75/164.93 ! [V_d,V_b,V_c,V_a,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 164.75/164.93 => 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))) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__greatest,axiom, % 164.75/164.93 ! [V_z,V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 164.75/164.93 => 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))) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_le__infI,axiom, % 164.75/164.93 ! [V_b,V_a,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 164.75/164.93 => 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))) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__absorb2,axiom, % 164.75/164.93 ! [V_x,V_y,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__absorb1,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_le__infI2,axiom, % 164.75/164.93 ! [V_a,V_x,V_b,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 164.75/164.93 => 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)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_le__infI1,axiom, % 164.75/164.93 ! [V_b,V_x,V_a,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 164.75/164.93 => 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)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_le__inf__iff,axiom, % 164.75/164.93 ! [V_z_2,V_y_2,V_x_2,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y_2),V_z_2))) % 164.75/164.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 164.75/164.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_le__iff__inf,axiom, % 164.75/164.93 ! [V_y_2,V_x_2,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 164.75/164.93 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__le2,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__sup__ord_I2_J,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__le1,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__sup__ord_I1_J,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_less__infI1,axiom, % 164.75/164.93 ! [V_b,V_x,V_a,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 164.75/164.93 => 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)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_less__infI2,axiom, % 164.75/164.93 ! [V_a,V_x,V_b,T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 164.75/164.93 => 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)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__diff,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__bot__left,axiom, % 164.75/164.93 ! [V_x,T_a] : % 164.75/164.93 ( class_Lattices_Obounded__lattice__bot(T_a) % 164.75/164.93 => 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) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__bot__right,axiom, % 164.75/164.93 ! [V_x,T_a] : % 164.75/164.93 ( class_Lattices_Obounded__lattice__bot(T_a) % 164.75/164.93 => 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) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_sup__inf__distrib2,axiom, % 164.75/164.93 ! [V_x,V_z,V_y,T_a] : % 164.75/164.93 ( class_Lattices_Odistrib__lattice(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__sup__distrib2,axiom, % 164.75/164.93 ! [V_x,V_z,V_y,T_a] : % 164.75/164.93 ( class_Lattices_Odistrib__lattice(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_sup__inf__distrib1,axiom, % 164.75/164.93 ! [V_z,V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Odistrib__lattice(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__sup__distrib1,axiom, % 164.75/164.93 ! [V_z,V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Odistrib__lattice(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_sup__inf__absorb,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => 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 ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__sup__absorb,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => 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 ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 164.75/164.93 ! [V_a2_2,V_a1_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_a2_2) ). % 164.75/164.93 % 164.75/164.93 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 164.75/164.93 ! [V_z_2,V_f_2,T_b,T_a] : c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__Some,axiom, % 164.75/164.93 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a),V_A_2) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__add__comm,axiom, % 164.75/164.93 ! [V_m2_2,V_m1_2,T_b,T_a] : % 164.75/164.93 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m1_2)),c_Map_Odom(T_a,T_b,V_m2_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2) = c_Map_Omap__add(T_a,T_b,V_m2_2,V_m1_2) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__iff,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.93 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.75/164.93 & hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_IntD1,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_IntD2,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__empty__left,axiom, % 164.75/164.93 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__empty__right,axiom, % 164.75/164.93 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_disjoint__iff__not__equal,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 <=> ! [B_x] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.75/164.93 => ! [B_xa] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) % 164.75/164.93 => B_x != B_xa ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_insert__inter__insert,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_a_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__mono,axiom, % 164.75/164.93 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__greatest,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_C_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__absorb1,axiom, % 164.75/164.93 ! [V_A_2,V_B_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__absorb2,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__lower2,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__lower1,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__Un__distrib,axiom, % 164.75/164.93 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Un__Int__distrib,axiom, % 164.75/164.93 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__Un__distrib2,axiom, % 164.75/164.93 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Un__Int__distrib2,axiom, % 164.75/164.93 ! [V_A_2,V_C_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Un__Int__crazy,axiom, % 164.75/164.93 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Diff__Int__distrib,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_C_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__Diff,axiom, % 164.75/164.93 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Diff__Int__distrib2,axiom, % 164.75/164.93 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Diff__Int2,axiom, % 164.75/164.93 ! [V_B_2,V_C_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__inj__on__le,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),V_B_2)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__bij__eq,axiom, % 164.75/164.93 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),V_B_2)) % 164.75/164.93 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),V_B_2)),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 164.75/164.93 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_restrict__restrict,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_m_2,T_b,T_a] : c_Map_Orestrict__map(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_B_2) = c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_fun__left__comm__idem__inf,axiom, % 164.75/164.93 ! [T_a] : % 164.75/164.93 ( class_Lattices_Osemilattice__inf(T_a) % 164.75/164.93 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_fold__graph_Oequations_I1_J,axiom, % 164.75/164.93 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_fold__graph_OemptyI,axiom, % 164.75/164.93 ! [V_z_2,V_f_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_z_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_empty__fold__graphE,axiom, % 164.75/164.93 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)) % 164.75/164.93 => V_x_2 = V_z_2 ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_fold__graph__imp__finite,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 164.75/164.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__add__None,axiom, % 164.75/164.93 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] : % 164.75/164.93 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a) % 164.75/164.93 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 164.75/164.93 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__add__find__right,axiom, % 164.75/164.93 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] : % 164.75/164.93 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) % 164.75/164.93 => hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__Int__eq,axiom, % 164.75/164.93 ! [V_x_2,V_S_2,V_R_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)),V_x_2)) % 164.75/164.93 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Sup__fin_Osingleton,axiom, % 164.75/164.93 ! [V_x_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Sup__fin_Ounion__inter,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_empty__map__add,axiom, % 164.75/164.93 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)),V_m_2) = V_m_2 ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__add__empty,axiom, % 164.75/164.93 ! [V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b))) = V_m_2 ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__add__def,axiom, % 164.75/164.93 ! [V_x_2,V_m2_2,V_m1_2,T_a,T_b] : hAPP(c_Map_Omap__add(T_b,T_a,V_m1_2,V_m2_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,hAPP(V_m1_2,V_x_2),c_Option_Ooption_OSome(T_a)),hAPP(V_m2_2,V_x_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__Un,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.93 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 164.75/164.93 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_finite__imageD,axiom, % 164.75/164.93 ! [V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 164.75/164.93 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 164.75/164.93 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__Un__image__eq__iff,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.93 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) % 164.75/164.93 <=> V_A_2 = V_B_2 ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_distrib__sup__le,axiom, % 164.75/164.93 ! [V_z,V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => 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)))) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_distrib__inf__le,axiom, % 164.75/164.93 ! [V_z,V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => 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)))) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__insert__le,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)))) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__mono,axiom, % 164.75/164.93 ! [V_A_2,V_B_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__seteq,axiom, % 164.75/164.93 ! [V_A_2,V_B_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) % 164.75/164.93 => V_A_2 = V_B_2 ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__image__le,axiom, % 164.75/164.93 ! [V_f_2,T_b,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_compl__inf__bot,axiom, % 164.75/164.93 ! [V_x,T_a] : % 164.75/164.93 ( class_Lattices_Oboolean__algebra(T_a) % 164.75/164.93 => 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) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inf__compl__bot,axiom, % 164.75/164.93 ! [V_x,T_a] : % 164.75/164.93 ( class_Lattices_Oboolean__algebra(T_a) % 164.75/164.93 => 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) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_diff__eq,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Oboolean__algebra(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_compl__sup,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Oboolean__algebra(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_compl__inf,axiom, % 164.75/164.93 ! [V_y,V_x,T_a] : % 164.75/164.93 ( class_Lattices_Oboolean__algebra(T_a) % 164.75/164.93 => 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)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_diff__card__le__card__Diff,axiom, % 164.75/164.93 ! [V_A_2,V_B_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__insert__left__if1,axiom, % 164.75/164.93 ! [V_B_2,V_C_2,V_a_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__insert__right__if1,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_a_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__insert__left__if0,axiom, % 164.75/164.93 ! [V_B_2,V_C_2,V_a_2,T_a] : % 164.75/164.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__insert__right__if0,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_a_2,T_a] : % 164.75/164.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__insert__left,axiom, % 164.75/164.93 ! [V_B_2,V_C_2,V_a_2,T_a] : % 164.75/164.93 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) ) % 164.75/164.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Int__insert__right,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_a_2,T_a] : % 164.75/164.93 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 164.75/164.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__strict__subset,axiom, % 164.75/164.93 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_image__Int__subset,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_B_2)))) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Diff__triv,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Diff__disjoint,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Un__Int__assoc__eq,axiom, % 164.75/164.93 ! [V_C_2,V_B_2,V_A_2,T_a] : % 164.75/164.93 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 164.75/164.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_psubset__card__mono,axiom, % 164.75/164.93 ! [V_A_2,V_B_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Diff__Int,axiom, % 164.75/164.93 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Diff__Un,axiom, % 164.75/164.93 ! [V_C_2,V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Un__Diff__Int,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ). % 164.75/164.93 % 164.75/164.93 fof(fact_Compl__disjoint,axiom, % 164.75/164.93 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Compl__disjoint2,axiom, % 164.75/164.93 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Compl__Un,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Compl__Int,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Diff__eq,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Diff__Compl,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Sup__fin_Oin__idem,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_dom__restrict,axiom, % 164.75/164.93 ! [V_A_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_m_2)),V_A_2) ). % 164.75/164.93 % 164.75/164.93 fof(fact_fold__graph_OinsertI,axiom, % 164.75/164.93 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 164.75/164.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 164.75/164.93 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 164.75/164.93 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 164.75/164.93 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 164.75/164.93 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 164.75/164.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 164.75/164.93 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 164.75/164.93 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] : % 164.75/164.93 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2))) % 164.75/164.93 => hAPP(c_Map_Omap__add(T_a,T_b,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__comp__simps_I1_J,axiom, % 164.75/164.93 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] : % 164.75/164.93 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 164.75/164.93 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__comp__Some__iff,axiom, % 164.75/164.93 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 164.75/164.93 ( c_Map_Omap__comp(T_b,T_a,T_c,V_m1_2,V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) % 164.75/164.93 <=> ? [B_k_H] : % 164.75/164.93 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 164.75/164.93 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__comp__simps_I2_J,axiom, % 164.75/164.93 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] : % 164.75/164.93 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2) % 164.75/164.93 => c_Map_Omap__comp(T_a,T_c,T_b,V_m1_2,V_m2_2,V_k_2) = hAPP(V_m1_2,V_k_H_2) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__add__SomeD,axiom, % 164.75/164.93 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 164.75/164.93 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 164.75/164.93 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 164.75/164.93 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 164.75/164.93 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__add__Some__iff,axiom, % 164.75/164.93 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 164.75/164.93 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 164.75/164.93 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 164.75/164.93 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 164.75/164.93 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_dom__map__add,axiom, % 164.75/164.93 ! [V_n_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_n_2)),c_Map_Odom(T_a,T_b,V_m_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__add__upd,axiom, % 164.75/164.93 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__add(T_a,T_b,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_endo__inj__surj,axiom, % 164.75/164.93 ! [V_f_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2)),V_A_2)) % 164.75/164.93 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 164.75/164.93 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_finite__surj__inj,axiom, % 164.75/164.93 ! [V_f_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2))) % 164.75/164.93 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__image__set__diff,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 164.75/164.93 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__fun__updI,axiom, % 164.75/164.93 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 164.75/164.93 => c_Fun_Oinj__on(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2),V_A_2) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__Diff__subset,axiom, % 164.75/164.93 ! [V_A_2,V_B_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 164.75/164.93 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__psubset,axiom, % 164.75/164.93 ! [V_A_2,V_B_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2))) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_disjoint__eq__subset__Compl,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Sup__fin_Oinsert__idem,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Sup__fin_Osubset__idem,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Sup__fin_Ounion__idem,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) ) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__comp__empty_I2_J,axiom, % 164.75/164.93 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,hAPP(c_COMBK(tc_Option_Ooption(T_a),T_b),c_Option_Ooption_ONone(T_a)),V_m_2,V_x_2) = c_Option_Ooption_ONone(T_a) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__comp__empty_I1_J,axiom, % 164.75/164.93 ! [V_x_2,V_m_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_m_2,hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b)),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 164.75/164.93 % 164.75/164.93 fof(fact_map__comp__def,axiom, % 164.75/164.93 ! [V_k_2,V_g_2,V_f_2,T_c,T_a,T_b] : c_Map_Omap__comp(T_b,T_a,T_c,V_f_2,V_g_2,V_k_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_b,c_Option_Ooption_ONone(T_a),V_f_2),hAPP(V_g_2,V_k_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Sup__fin_Oidem,axiom, % 164.75/164.93 ! [V_x,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_folding__image__simple_Ounion__inter,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 164.75/164.93 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__Diff1__le,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Sup__fin_Oinsert,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Sup__fin_Oinsert__remove,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 164.75/164.93 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_folding__one_Ounion__inter,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 164.75/164.93 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_folding__one_Ounion__disjoint,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 164.75/164.93 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__iff__card__le,axiom, % 164.75/164.93 ! [V_B_2,T_b,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 164.75/164.93 => ( ? [B_f] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 164.75/164.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_B_2)) ) % 164.75/164.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__iff__surj,axiom, % 164.75/164.93 ! [V_A_H_2,T_b,T_a,V_A_2] : % 164.75/164.93 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => ( ? [B_f] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 164.75/164.93 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,B_f),V_A_2)),V_A_H_2)) ) % 164.75/164.93 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_fold1Set_Ointros,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2)) % 164.75/164.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.75/164.93 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),V_x_2)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Sup__fin_Oclosed,axiom, % 164.75/164.93 ! [V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Inf__fin_Oremove,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 ) % 164.75/164.93 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 164.75/164.93 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] : % 164.75/164.93 ( c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) % 164.75/164.93 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 164.75/164.93 | ? [B_x,B_y] : % 164.75/164.93 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 164.75/164.93 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2)) % 164.75/164.93 & c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_the__inv__into__into,axiom, % 164.75/164.93 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Sup__fin_Ohom__commute,axiom, % 164.75/164.93 ! [V_N_2,V_h_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 164.75/164.93 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__Diff__singleton__if,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 164.75/164.93 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__Diff__singleton,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_one__reorient,axiom, % 164.75/164.93 ! [V_x_2,T_a] : % 164.75/164.93 ( class_Groups_Oone(T_a) % 164.75/164.93 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 164.75/164.93 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 164.75/164.93 ! [V_N_2] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 164.75/164.93 <=> ? [B_m] : % 164.75/164.93 ! [B_x] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_fold1Set__nonempty,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,V_f_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2)) % 164.75/164.93 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_empty__fold1SetE,axiom, % 164.75/164.93 ! [V_x_2,V_f_2,T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_x_2)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Inf__fin_Osingleton,axiom, % 164.75/164.93 ! [V_x_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_finite__nat__set__iff__bounded,axiom, % 164.75/164.93 ! [V_N_2] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 164.75/164.93 <=> ? [B_m] : % 164.75/164.93 ! [B_x] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_the__inv__into__f__f,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_the__inv__into__f__eq,axiom, % 164.75/164.93 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_sup__Inf__absorb,axiom, % 164.75/164.93 ! [V_a_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = V_a_2 ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Inf__fin_Oin__idem,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_the__inv__into__onto,axiom, % 164.75/164.93 ! [V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => hAPP(c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_inj__on__the__inv__into,axiom, % 164.75/164.93 ! [V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_fold1Set__sing,axiom, % 164.75/164.93 ! [V_b_2,V_a_2,V_f_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_b_2)) % 164.75/164.93 <=> V_a_2 = V_b_2 ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_the__inv__into__def,axiom, % 164.75/164.93 ! [V_x_2,V_f_2,V_A_2,T_b,T_a] : hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_x_2))) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Inf__fin_Oinsert__idem,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Inf__fin_Osubset__idem,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Inf__fin_Ounion__idem,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Inf__le__Sup,axiom, % 164.75/164.93 ! [V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2))) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_f__the__inv__into__f,axiom, % 164.75/164.93 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] : % 164.75/164.93 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 164.75/164.93 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_card__Diff__insert,axiom, % 164.75/164.93 ! [V_B_2,V_a_2,V_A_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.75/164.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 164.75/164.93 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Inf__fin_Oinsert,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Inf__fin_Oinsert__remove,axiom, % 164.75/164.93 ! [V_x_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 164.75/164.93 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Inf__fin_Ounion__inter,axiom, % 164.75/164.93 ! [V_B_2,V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.93 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_less__diff__iff,axiom, % 164.75/164.93 ! [V_n_2,V_m_2,V_k_2] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 164.75/164.93 => ( 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))) % 164.75/164.93 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_diff__less__mono,axiom, % 164.75/164.93 ! [V_c,V_b,V_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 164.75/164.93 => 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))) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_Inf__fin_Oclosed,axiom, % 164.75/164.93 ! [V_A_2,T_a] : % 164.75/164.93 ( class_Lattices_Olattice(T_a) % 164.75/164.93 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.93 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.93 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_ord_OatMost__iff,axiom, % 164.75/164.93 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))) % 164.75/164.93 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_ord_OatLeast__iff,axiom, % 164.75/164.93 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))) % 164.75/164.93 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_ord_OlessThan__iff,axiom, % 164.75/164.93 ! [V_k_2,V_less_2,V_i_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))) % 164.75/164.93 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_ord_OgreaterThan__iff,axiom, % 164.75/164.93 ! [V_k_2,V_less_2,V_i_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))) % 164.75/164.93 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_ord_OatLeastAtMost__iff,axiom, % 164.75/164.93 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2))) % 164.75/164.93 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 164.75/164.93 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 164.75/164.93 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))) % 164.75/164.93 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 164.75/164.93 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_nat__less__cases,axiom, % 164.75/164.93 ! [V_P_2,V_n_2,V_m_2] : % 164.75/164.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 164.75/164.93 => ( ( V_m_2 = V_n_2 % 164.75/164.93 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 164.75/164.93 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 164.75/164.93 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 164.75/164.93 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_less__not__refl3,axiom, % 164.75/164.93 ! [V_t,V_s] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 164.75/164.93 => V_s != V_t ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_less__not__refl2,axiom, % 164.75/164.93 ! [V_m,V_n] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 164.75/164.93 => V_m != V_n ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_less__irrefl__nat,axiom, % 164.75/164.93 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_linorder__neqE__nat,axiom, % 164.75/164.93 ! [V_y,V_x] : % 164.75/164.93 ( V_x != V_y % 164.75/164.93 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_nat__neq__iff,axiom, % 164.75/164.93 ! [V_n_2,V_m_2] : % 164.75/164.93 ( V_m_2 != V_n_2 % 164.75/164.93 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 164.75/164.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_less__not__refl,axiom, % 164.75/164.93 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_le__antisym,axiom, % 164.75/164.93 ! [V_n,V_m] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 164.75/164.93 => V_m = V_n ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_le__trans,axiom, % 164.75/164.93 ! [V_k,V_j,V_i] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 164.75/164.93 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_eq__imp__le,axiom, % 164.75/164.93 ! [V_n,V_m] : % 164.75/164.93 ( V_m = V_n % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_nat__le__linear,axiom, % 164.75/164.93 ! [V_n,V_m] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 164.75/164.93 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_le__refl,axiom, % 164.75/164.93 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 164.75/164.93 % 164.75/164.93 fof(fact_diff__commute,axiom, % 164.75/164.93 ! [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) ). % 164.75/164.93 % 164.75/164.93 fof(fact_less__or__eq__imp__le,axiom, % 164.75/164.93 ! [V_n,V_m] : % 164.75/164.93 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.75/164.93 | V_m = V_n ) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_le__neq__implies__less,axiom, % 164.75/164.93 ! [V_n,V_m] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 164.75/164.93 => ( V_m != V_n % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_less__imp__le__nat,axiom, % 164.75/164.93 ! [V_n,V_m] : % 164.75/164.93 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.75/164.93 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 164.75/164.93 % 164.75/164.93 fof(fact_le__eq__less__or__eq,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.75/164.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 164.75/164.94 | V_m_2 = V_n_2 ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__less__le,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 164.75/164.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.75/164.94 & V_m_2 != V_n_2 ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__imp__diff__less,axiom, % 164.75/164.94 ! [V_n,V_k,V_j] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__less__mono2,axiom, % 164.75/164.94 ! [V_l,V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 164.75/164.94 => 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))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__diff__iff,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_k_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 164.75/164.94 => ( 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))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Nat_Odiff__diff__eq,axiom, % 164.75/164.94 ! [V_n,V_m,V_k] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 164.75/164.94 => 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) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_eq__diff__iff,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_k_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 164.75/164.94 => ( 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) % 164.75/164.94 <=> V_m_2 = V_n_2 ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__diff__cancel,axiom, % 164.75/164.94 ! [V_n,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 164.75/164.94 => 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 ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__le__mono,axiom, % 164.75/164.94 ! [V_l,V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__le__mono2,axiom, % 164.75/164.94 ! [V_l,V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__le__self,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 164.75/164.94 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 164.75/164.94 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 164.75/164.94 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_ord_OatLeastLessThan__iff,axiom, % 164.75/164.94 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))) % 164.75/164.94 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 164.75/164.94 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_card_Oremove,axiom, % 164.75/164.94 ! [V_x_2,V_A_2,T_a] : % 164.75/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.94 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_termination__basic__simps_I5_J,axiom, % 164.75/164.94 ! [V_y,V_x] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_,axiom, % 164.75/164.94 ! [V_y_2,V_x_2,T_a] : c_Smallcheck_Oorelse(T_a,V_x_2,V_y_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_a),T_a,V_y_2,c_Option_Ooption_OSome(T_a)),V_x_2) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Inf__fin_Ohom__commute,axiom, % 164.75/164.94 ! [V_N_2,V_h_2,T_a] : % 164.75/164.94 ( class_Lattices_Olattice(T_a) % 164.75/164.94 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 164.75/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 164.75/164.94 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.94 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_a,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_card_Oinsert__remove,axiom, % 164.75/164.94 ! [V_x_2,V_A_2,T_a] : % 164.75/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_card__Suc__Diff1,axiom, % 164.75/164.94 ! [V_x_2,V_A_2,T_a] : % 164.75/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.94 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_image__eq__fold__image,axiom, % 164.75/164.94 ! [V_f_2,T_b,V_A_2,T_a] : % 164.75/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_b,tc_HOL_Obool),T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_lessI,axiom, % 164.75/164.94 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__mono,axiom, % 164.75/164.94 ! [V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_inj__on__add__nat,axiom, % 164.75/164.94 ! [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) ). % 164.75/164.94 % 164.75/164.94 fof(fact_inj__Suc,axiom, % 164.75/164.94 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__inject,axiom, % 164.75/164.94 ! [V_y,V_x] : % 164.75/164.94 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 164.75/164.94 => V_x = V_y ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__add__right__cancel,axiom, % 164.75/164.94 ! [V_n_2,V_k_2,V_m_2] : % 164.75/164.94 ( 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) % 164.75/164.94 <=> V_m_2 = V_n_2 ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__add__left__cancel,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_k_2] : % 164.75/164.94 ( 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) % 164.75/164.94 <=> V_m_2 = V_n_2 ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__add__assoc,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat_Oinject,axiom, % 164.75/164.94 ! [V_nat_H_2,V_nat_2] : % 164.75/164.94 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 164.75/164.94 <=> V_nat_2 = V_nat_H_2 ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__Suc__shift,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__Suc,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__add__left__commute,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__Suc__right,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__add__commute,axiom, % 164.75/164.94 ! [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) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__n__not__n,axiom, % 164.75/164.94 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 164.75/164.94 % 164.75/164.94 fof(fact_n__not__Suc__n,axiom, % 164.75/164.94 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__add__Suc1,axiom, % 164.75/164.94 ! [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)))) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__add__Suc2,axiom, % 164.75/164.94 ! [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)))) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__iff__Suc__add,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 164.75/164.94 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_termination__basic__simps_I4_J,axiom, % 164.75/164.94 ! [V_y,V_z,V_x] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_termination__basic__simps_I3_J,axiom, % 164.75/164.94 ! [V_z,V_y,V_x] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__right__imp__eq,axiom, % 164.75/164.94 ! [V_c,V_a,V_b,T_a] : % 164.75/164.94 ( class_Groups_Ocancel__semigroup__add(T_a) % 164.75/164.94 => ( 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) % 164.75/164.94 => V_b = V_c ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__imp__eq,axiom, % 164.75/164.94 ! [V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 164.75/164.94 => ( 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) % 164.75/164.94 => V_b = V_c ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__left__imp__eq,axiom, % 164.75/164.94 ! [V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Ocancel__semigroup__add(T_a) % 164.75/164.94 => ( 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) % 164.75/164.94 => V_b = V_c ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__right__cancel,axiom, % 164.75/164.94 ! [V_ca_2,V_a_2,V_b_2,T_a] : % 164.75/164.94 ( class_Groups_Ocancel__semigroup__add(T_a) % 164.75/164.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2) % 164.75/164.94 <=> V_b_2 = V_ca_2 ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__left__cancel,axiom, % 164.75/164.94 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 164.75/164.94 ( class_Groups_Ocancel__semigroup__add(T_a) % 164.75/164.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2) % 164.75/164.94 <=> V_b_2 = V_ca_2 ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 164.75/164.94 ! [V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oab__semigroup__add(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_termination__basic__simps_I2_J,axiom, % 164.75/164.94 ! [V_y,V_z,V_x] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_termination__basic__simps_I1_J,axiom, % 164.75/164.94 ! [V_z,V_y,V_x] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__Suc__diff__eq1,axiom, % 164.75/164.94 ! [V_m,V_j,V_k] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__Suc__diff__eq2,axiom, % 164.75/164.94 ! [V_m,V_j,V_k] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__le__cancel__right,axiom, % 164.75/164.94 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 164.75/164.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_ca_2))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__le__cancel__left,axiom, % 164.75/164.94 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 164.75/164.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_b_2))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__right__mono,axiom, % 164.75/164.94 ! [V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.75/164.94 => 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))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__left__mono,axiom, % 164.75/164.94 ! [V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.75/164.94 => 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))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__mono,axiom, % 164.75/164.94 ! [V_d,V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 164.75/164.94 => 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))) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__le__imp__le__right,axiom, % 164.75/164.94 ! [V_b,V_c,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 164.75/164.94 => ( 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))) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__le__imp__le__left,axiom, % 164.75/164.94 ! [V_b,V_a,V_c,T_a] : % 164.75/164.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 164.75/164.94 => ( 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))) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__less__cancel__right,axiom, % 164.75/164.94 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 164.75/164.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_ca_2))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__less__cancel__left,axiom, % 164.75/164.94 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 164.75/164.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_b_2))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__strict__right__mono,axiom, % 164.75/164.94 ! [V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.75/164.94 => 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))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__strict__left__mono,axiom, % 164.75/164.94 ! [V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.75/164.94 => 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))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__strict__mono,axiom, % 164.75/164.94 ! [V_d,V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 164.75/164.94 => 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))) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__less__imp__less__right,axiom, % 164.75/164.94 ! [V_b,V_c,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 164.75/164.94 => ( 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))) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__less__imp__less__left,axiom, % 164.75/164.94 ! [V_b,V_a,V_c,T_a] : % 164.75/164.94 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 164.75/164.94 => ( 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))) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__add__cancel,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Ogroup__add(T_a) % 164.75/164.94 => 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 ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__diff__cancel,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Ogroup__add(T_a) % 164.75/164.94 => 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 ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_minus__add__cancel,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Ogroup__add(T_a) % 164.75/164.94 => 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 ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__minus__cancel,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Ogroup__add(T_a) % 164.75/164.94 => 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 ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_minus__add,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Ogroup__add(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_minus__add__distrib,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oab__group__add(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__less__SucD,axiom, % 164.75/164.94 ! [V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__lessD,axiom, % 164.75/164.94 ! [V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__SucE,axiom, % 164.75/164.94 ! [V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 164.75/164.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.75/164.94 => V_m = V_n ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__trans__Suc,axiom, % 164.75/164.94 ! [V_k,V_j,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__lessI,axiom, % 164.75/164.94 ! [V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.75/164.94 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__SucI,axiom, % 164.75/164.94 ! [V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__antisym,axiom, % 164.75/164.94 ! [V_m,V_n] : % 164.75/164.94 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 164.75/164.94 => V_m = V_n ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_not__less__less__Suc__eq,axiom, % 164.75/164.94 ! [V_m_2,V_n_2] : % 164.75/164.94 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 164.75/164.94 <=> V_n_2 = V_m_2 ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__less__eq,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( 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))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__Suc__eq,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 164.75/164.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 164.75/164.94 | V_m_2 = V_n_2 ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_not__less__eq,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__n__not__le__n,axiom, % 164.75/164.94 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_not__less__eq__eq,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__Suc__eq,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 164.75/164.94 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.75/164.94 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__le__mono,axiom, % 164.75/164.94 ! [V_m_2,V_n_2] : % 164.75/164.94 ( 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))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__SucI,axiom, % 164.75/164.94 ! [V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__SucE,axiom, % 164.75/164.94 ! [V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 164.75/164.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 164.75/164.94 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__leD,axiom, % 164.75/164.94 ! [V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__lessD1,axiom, % 164.75/164.94 ! [V_k,V_j,V_i] : % 164.75/164.94 ( 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)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__add__eq__less,axiom, % 164.75/164.94 ! [V_n,V_m,V_l,V_k] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 164.75/164.94 => ( 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) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__less__mono,axiom, % 164.75/164.94 ! [V_l,V_k,V_j,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 164.75/164.94 => 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))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__less__mono1,axiom, % 164.75/164.94 ! [V_k,V_j,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_trans__less__add2,axiom, % 164.75/164.94 ! [V_m,V_j,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_trans__less__add1,axiom, % 164.75/164.94 ! [V_m,V_j,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__add__left__cancel__less,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_k_2] : % 164.75/164.94 ( 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))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_not__add__less2,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_not__add__less1,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__Suc__Suc,axiom, % 164.75/164.94 ! [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) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__diff__diff,axiom, % 164.75/164.94 ! [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) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__add2,axiom, % 164.75/164.94 ! [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))) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__add1,axiom, % 164.75/164.94 ! [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))) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__iff__add,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.75/164.94 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__add__left__cancel__le,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_k_2] : % 164.75/164.94 ( 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))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_trans__le__add1,axiom, % 164.75/164.94 ! [V_m,V_j,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_trans__le__add2,axiom, % 164.75/164.94 ! [V_m,V_j,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__le__mono1,axiom, % 164.75/164.94 ! [V_k,V_j,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__le__mono,axiom, % 164.75/164.94 ! [V_l,V_k,V_j,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 164.75/164.94 => 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))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__leD2,axiom, % 164.75/164.94 ! [V_n,V_k,V_m] : % 164.75/164.94 ( 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)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__leD1,axiom, % 164.75/164.94 ! [V_n,V_k,V_m] : % 164.75/164.94 ( 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)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__leE,axiom, % 164.75/164.94 ! [V_n,V_k,V_m] : % 164.75/164.94 ( 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)) % 164.75/164.94 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 164.75/164.94 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__add__inverse2,axiom, % 164.75/164.94 ! [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 ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__add__inverse,axiom, % 164.75/164.94 ! [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 ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__diff__left,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__cancel,axiom, % 164.75/164.94 ! [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) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__cancel2,axiom, % 164.75/164.94 ! [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) ). % 164.75/164.94 % 164.75/164.94 fof(fact_fold__image__empty,axiom, % 164.75/164.94 ! [V_z_2,V_g_2,V_f_2,T_b,T_a] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__less__le__mono,axiom, % 164.75/164.94 ! [V_d,V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 164.75/164.94 => 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))) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__le__less__mono,axiom, % 164.75/164.94 ! [V_d,V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 164.75/164.94 => 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))) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__def,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Ogroup__add(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_ab__diff__minus,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oab__group__add(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__minus__eq__add,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Ogroup__add(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__eq__Suc__le,axiom, % 164.75/164.94 ! [V_m_2,V_n_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__Suc__eq__le,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__le__eq,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__imp__less__Suc,axiom, % 164.75/164.94 ! [V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__leI,axiom, % 164.75/164.94 ! [V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__less__Suc__eq,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 164.75/164.94 <=> V_n_2 = V_m_2 ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__le__lessD,axiom, % 164.75/164.94 ! [V_n,V_m] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__less__Suc,axiom, % 164.75/164.94 ! [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))) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__diff__le,axiom, % 164.75/164.94 ! [V_m,V_n] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__diff__inverse,axiom, % 164.75/164.94 ! [V_n,V_m] : % 164.75/164.94 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.75/164.94 => 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 ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__diff__conv,axiom, % 164.75/164.94 ! [V_k_2,V_j_2,V_i_2] : % 164.75/164.94 ( 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))) % 164.75/164.94 <=> 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__diff__right,axiom, % 164.75/164.94 ! [V_i,V_j,V_k] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__diff__conv,axiom, % 164.75/164.94 ! [V_i_2,V_k_2,V_j_2] : % 164.75/164.94 ( 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)) % 164.75/164.94 <=> 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__add__diff,axiom, % 164.75/164.94 ! [V_m,V_n,V_k] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__add__diff__inverse,axiom, % 164.75/164.94 ! [V_m,V_n] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 164.75/164.94 => 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 ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__diff__assoc,axiom, % 164.75/164.94 ! [V_i,V_j,V_k] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__diff__conv2,axiom, % 164.75/164.94 ! [V_i_2,V_j_2,V_k_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 164.75/164.94 => ( 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))) % 164.75/164.94 <=> 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)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__add__diff__inverse2,axiom, % 164.75/164.94 ! [V_m,V_n] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 164.75/164.94 => 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 ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__imp__diff__is__add,axiom, % 164.75/164.94 ! [V_k_2,V_j_2,V_i_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 164.75/164.94 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 164.75/164.94 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__add__assoc,axiom, % 164.75/164.94 ! [V_i,V_j,V_k] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__diff__assoc2,axiom, % 164.75/164.94 ! [V_i,V_j,V_k] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__add__assoc2,axiom, % 164.75/164.94 ! [V_i,V_j,V_k] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__Suc__1,axiom, % 164.75/164.94 ! [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 ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__eq__Suc__le__raw,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 164.75/164.94 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.94 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 164.75/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.75/164.94 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_card__insert__disjoint,axiom, % 164.75/164.94 ! [V_x_2,V_A_2,T_a] : % 164.75/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.94 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_card__insert__if,axiom, % 164.75/164.94 ! [V_x_2,V_A_2,T_a] : % 164.75/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.94 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) % 164.75/164.94 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.94 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_card__Un__Int,axiom, % 164.75/164.94 ! [V_B_2,V_A_2,T_a] : % 164.75/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_card_Ounion__inter,axiom, % 164.75/164.94 ! [V_B_2,V_A_2,T_a] : % 164.75/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.94 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_card__insert,axiom, % 164.75/164.94 ! [V_x_2,V_A_2,T_a] : % 164.75/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_card__Un__disjoint,axiom, % 164.75/164.94 ! [V_B_2,V_A_2,T_a] : % 164.75/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.94 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.94 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_card_Oinsert,axiom, % 164.75/164.94 ! [V_x_2,V_A_2,T_a] : % 164.75/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.75/164.94 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__Suc__eq__diff__pred,axiom, % 164.75/164.94 ! [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) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__eq__plus1__left,axiom, % 164.75/164.94 ! [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) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__eq__plus1,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 164.75/164.94 ! [V_y,V_x,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__ring__1(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__add__one,axiom, % 164.75/164.94 ! [V_a,T_a] : % 164.75/164.94 ( class_Rings_Olinordered__semidom(T_a) % 164.75/164.94 => 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)))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Body__triple__valid__Suc,axiom, % 164.75/164.94 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] : % 164.75/164.94 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)) % 164.75/164.94 <=> c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__monoid__big_OF__eq,axiom, % 164.75/164.94 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.94 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 164.75/164.94 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.75/164.94 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) % 164.75/164.94 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.75/164.94 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_fold__Un__disjoint,axiom, % 164.75/164.94 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 164.75/164.94 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.75/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.94 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.75/164.94 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) ) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 164.75/164.94 ! [V_z,V_y,V_x,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_crossproduct__noteq,axiom, % 164.75/164.94 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 164.75/164.94 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 164.75/164.94 => ( ( V_a_2 != V_b_2 % 164.75/164.94 & V_ca_2 != V_d_2 ) % 164.75/164.94 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__class_Odistrib,axiom, % 164.75/164.94 ! [V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 164.75/164.94 ! [V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 164.75/164.94 ! [V_b,V_m,V_a,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_combine__common__factor,axiom, % 164.75/164.94 ! [V_c,V_b,V_e,V_a,T_a] : % 164.75/164.94 ( class_Rings_Osemiring(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_crossproduct__eq,axiom, % 164.75/164.94 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] : % 164.75/164.94 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 164.75/164.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2)) % 164.75/164.94 <=> ( V_w_2 = V_x_2 % 164.75/164.94 | V_y_2 = V_z_2 ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_minus__mult__right,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Rings_Oring(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_minus__mult__left,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Rings_Oring(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_minus__mult__commute,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Rings_Oring(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_minus__mult__minus,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Rings_Oring(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_square__eq__iff,axiom, % 164.75/164.94 ! [V_b_2,V_a_2,T_a] : % 164.75/164.94 ( class_Rings_Oidom(T_a) % 164.75/164.94 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2) % 164.75/164.94 <=> ( V_a_2 = V_b_2 % 164.75/164.94 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_times_Oidem,axiom, % 164.75/164.94 ! [V_a,T_a] : % 164.75/164.94 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 164.75/164.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_mult__idem,axiom, % 164.75/164.94 ! [V_x,T_a] : % 164.75/164.94 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 164.75/164.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_mult__left__idem,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 164.75/164.94 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 164.75/164.94 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 164.75/164.94 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 164.75/164.94 ! [V_rx,V_ly,V_lx,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 164.75/164.94 ! [V_rx,V_ly,V_lx,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 164.75/164.94 ! [V_ry,V_rx,V_lx,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 164.75/164.94 ! [V_ry,V_rx,V_lx,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 164.75/164.94 ! [V_b,V_a,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 164.75/164.94 ! [V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Groups_Oab__semigroup__mult(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 164.75/164.94 ! [V_a,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 164.75/164.94 ! [V_a,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_mult__1__left,axiom, % 164.75/164.94 ! [V_a,T_a] : % 164.75/164.94 ( class_Groups_Omonoid__mult(T_a) % 164.75/164.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_mult__1,axiom, % 164.75/164.94 ! [V_a,T_a] : % 164.75/164.94 ( class_Groups_Ocomm__monoid__mult(T_a) % 164.75/164.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_mult__1__right,axiom, % 164.75/164.94 ! [V_a,T_a] : % 164.75/164.94 ( class_Groups_Omonoid__mult(T_a) % 164.75/164.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_mult_Ocomm__neutral,axiom, % 164.75/164.94 ! [V_a,T_a] : % 164.75/164.94 ( class_Groups_Ocomm__monoid__mult(T_a) % 164.75/164.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__mult__cancel1,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_k_2] : % 164.75/164.94 ( 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) % 164.75/164.94 <=> V_m_2 = V_n_2 ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__mult__distrib2,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_add__mult__distrib,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_mult__le__mono,axiom, % 164.75/164.94 ! [V_l,V_k,V_j,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 164.75/164.94 => 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))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_mult__le__mono2,axiom, % 164.75/164.94 ! [V_k,V_j,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_mult__le__mono1,axiom, % 164.75/164.94 ! [V_k,V_j,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 164.75/164.94 => 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))) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__cube,axiom, % 164.75/164.94 ! [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)))) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__square,axiom, % 164.75/164.94 ! [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))) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__mult__distrib,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_diff__mult__distrib2,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__mult__eq__1__iff,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 164.75/164.94 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 164.75/164.94 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__mult__1__right,axiom, % 164.75/164.94 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__1__eq__mult__iff,axiom, % 164.75/164.94 ! [V_n_2,V_m_2] : % 164.75/164.94 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 164.75/164.94 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 164.75/164.94 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__mult__1,axiom, % 164.75/164.94 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__1__mult,axiom, % 164.75/164.94 ! [V_n,V_m,T_a] : % 164.75/164.94 ( class_Rings_Olinordered__semidom(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 164.75/164.94 => 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))) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_eq__add__iff2,axiom, % 164.75/164.94 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 164.75/164.94 ( class_Rings_Oring(T_a) % 164.75/164.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) % 164.75/164.94 <=> V_ca_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_eq__add__iff1,axiom, % 164.75/164.94 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 164.75/164.94 ( class_Rings_Oring(T_a) % 164.75/164.94 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) % 164.75/164.94 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2) = V_d_2 ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 164.75/164.94 ! [V_m,V_a,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 164.75/164.94 ! [V_a,V_m,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 164.75/164.94 ! [V_m,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_square__eq__1__iff,axiom, % 164.75/164.94 ! [V_x_2,T_a] : % 164.75/164.94 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 164.75/164.94 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 164.75/164.94 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a) % 164.75/164.94 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 164.75/164.94 ! [V_x,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__ring__1(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_fun__left__comm__idem,axiom, % 164.75/164.94 ! [T_a] : % 164.75/164.94 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 164.75/164.94 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__add__iff1,axiom, % 164.75/164.94 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 164.75/164.94 ( class_Rings_Oordered__ring(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_le__add__iff2,axiom, % 164.75/164.94 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 164.75/164.94 ( class_Rings_Oordered__ring(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__add__iff2,axiom, % 164.75/164.94 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 164.75/164.94 ( class_Rings_Oordered__ring(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_less__add__iff1,axiom, % 164.75/164.94 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 164.75/164.94 ( class_Rings_Oordered__ring(T_a) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_triple__valid__Suc,axiom, % 164.75/164.94 ! [V_t,V_n,T_a] : % 164.75/164.94 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 164.75/164.94 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__mult__less__cancel1,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_k_2] : % 164.75/164.94 ( 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))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_mult__Suc__right,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_mult__Suc,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.75/164.94 fof(fact_Suc__mult__le__cancel1,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_k_2] : % 164.75/164.94 ( 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))) % 164.75/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_fold__graph__insert__swap,axiom, % 164.75/164.94 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] : % 164.75/164.94 ( class_Groups_Oab__semigroup__mult(T_a) % 164.75/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_y_2)) % 164.75/164.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 164.75/164.94 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2),V_y_2))) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_linorder__neqE__linordered__idom,axiom, % 164.75/164.94 ! [V_y,V_x,T_a] : % 164.75/164.94 ( class_Rings_Olinordered__idom(T_a) % 164.75/164.94 => ( V_x != V_y % 164.75/164.94 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.75/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 164.75/164.94 ! [V_d,V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 164.75/164.94 ! [V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 164.75/164.94 ! [V_c,V_b,V_a,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 164.75/164.94 ! [V_d,V_c,V_a,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 164.75/164.94 ! [V_d,V_c,V_a,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 164.75/164.94 ! [V_c,V_a,T_a] : % 164.75/164.94 ( class_Rings_Ocomm__semiring__1(T_a) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_fold__image__distrib,axiom, % 164.75/164.94 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 164.75/164.94 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.75/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_b)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_fold__image__insert,axiom, % 164.75/164.94 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] : % 164.75/164.94 ( class_Groups_Oab__semigroup__mult(T_b) % 164.75/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.75/164.94 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2)) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_comm__monoid__big_Oinfinite,axiom, % 164.75/164.94 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 164.75/164.94 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 164.75/164.94 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.75/164.94 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_fold__graph__permute__diff,axiom, % 164.75/164.94 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] : % 164.75/164.94 ( class_Groups_Oab__semigroup__mult(T_a) % 164.75/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2),V_x_2)) % 164.75/164.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.75/164.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 164.75/164.94 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_fold__image__Un__Int,axiom, % 164.75/164.94 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 164.75/164.94 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.75/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.75/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.75/164.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__less__add__iff1,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 164.75/164.94 => ( 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))) % 164.75/164.94 <=> 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)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__less__add__iff2,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 164.75/164.94 => ( 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))) % 164.75/164.94 <=> 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))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__le__add__iff1,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 164.75/164.94 => ( 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))) % 164.75/164.94 <=> 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)) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__diff__add__eq1,axiom, % 164.75/164.94 ! [V_n,V_m,V_u,V_i,V_j] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 164.75/164.94 => 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) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__eq__add__iff1,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 164.75/164.94 => ( 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) % 164.75/164.94 <=> 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 ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__le__add__iff2,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 164.75/164.94 => ( 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))) % 164.75/164.94 <=> 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))) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__diff__add__eq2,axiom, % 164.75/164.94 ! [V_n,V_m,V_u,V_j,V_i] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 164.75/164.94 => 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)) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__eq__add__iff2,axiom, % 164.75/164.94 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 164.75/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 164.75/164.94 => ( 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) % 164.75/164.94 <=> 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) ) ) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__mult__commute,axiom, % 164.75/164.94 ! [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) ). % 164.75/164.94 % 164.75/164.94 fof(fact_nat__mult__assoc,axiom, % 164.75/164.94 ! [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)) ). % 164.75/164.94 % 164.98/164.94 fof(fact_left__add__mult__distrib,axiom, % 164.98/164.94 ! [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) ). % 164.98/164.94 % 164.98/164.94 fof(fact_fold__image__Un__one,axiom, % 164.98/164.94 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 164.98/164.94 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 164.98/164.94 => ( ! [B_x] : % 164.98/164.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) % 164.98/164.94 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 164.98/164.94 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_T_2)) ) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_compl__unique,axiom, % 164.98/164.94 ! [V_y,V_x,T_a] : % 164.98/164.94 ( class_Lattices_Oboolean__algebra(T_a) % 164.98/164.94 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 164.98/164.94 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 164.98/164.94 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_insert__fold1SetE,axiom, % 164.98/164.94 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] : % 164.98/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2)),V_x_2)) % 164.98/164.94 => ~ ! [B_a,B_A] : % 164.98/164.94 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2)) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_fold1Set_Oequations,axiom, % 164.98/164.94 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] : % 164.98/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2)),V_a3_2)) % 164.98/164.94 <=> ? [B_a,B_A] : % 164.98/164.94 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 164.98/164.94 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2)) % 164.98/164.94 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_fold1__Un,axiom, % 164.98/164.94 ! [V_B_2,V_A_2,T_a] : % 164.98/164.94 ( class_Groups_Oab__semigroup__mult(T_a) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.94 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.94 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_Option_Omap__def,axiom, % 164.98/164.94 ! [V_f_2,T_b,T_a] : hAPP(c_Option_Omap(T_a,T_b),V_f_2) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(T_b),T_a,c_Option_Ooption_ONone(T_b),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 164.98/164.94 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 164.98/164.94 => ( ! [B_x] : % 164.98/164.94 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.98/164.94 => hAPP(V_g_2,B_x) = V_z_2 ) % 164.98/164.94 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_fold1__insert,axiom, % 164.98/164.94 ! [V_x_2,V_A_2,T_a] : % 164.98/164.94 ( class_Groups_Oab__semigroup__mult(T_a) % 164.98/164.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.98/164.94 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_UNIV__I,axiom, % 164.98/164.94 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 164.98/164.94 % 164.98/164.94 fof(fact_top__apply,axiom, % 164.98/164.94 ! [V_x_2,T_b,T_a] : % 164.98/164.94 ( class_Orderings_Otop(T_a) % 164.98/164.94 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_finite__Prod__UNIV,axiom, % 164.98/164.94 ! [T_b,T_a] : % 164.98/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 164.98/164.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_finite__option__UNIV,axiom, % 164.98/164.94 ! [T_a] : % 164.98/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)))) % 164.98/164.94 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_finite__Plus__UNIV__iff,axiom, % 164.98/164.94 ! [T_b,T_a] : % 164.98/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)))) % 164.98/164.94 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 164.98/164.94 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_finite__fun__UNIVD2,axiom, % 164.98/164.94 ! [T_b,T_a] : % 164.98/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))) % 164.98/164.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_UNIV__not__empty,axiom, % 164.98/164.94 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_finite__UNIV,axiom, % 164.98/164.94 ! [T_a] : % 164.98/164.94 ( class_Finite__Set_Ofinite(T_a) % 164.98/164.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_subset__UNIV,axiom, % 164.98/164.94 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 164.98/164.94 % 164.98/164.94 fof(fact_Un__UNIV__left,axiom, % 164.98/164.94 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_Un__UNIV__right,axiom, % 164.98/164.94 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_Int__UNIV__left,axiom, % 164.98/164.94 ! [V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = V_B_2 ). % 164.98/164.94 % 164.98/164.94 fof(fact_Int__UNIV__right,axiom, % 164.98/164.94 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ). % 164.98/164.94 % 164.98/164.94 fof(fact_inj__eq,axiom, % 164.98/164.94 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 164.98/164.94 <=> V_x_2 = V_y_2 ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_injD,axiom, % 164.98/164.94 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 164.98/164.94 => V_x_2 = V_y_2 ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_card__UNIV__unit,axiom, % 164.98/164.94 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) ). % 164.98/164.94 % 164.98/164.94 fof(fact_infinite__UNIV__nat,axiom, % 164.98/164.94 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 164.98/164.94 % 164.98/164.94 fof(fact_option__map__is__None,axiom, % 164.98/164.94 ! [V_opt_2,V_f_2,T_a,T_b] : % 164.98/164.94 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a) % 164.98/164.94 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_option__map__None,axiom, % 164.98/164.94 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),c_Option_Ooption_ONone(T_b)) = c_Option_Ooption_ONone(T_a) ). % 164.98/164.94 % 164.98/164.94 fof(fact_option__map__Some,axiom, % 164.98/164.94 ! [V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = hAPP(c_Option_Ooption_OSome(T_a),hAPP(V_f_2,V_x_2)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_option__map__eq__Some,axiom, % 164.98/164.94 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] : % 164.98/164.94 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_xo_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 164.98/164.94 <=> ? [B_z] : % 164.98/164.94 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z) % 164.98/164.94 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_range__composition,axiom, % 164.98/164.94 ! [V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBB(T_c,T_a,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 164.98/164.94 % 164.98/164.94 fof(fact_inj__fun,axiom, % 164.98/164.94 ! [T_c,V_f_2,T_b,T_a] : % 164.98/164.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_b),T_a),c_COMBK(T_b,T_c)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_top__greatest,axiom, % 164.98/164.94 ! [V_x,T_a] : % 164.98/164.94 ( class_Orderings_Otop(T_a) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_sup__top__right,axiom, % 164.98/164.94 ! [V_x,T_a] : % 164.98/164.94 ( class_Lattices_Obounded__lattice__top(T_a) % 164.98/164.94 => 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) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_sup__top__left,axiom, % 164.98/164.94 ! [V_x,T_a] : % 164.98/164.94 ( class_Lattices_Obounded__lattice__top(T_a) % 164.98/164.94 => 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) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_inf__top__left,axiom, % 164.98/164.94 ! [V_x,T_a] : % 164.98/164.94 ( class_Lattices_Obounded__lattice__top(T_a) % 164.98/164.94 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_inf__top__right,axiom, % 164.98/164.94 ! [V_x,T_a] : % 164.98/164.94 ( class_Lattices_Obounded__lattice__top(T_a) % 164.98/164.94 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_inf__eq__top__iff,axiom, % 164.98/164.94 ! [V_y_2,V_x_2,T_a] : % 164.98/164.94 ( class_Lattices_Obounded__lattice__top(T_a) % 164.98/164.94 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a) % 164.98/164.94 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a) % 164.98/164.94 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_UNIV__option__conv,axiom, % 164.98/164.94 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(c_Set_Oimage(T_a,tc_Option_Ooption(T_a),c_Option_Ooption_OSome(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 164.98/164.94 % 164.98/164.94 fof(fact_dom__option__map,axiom, % 164.98/164.94 ! [V_m_2,V_f_2,T_c,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b)),T_a),c_Option_Omap(T_c,T_b)),V_f_2)),V_m_2)) = c_Map_Odom(T_a,T_c,V_m_2) ). % 164.98/164.94 % 164.98/164.94 fof(fact_range__eqI,axiom, % 164.98/164.94 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] : % 164.98/164.94 ( V_b_2 = hAPP(V_f_2,V_x_2) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_rangeI,axiom, % 164.98/164.94 ! [T_b,V_x_2,V_f_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ). % 164.98/164.94 % 164.98/164.94 fof(fact_Diff__UNIV,axiom, % 164.98/164.94 ! [V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 164.98/164.94 ! [V_A_2,T_a] : % 164.98/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 164.98/164.94 => ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_inj__image__eq__iff,axiom, % 164.98/164.94 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => ( hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2) % 164.98/164.94 <=> V_A_2 = V_B_2 ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_Compl__empty__eq,axiom, % 164.98/164.94 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_Compl__UNIV__eq,axiom, % 164.98/164.94 ! [T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_finite__compl,axiom, % 164.98/164.94 ! [V_A_2,T_a] : % 164.98/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 164.98/164.94 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_Compl__partition,axiom, % 164.98/164.94 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_Compl__partition2,axiom, % 164.98/164.94 ! [V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_Compl__eq__Diff__UNIV,axiom, % 164.98/164.94 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_A_2) ). % 164.98/164.94 % 164.98/164.94 fof(fact_fold1__singleton__def,axiom, % 164.98/164.94 ! [V_a_2,V_f_2,T_a,V_g_2] : % 164.98/164.94 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2) % 164.98/164.94 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_fold1__singleton,axiom, % 164.98/164.94 ! [V_a_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ). % 164.98/164.94 % 164.98/164.94 fof(fact_inj__singleton,axiom, % 164.98/164.94 ! [T_a] : c_Fun_Oinj__on(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ). % 164.98/164.94 % 164.98/164.94 fof(fact_finite__range__imageI,axiom, % 164.98/164.94 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 164.98/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 164.98/164.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,hAPP(hAPP(c_COMBB(T_a,T_c,T_b),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_the__inv__f__f,axiom, % 164.98/164.94 ! [V_x_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_dom__const,axiom, % 164.98/164.94 ! [V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_a),c_Option_Ooption_OSome(T_b)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_folding__one_Oeq__fold,axiom, % 164.98/164.94 ! [V_A_2,V_F_2,V_f_2,T_a] : % 164.98/164.94 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_compl__bot__eq,axiom, % 164.98/164.94 ! [T_a] : % 164.98/164.94 ( class_Lattices_Oboolean__algebra(T_a) % 164.98/164.94 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_compl__top__eq,axiom, % 164.98/164.94 ! [T_a] : % 164.98/164.94 ( class_Lattices_Oboolean__algebra(T_a) % 164.98/164.94 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_sup__compl__top,axiom, % 164.98/164.94 ! [V_x,T_a] : % 164.98/164.94 ( class_Lattices_Oboolean__algebra(T_a) % 164.98/164.94 => 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) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_compl__sup__top,axiom, % 164.98/164.94 ! [V_x,T_a] : % 164.98/164.94 ( class_Lattices_Oboolean__algebra(T_a) % 164.98/164.94 => 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) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_range__ex1__eq,axiom, % 164.98/164.94 ! [V_b_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) % 164.98/164.94 <=> ? [B_x] : % 164.98/164.94 ( V_b_2 = hAPP(V_f_2,B_x) % 164.98/164.94 & ! [B_y] : % 164.98/164.94 ( V_b_2 = hAPP(V_f_2,B_y) % 164.98/164.94 => B_y = B_x ) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_inj__image__mem__iff,axiom, % 164.98/164.94 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 164.98/164.94 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_finite__UNIV__inj__surj,axiom, % 164.98/164.94 ! [V_f_2,T_a] : % 164.98/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 164.98/164.94 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_finite__UNIV__surj__inj,axiom, % 164.98/164.94 ! [V_f_2,T_a] : % 164.98/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 164.98/164.94 => ( hAPP(c_Set_Oimage(T_a,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.94 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_inj__image__subset__iff,axiom, % 164.98/164.94 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2))) % 164.98/164.94 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_image__Int,axiom, % 164.98/164.94 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_image__set__diff,axiom, % 164.98/164.94 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_surj__Compl__image__subset,axiom, % 164.98/164.94 ! [V_A_2,V_f_2,T_a,T_b] : % 164.98/164.94 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_fold1__def,axiom, % 164.98/164.94 ! [V_A_2,V_f_2,T_a] : hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_Sup__fin_OF__eq,axiom, % 164.98/164.94 ! [V_A_2,T_a] : % 164.98/164.94 ( class_Lattices_Olattice(T_a) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_A_2) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_Inf__fin_OF__eq,axiom, % 164.98/164.94 ! [V_A_2,T_a] : % 164.98/164.94 ( class_Lattices_Olattice(T_a) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_finite__range__updI,axiom, % 164.98/164.94 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 164.98/164.94 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),V_f_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_a),V_b_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_inj__image__Compl__subset,axiom, % 164.98/164.94 ! [V_A_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_fold1__belowI,axiom, % 164.98/164.94 ! [V_a_2,V_A_2,T_a] : % 164.98/164.94 ( class_Lattices_Osemilattice__inf(T_a) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2)),V_a_2)) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_below__fold1__iff,axiom, % 164.98/164.94 ! [V_x_2,V_A_2,T_a] : % 164.98/164.94 ( class_Lattices_Osemilattice__inf(T_a) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.94 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_A_2))) % 164.98/164.94 <=> ! [B_x] : % 164.98/164.94 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_fold1__insert__idem,axiom, % 164.98/164.94 ! [V_x_2,V_A_2,T_a] : % 164.98/164.94 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 164.98/164.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_fold1__Un2,axiom, % 164.98/164.94 ! [V_B_2,V_A_2,T_a] : % 164.98/164.94 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.94 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.94 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_B_2)) ) ) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_semilattice__big_OF__eq,axiom, % 164.98/164.94 ! [V_A_2,V_F_2,V_f_2,T_a] : % 164.98/164.94 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_fold1__in,axiom, % 164.98/164.94 ! [V_A_2,T_a] : % 164.98/164.94 ( class_Groups_Oab__semigroup__mult(T_a) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.94 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_A_2)),V_A_2)) ) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_hom__fold1__commute,axiom, % 164.98/164.94 ! [V_N_2,V_h_2,T_a] : % 164.98/164.94 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 164.98/164.94 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 164.98/164.94 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.94 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_inj__vimage__singleton,axiom, % 164.98/164.94 ! [V_a_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_a),c_HOL_OThe(T_a,hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_inj__on__diff__nat,axiom, % 164.98/164.94 ! [V_k_2,V_N_2] : % 164.98/164.94 ( ! [B_x] : % 164.98/164.94 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 164.98/164.94 => 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) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_setsum__diff1,axiom, % 164.98/164.94 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 164.98/164.94 ( class_Groups_Oab__group__add(T_b) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 164.98/164.94 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) ) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_setsum__diff1__ring,axiom, % 164.98/164.94 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 164.98/164.94 ( class_Rings_Oring(T_b) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_setsum__diff1_H,axiom, % 164.98/164.94 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 164.98/164.94 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.94 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_top1I,axiom, % 164.98/164.94 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_vimageI,axiom, % 164.98/164.94 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] : % 164.98/164.94 ( hAPP(V_f_2,V_a_2) = V_b_2 % 164.98/164.94 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2)) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_vimage__ident,axiom, % 164.98/164.94 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 164.98/164.94 % 164.98/164.94 fof(fact_vimage__UNIV,axiom, % 164.98/164.94 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_setsum__commute,axiom, % 164.98/164.94 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 164.98/164.94 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_a),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))),V_A_2)),V_B_2) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_vimage__code,axiom, % 164.98/164.94 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2)) % 164.98/164.94 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_vimageI2,axiom, % 164.98/164.94 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] : % 164.98/164.94 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2)) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_vimageD,axiom, % 164.98/164.94 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] : % 164.98/164.94 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2))) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_vimage__eq,axiom, % 164.98/164.94 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] : % 164.98/164.94 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) % 164.98/164.94 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_vimage__empty,axiom, % 164.98/164.94 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_vimage__mono,axiom, % 164.98/164.94 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 164.98/164.94 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.98/164.94 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_surj__image__vimage__eq,axiom, % 164.98/164.94 ! [V_A_2,V_f_2,T_a,T_b] : % 164.98/164.94 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.94 => hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = V_A_2 ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_vimage__Un,axiom, % 164.98/164.94 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_vimage__Int,axiom, % 164.98/164.94 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_vimage__Diff,axiom, % 164.98/164.94 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_vimage__Compl,axiom, % 164.98/164.94 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2)) ). % 164.98/164.94 % 164.98/164.94 fof(fact_setsum__addf,axiom, % 164.98/164.94 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.94 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_setsum__product,axiom, % 164.98/164.94 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( class_Rings_Osemiring__0(T_a) % 164.98/164.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_a),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_a),tc_fun(tc_fun(T_c,T_a),tc_fun(T_c,T_a)),T_b),c_COMBB(T_a,T_a,T_c)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_setsum__left__distrib,axiom, % 164.98/164.94 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( class_Rings_Osemiring__0(T_a) % 164.98/164.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_r_2)),V_A_2) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_setsum__right__distrib,axiom, % 164.98/164.94 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] : % 164.98/164.94 ( class_Rings_Osemiring__0(T_a) % 164.98/164.94 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r_2)),V_f_2)),V_A_2) ) ). % 164.98/164.94 % 164.98/164.94 fof(fact_setsum__subtractf,axiom, % 164.98/164.94 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 164.98/164.94 ( class_Groups_Oab__group__add(T_a) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),V_A_2)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__negf,axiom, % 164.98/164.95 ! [V_A_2,V_f_2,T_b,T_a] : % 164.98/164.95 ( class_Groups_Oab__group__add(T_a) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_finite__vimageD,axiom, % 164.98/164.95 ! [V_F_2,V_h_2,T_b,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2))) % 164.98/164.95 => ( hAPP(c_Set_Oimage(T_a,T_b,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) % 164.98/164.95 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_image__vimage__subset,axiom, % 164.98/164.95 ! [V_A_2,V_f_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))),V_A_2)) ). % 164.98/164.95 % 164.98/164.95 fof(fact_vimage__subsetD,axiom, % 164.98/164.95 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] : % 164.98/164.95 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2)),V_A_2)) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_image__vimage__eq,axiom, % 164.98/164.95 ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 164.98/164.95 % 164.98/164.95 fof(fact_finite__vimageI,axiom, % 164.98/164.95 ! [V_h_2,T_b,V_F_2,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 164.98/164.95 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 164.98/164.95 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_inj__vimage__image__eq,axiom, % 164.98/164.95 ! [V_A_2,V_f_2,T_b,T_a] : % 164.98/164.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.95 => hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) = V_A_2 ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum_Odistrib,axiom, % 164.98/164.95 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Oplus__class_Oplus(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_h_2),V_A_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_card__eq__setsum,axiom, % 164.98/164.95 ! [V_A_2,T_a] : hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ). % 164.98/164.95 % 164.98/164.95 fof(fact_vimage__const,axiom, % 164.98/164.95 ! [T_b,V_A_2,V_ca_2,T_a] : % 164.98/164.95 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.98/164.95 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 164.98/164.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.98/164.95 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_vimage__singleton__eq,axiom, % 164.98/164.95 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 164.98/164.95 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_vimage__insert,axiom, % 164.98/164.95 ! [V_B_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)) ). % 164.98/164.95 % 164.98/164.95 fof(fact_vimage__subsetI,axiom, % 164.98/164.95 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 164.98/164.95 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2)),V_A_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_vimage__if,axiom, % 164.98/164.95 ! [V_B_2,T_b,V_d_2,V_A_2,V_ca_2,T_a] : % 164.98/164.95 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.98/164.95 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 164.98/164.95 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 164.98/164.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 164.98/164.95 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 164.98/164.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 164.98/164.95 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 164.98/164.95 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) ) % 164.98/164.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 164.98/164.95 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__insert,axiom, % 164.98/164.95 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 164.98/164.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_F_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum_Oinsert,axiom, % 164.98/164.95 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__Un__Int,axiom, % 164.98/164.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__diff,axiom, % 164.98/164.95 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Oab__group__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__diff__nat,axiom, % 164.98/164.95 ! [V_f_2,V_A_2,V_B_2,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum_Oinsert__remove,axiom, % 164.98/164.95 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__Un__disjoint,axiom, % 164.98/164.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__Un,axiom, % 164.98/164.95 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Oab__group__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__diff1__nat,axiom, % 164.98/164.95 ! [V_f_2,V_A_2,V_a_2,T_a] : % 164.98/164.95 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 164.98/164.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__Un__nat,axiom, % 164.98/164.95 ! [V_f_2,V_B_2,V_A_2,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum_Oremove,axiom, % 164.98/164.95 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_finite__fun__UNIVD1,axiom, % 164.98/164.95 ! [T_b,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))) % 164.98/164.95 => ( hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 164.98/164.95 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_iso__tuple__UNIV__I,axiom, % 164.98/164.95 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__strict__mono,axiom, % 164.98/164.95 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) ) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.95 => ( ! [B_x] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2))) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_finite__range__map__of__map__add,axiom, % 164.98/164.95 ! [V_l_2,V_f_2,T_b,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) % 164.98/164.95 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),c_Map_Omap__add(T_b,T_a,V_f_2,hAPP(c_Map_Omap__of(T_b,T_a),V_l_2))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 164.98/164.95 ! [V_n_2,V_m_2] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 164.98/164.95 <=> 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)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_finite__map__freshness,axiom, % 164.98/164.95 ! [V_f_2,T_b,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2))) % 164.98/164.95 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 164.98/164.95 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod_Oremove,axiom, % 164.98/164.95 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_less__zeroE,axiom, % 164.98/164.95 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 164.98/164.95 % 164.98/164.95 fof(fact_le0,axiom, % 164.98/164.95 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zero__less__Suc,axiom, % 164.98/164.95 ! [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))) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__zero__iff,axiom, % 164.98/164.95 ! [V_f_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( ( class_Rings_Ocomm__semiring__1(T_b) % 164.98/164.95 & class_Rings_Ono__zero__divisors(T_b) ) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) % 164.98/164.95 <=> ? [B_x] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.98/164.95 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__zero,axiom, % 164.98/164.95 ! [V_f_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Rings_Ocomm__semiring__1(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( ? [B_x] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.98/164.95 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zero__reorient,axiom, % 164.98/164.95 ! [V_x_2,T_a] : % 164.98/164.95 ( class_Groups_Ozero(T_a) % 164.98/164.95 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 164.98/164.95 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_nat__case__0,axiom, % 164.98/164.95 ! [V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 164.98/164.95 % 164.98/164.95 fof(fact_bot__nat__def,axiom, % 164.98/164.95 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__pos__nat__iff,axiom, % 164.98/164.95 ! [V_f_2,V_S_2,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_S_2))) % 164.98/164.95 <=> ! [B_x] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__0__iff,axiom, % 164.98/164.95 ! [V_a_2,V_b_2,T_a] : % 164.98/164.95 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 164.98/164.95 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) % 164.98/164.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__0__left,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Groups_Omonoid__add(T_a) % 164.98/164.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__0,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_double__zero__sym,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Olinordered__ab__group__add(T_a) % 164.98/164.95 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) % 164.98/164.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__0__right,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Groups_Omonoid__add(T_a) % 164.98/164.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add_Ocomm__neutral,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_divisors__zero,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Ono__zero__divisors(T_a) % 164.98/164.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_no__zero__divisors,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Ono__zero__divisors(T_a) % 164.98/164.95 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__eq__0__iff,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,T_a] : % 164.98/164.95 ( class_Rings_Oring__no__zero__divisors(T_a) % 164.98/164.95 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.95 => 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) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__zero__right,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Rings_Omult__zero(T_a) % 164.98/164.95 => 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) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.95 => 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) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__zero__left,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Rings_Omult__zero(T_a) % 164.98/164.95 => 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) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_right__minus__eq,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Ogroup__add(T_a) % 164.98/164.95 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 <=> V_a_2 = V_b_2 ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_eq__iff__diff__eq__0,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Oab__group__add(T_a) % 164.98/164.95 => ( V_a_2 = V_b_2 % 164.98/164.95 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_diff__self,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Groups_Ogroup__add(T_a) % 164.98/164.95 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_diff__0__right,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Groups_Ogroup__add(T_a) % 164.98/164.95 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_one__neq__zero,axiom, % 164.98/164.95 ! [T_a] : % 164.98/164.95 ( class_Rings_Ozero__neq__one(T_a) % 164.98/164.95 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zero__neq__one,axiom, % 164.98/164.95 ! [T_a] : % 164.98/164.95 ( class_Rings_Ozero__neq__one(T_a) % 164.98/164.95 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_minus__zero,axiom, % 164.98/164.95 ! [T_a] : % 164.98/164.95 ( class_Groups_Ogroup__add(T_a) % 164.98/164.95 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_neg__0__equal__iff__equal,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Ogroup__add(T_a) % 164.98/164.95 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 164.98/164.95 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_equal__neg__zero,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Olinordered__ab__group__add(T_a) % 164.98/164.95 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 164.98/164.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_neg__equal__0__iff__equal,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Ogroup__add(T_a) % 164.98/164.95 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_neg__equal__zero,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Olinordered__ab__group__add(T_a) % 164.98/164.95 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2 % 164.98/164.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__eq__0__iff,axiom, % 164.98/164.95 ! [V_f_2,V_F_2,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 164.98/164.95 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 <=> ! [B_x] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 164.98/164.95 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_Zero__not__Suc,axiom, % 164.98/164.95 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 164.98/164.95 % 164.98/164.95 fof(fact_nat_Osimps_I2_J,axiom, % 164.98/164.95 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 164.98/164.95 % 164.98/164.95 fof(fact_Suc__not__Zero,axiom, % 164.98/164.95 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.95 % 164.98/164.95 fof(fact_nat_Osimps_I3_J,axiom, % 164.98/164.95 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.95 % 164.98/164.95 fof(fact_Zero__neq__Suc,axiom, % 164.98/164.95 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 164.98/164.95 % 164.98/164.95 fof(fact_Suc__neq__Zero,axiom, % 164.98/164.95 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.95 % 164.98/164.95 fof(fact_gr0I,axiom, % 164.98/164.95 ! [V_n] : % 164.98/164.95 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_gr__implies__not0,axiom, % 164.98/164.95 ! [V_n,V_m] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.98/164.95 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_less__nat__zero__code,axiom, % 164.98/164.95 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 164.98/164.95 % 164.98/164.95 fof(fact_neq0__conv,axiom, % 164.98/164.95 ! [V_n_2] : % 164.98/164.95 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_not__less0,axiom, % 164.98/164.95 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 164.98/164.95 % 164.98/164.95 fof(fact_plus__nat_Oadd__0,axiom, % 164.98/164.95 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 164.98/164.95 % 164.98/164.95 fof(fact_Nat_Oadd__0__right,axiom, % 164.98/164.95 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__is__0,axiom, % 164.98/164.95 ! [V_n_2,V_m_2] : % 164.98/164.95 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__eq__self__zero,axiom, % 164.98/164.95 ! [V_n,V_m] : % 164.98/164.95 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 164.98/164.95 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_le__0__eq,axiom, % 164.98/164.95 ! [V_n_2] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 164.98/164.95 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 164.98/164.95 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__timesf,axiom, % 164.98/164.95 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_a) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),V_A_2)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_diffs0__imp__equal,axiom, % 164.98/164.95 ! [V_n,V_m] : % 164.98/164.95 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 => V_m = V_n ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_diff__self__eq__0,axiom, % 164.98/164.95 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.95 % 164.98/164.95 fof(fact_minus__nat_Odiff__0,axiom, % 164.98/164.95 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 164.98/164.95 % 164.98/164.95 fof(fact_diff__0__eq__0,axiom, % 164.98/164.95 ! [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) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__cancel2,axiom, % 164.98/164.95 ! [V_n_2,V_k_2,V_m_2] : % 164.98/164.95 ( 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) % 164.98/164.95 <=> ( V_m_2 = V_n_2 % 164.98/164.95 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__cancel1,axiom, % 164.98/164.95 ! [V_n_2,V_m_2,V_k_2] : % 164.98/164.95 ( 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) % 164.98/164.95 <=> ( V_m_2 = V_n_2 % 164.98/164.95 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__is__0,axiom, % 164.98/164.95 ! [V_n_2,V_m_2] : % 164.98/164.95 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__0__right,axiom, % 164.98/164.95 ! [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) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__0,axiom, % 164.98/164.95 ! [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) ). % 164.98/164.95 % 164.98/164.95 fof(fact_nat__mult__eq__cancel__disj,axiom, % 164.98/164.95 ! [V_n_2,V_m_2,V_k_2] : % 164.98/164.95 ( 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) % 164.98/164.95 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 | V_m_2 = V_n_2 ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__1,axiom, % 164.98/164.95 ! [V_A_2,T_b,T_a] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_a) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Oone__class_Oone(T_a))),V_A_2) = c_Groups_Oone__class_Oone(T_a) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__0,axiom, % 164.98/164.95 ! [V_A_2,T_b,T_a] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_A_2) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod_Oempty,axiom, % 164.98/164.95 ! [V_g_2,T_b,T_a] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_a) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__empty,axiom, % 164.98/164.95 ! [V_f_2,T_b,T_a] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_a) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_a) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__infinite,axiom, % 164.98/164.95 ! [V_f_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod_Oinfinite,axiom, % 164.98/164.95 ! [V_g_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__eq__1__iff,axiom, % 164.98/164.95 ! [V_f_2,V_F_2,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 164.98/164.95 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 164.98/164.95 <=> ! [B_x] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 164.98/164.95 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod_Odistrib,axiom, % 164.98/164.95 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Groups_Otimes__class_Otimes(T_b)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_h_2),V_A_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__nonpos__nonpos,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__increasing2,axiom, % 164.98/164.95 ! [V_a,V_b,V_c,T_a] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__increasing,axiom, % 164.98/164.95 ! [V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__nonneg__eq__0__iff,axiom, % 164.98/164.95 ! [V_y_2,V_x_2,T_a] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 164.98/164.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__nonneg__nonneg,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Olinordered__ab__group__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Olinordered__ab__group__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zero__le__square,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring(T_a) % 164.98/164.95 => 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))) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zero__le__mult__iff,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))) % 164.98/164.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 164.98/164.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__le__0__iff,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 164.98/164.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__nonneg__nonneg,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Oordered__cancel__semiring(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__nonneg__nonpos,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Oordered__cancel__semiring(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__nonneg__nonpos2,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Oordered__cancel__semiring(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__nonpos__nonneg,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Oordered__cancel__semiring(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__nonpos__nonpos,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Oordered__ring(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__right__mono,axiom, % 164.98/164.95 ! [V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Oordered__semiring(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__left__mono,axiom, % 164.98/164.95 ! [V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Oordered__semiring(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__mult__left__mono,axiom, % 164.98/164.95 ! [V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Oordered__comm__semiring(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__right__mono__neg,axiom, % 164.98/164.95 ! [V_c,V_a,V_b,T_a] : % 164.98/164.95 ( class_Rings_Oordered__ring(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__left__mono__neg,axiom, % 164.98/164.95 ! [V_c,V_a,V_b,T_a] : % 164.98/164.95 ( class_Rings_Oordered__ring(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__mono_H,axiom, % 164.98/164.95 ! [V_d,V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Oordered__semiring(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => 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))) ) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__mono,axiom, % 164.98/164.95 ! [V_d,V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Oordered__semiring(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => 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))) ) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_split__mult__pos__le,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Oordered__ring(T_a) % 164.98/164.95 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 164.98/164.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 164.98/164.95 => 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))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_split__mult__neg__le,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Oordered__cancel__semiring(T_a) % 164.98/164.95 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 164.98/164.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 164.98/164.95 => 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))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_pos__add__strict,axiom, % 164.98/164.95 ! [V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Olinordered__ab__group__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Olinordered__ab__group__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__pos__pos,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__neg__neg,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_not__square__less__zero,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring(T_a) % 164.98/164.95 => ~ 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))) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__less__cancel__right__disj,axiom, % 164.98/164.95 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))) % 164.98/164.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 164.98/164.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__less__cancel__left__disj,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 164.98/164.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 164.98/164.95 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__less__cancel__left__pos,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__pos__pos,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__pos__neg,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__pos__neg2,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zero__less__mult__pos,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( 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))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zero__less__mult__pos2,axiom, % 164.98/164.95 ! [V_a,V_b,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( 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))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__less__cancel__left__neg,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__neg__pos,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__neg__neg,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__strict__right__mono,axiom, % 164.98/164.95 ! [V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__strict__left__mono,axiom, % 164.98/164.95 ! [V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__mult__strict__left__mono,axiom, % 164.98/164.95 ! [V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__strict__right__mono__neg,axiom, % 164.98/164.95 ! [V_c,V_a,V_b,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__strict__left__mono__neg,axiom, % 164.98/164.95 ! [V_c,V_a,V_b,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_le__iff__diff__le__0,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_less__iff__diff__less__0,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_sum__squares__eq__zero__iff,axiom, % 164.98/164.95 ! [V_y_2,V_x_2,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__scale__eq__noteq,axiom, % 164.98/164.95 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 164.98/164.95 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 164.98/164.95 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 => ( ( V_a = V_b % 164.98/164.95 & V_c != V_d ) % 164.98/164.95 => 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)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zero__le__one,axiom, % 164.98/164.95 ! [T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.95 => 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))) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_not__one__le__zero,axiom, % 164.98/164.95 ! [T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.95 => ~ 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))) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_not__one__less__zero,axiom, % 164.98/164.95 ! [T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.95 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zero__less__one,axiom, % 164.98/164.95 ! [T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_neg__0__le__iff__le,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_le__minus__self__iff,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Olinordered__ab__group__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_neg__le__0__iff__le,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_minus__le__self__iff,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Olinordered__ab__group__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_less__minus__self__iff,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_neg__0__less__iff__less,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_neg__less__0__iff__less,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_neg__less__nonneg,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Olinordered__ab__group__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_right__minus,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Groups_Ogroup__add(T_a) % 164.98/164.95 => 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) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_eq__neg__iff__add__eq__0,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Ogroup__add(T_a) % 164.98/164.95 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 164.98/164.95 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_left__minus,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Groups_Ogroup__add(T_a) % 164.98/164.95 => 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) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_ab__left__minus,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Groups_Oab__group__add(T_a) % 164.98/164.95 => 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) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_minus__unique,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Groups_Ogroup__add(T_a) % 164.98/164.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_diff__0,axiom, % 164.98/164.95 ! [V_a,T_a] : % 164.98/164.95 ( class_Groups_Ogroup__add(T_a) % 164.98/164.95 => 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) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum_Oempty,axiom, % 164.98/164.95 ! [V_g_2,T_b,T_a] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__empty,axiom, % 164.98/164.95 ! [V_f_2,T_b,T_a] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum_Oinfinite,axiom, % 164.98/164.95 ! [V_g_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__infinite,axiom, % 164.98/164.95 ! [V_f_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__eq__Suc0__iff,axiom, % 164.98/164.95 ! [V_f_2,V_A_2,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 164.98/164.95 <=> ? [B_x] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.98/164.95 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 164.98/164.95 & ! [B_xa] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 164.98/164.95 => ( B_x != B_xa % 164.98/164.95 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_less__Suc__eq__0__disj,axiom, % 164.98/164.95 ! [V_n_2,V_m_2] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 164.98/164.95 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 | ? [B_j] : % 164.98/164.95 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_less__Suc0,axiom, % 164.98/164.95 ! [V_n_2] : % 164.98/164.95 ( 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)))) % 164.98/164.95 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_gr0__conv__Suc,axiom, % 164.98/164.95 ! [V_n_2] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 164.98/164.95 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_one__is__add,axiom, % 164.98/164.95 ! [V_n_2,V_m_2] : % 164.98/164.95 ( 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) % 164.98/164.95 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 164.98/164.95 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 164.98/164.95 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__is__1,axiom, % 164.98/164.95 ! [V_n_2,V_m_2] : % 164.98/164.95 ( 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)) % 164.98/164.95 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 164.98/164.95 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 164.98/164.95 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_finite__dom__map__of,axiom, % 164.98/164.95 ! [V_l_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_l_2)))) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__gr__0,axiom, % 164.98/164.95 ! [V_n_2,V_m_2] : % 164.98/164.95 ( 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))) % 164.98/164.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 164.98/164.95 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_card_Oempty,axiom, % 164.98/164.95 ! [T_a] : hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.95 % 164.98/164.95 fof(fact_card__infinite,axiom, % 164.98/164.95 ! [V_A_2,T_a] : % 164.98/164.95 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__eq__1__iff,axiom, % 164.98/164.95 ! [V_n_2,V_m_2] : % 164.98/164.95 ( 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)) % 164.98/164.95 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 164.98/164.95 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zero__less__diff,axiom, % 164.98/164.95 ! [V_m_2,V_n_2] : % 164.98/164.95 ( 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))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_diff__less,axiom, % 164.98/164.95 ! [V_m,V_n] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 164.98/164.95 => 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)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__less__mono2,axiom, % 164.98/164.95 ! [V_k,V_j,V_i] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 164.98/164.95 => 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))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__less__mono1,axiom, % 164.98/164.95 ! [V_k,V_j,V_i] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 164.98/164.95 => 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))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__less__cancel2,axiom, % 164.98/164.95 ! [V_n_2,V_k_2,V_m_2] : % 164.98/164.95 ( 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))) % 164.98/164.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__less__cancel1,axiom, % 164.98/164.95 ! [V_n_2,V_m_2,V_k_2] : % 164.98/164.95 ( 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))) % 164.98/164.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_nat__0__less__mult__iff,axiom, % 164.98/164.95 ! [V_n_2,V_m_2] : % 164.98/164.95 ( 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))) % 164.98/164.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 164.98/164.95 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_nat__mult__less__cancel1,axiom, % 164.98/164.95 ! [V_n_2,V_m_2,V_k_2] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 164.98/164.95 => ( 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))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_nat__mult__eq__cancel1,axiom, % 164.98/164.95 ! [V_n_2,V_m_2,V_k_2] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 164.98/164.95 => ( 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) % 164.98/164.95 <=> V_m_2 = V_n_2 ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_diff__add__0,axiom, % 164.98/164.95 ! [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) ). % 164.98/164.95 % 164.98/164.95 fof(fact_diff__is__0__eq_H,axiom, % 164.98/164.95 ! [V_n,V_m] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 164.98/164.95 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_diff__is__0__eq,axiom, % 164.98/164.95 ! [V_n_2,V_m_2] : % 164.98/164.95 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__eq__1__iff,axiom, % 164.98/164.95 ! [V_f_2,V_A_2,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 164.98/164.95 <=> ? [B_x] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.98/164.95 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 164.98/164.95 & ! [B_xa] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 164.98/164.95 => ( B_x != B_xa % 164.98/164.95 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_One__nat__def,axiom, % 164.98/164.95 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__eq__self__implies__10,axiom, % 164.98/164.95 ! [V_n,V_m] : % 164.98/164.95 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 164.98/164.95 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 164.98/164.95 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_nat__case__Suc,axiom, % 164.98/164.95 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__delta,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 164.98/164.95 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 164.98/164.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__delta_H,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 164.98/164.95 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 164.98/164.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_b))),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__nonpos__neg,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__neg__nonpos,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__strict__increasing2,axiom, % 164.98/164.95 ! [V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__strict__increasing,axiom, % 164.98/164.95 ! [V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__nonneg__pos,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__pos__nonneg,axiom, % 164.98/164.95 ! [V_b,V_a,T_a] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.95 => 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))) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__left__le__imp__le,axiom, % 164.98/164.95 ! [V_b,V_a,V_c,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( 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))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__right__le__imp__le,axiom, % 164.98/164.95 ! [V_b,V_c,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( 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))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__less__imp__less__left,axiom, % 164.98/164.95 ! [V_b,V_a,V_c,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( 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))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__left__less__imp__less,axiom, % 164.98/164.95 ! [V_b,V_a,V_c,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring(T_a) % 164.98/164.95 => ( 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))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__less__imp__less__right,axiom, % 164.98/164.95 ! [V_b,V_c,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( 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))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__right__less__imp__less,axiom, % 164.98/164.95 ! [V_b,V_c,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring(T_a) % 164.98/164.95 => ( 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))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__le__less__imp__less,axiom, % 164.98/164.95 ! [V_d,V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => 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))) ) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__less__le__imp__less,axiom, % 164.98/164.95 ! [V_d,V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => 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))) ) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__strict__mono_H,axiom, % 164.98/164.95 ! [V_d,V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => 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))) ) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__strict__mono,axiom, % 164.98/164.95 ! [V_d,V_c,V_b,V_a,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.95 => 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))) ) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__le__cancel__left__neg,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__le__cancel__left__pos,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_sum__squares__ge__zero,axiom, % 164.98/164.95 ! [V_y,V_x,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring(T_a) % 164.98/164.95 => 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)))) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_sum__squares__le__zero__iff,axiom, % 164.98/164.95 ! [V_y_2,V_x_2,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_not__sum__squares__lt__zero,axiom, % 164.98/164.95 ! [V_y,V_x,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring(T_a) % 164.98/164.95 => ~ 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))) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_sum__squares__gt__zero__iff,axiom, % 164.98/164.95 ! [V_y_2,V_x_2,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__ring__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))) % 164.98/164.95 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__left__le__one__le,axiom, % 164.98/164.95 ! [V_y,V_x,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 164.98/164.95 => 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)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__right__le__one__le,axiom, % 164.98/164.95 ! [V_y,V_x,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 164.98/164.95 => 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)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zero__less__two,axiom, % 164.98/164.95 ! [T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.95 => 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)))) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_card__eq__0__iff,axiom, % 164.98/164.95 ! [V_A_2,T_a] : % 164.98/164.95 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.95 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_card__ge__0__finite,axiom, % 164.98/164.95 ! [V_A_2,T_a] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) % 164.98/164.95 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_diff__Suc__less,axiom, % 164.98/164.95 ! [V_i,V_n] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.95 => 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)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_Suc__pred,axiom, % 164.98/164.95 ! [V_n] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.95 => 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 ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_one__less__mult,axiom, % 164.98/164.95 ! [V_m,V_n] : % 164.98/164.95 ( 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)) % 164.98/164.95 => ( 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)) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_n__less__n__mult__m,axiom, % 164.98/164.95 ! [V_m,V_n] : % 164.98/164.95 ( 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)) % 164.98/164.95 => ( 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)) % 164.98/164.95 => 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))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_n__less__m__mult__n,axiom, % 164.98/164.95 ! [V_m,V_n] : % 164.98/164.95 ( 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)) % 164.98/164.95 => ( 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)) % 164.98/164.95 => 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))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_nat__diff__split,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,V_P_2] : % 164.98/164.95 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 164.98/164.95 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 164.98/164.95 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 164.98/164.95 & ! [B_d] : % 164.98/164.95 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 164.98/164.95 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_nat__diff__split__asm,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,V_P_2] : % 164.98/164.95 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 164.98/164.95 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 164.98/164.95 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 164.98/164.95 | ? [B_d] : % 164.98/164.95 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 164.98/164.95 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_one__le__mult__iff,axiom, % 164.98/164.95 ! [V_n_2,V_m_2] : % 164.98/164.95 ( 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))) % 164.98/164.95 <=> ( 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)) % 164.98/164.95 & 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)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__le__cancel1,axiom, % 164.98/164.95 ! [V_n_2,V_m_2,V_k_2] : % 164.98/164.95 ( 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))) % 164.98/164.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__le__cancel2,axiom, % 164.98/164.95 ! [V_n_2,V_k_2,V_m_2] : % 164.98/164.95 ( 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))) % 164.98/164.95 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_nat__mult__le__cancel1,axiom, % 164.98/164.95 ! [V_n_2,V_m_2,V_k_2] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 164.98/164.95 => ( 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))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__insert,axiom, % 164.98/164.95 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod_Oinsert,axiom, % 164.98/164.95 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod_Ounion__inter,axiom, % 164.98/164.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__Un__Int,axiom, % 164.98/164.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__delta,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 164.98/164.95 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 164.98/164.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__delta_H,axiom, % 164.98/164.95 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 164.98/164.95 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = hAPP(V_b_2,V_a_2) ) % 164.98/164.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))),V_S_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod_OF__eq,axiom, % 164.98/164.95 ! [V_g_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) ) % 164.98/164.95 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod_Oeq__fold,axiom, % 164.98/164.95 ! [V_g_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),c_Groups_Oone__class_Oone(T_b)),V_A_2) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_Body__triple__valid__0,axiom, % 164.98/164.95 ! [V_Q_2,V_pn_2,V_P_2,T_a] : c_Hoare__Mirabelle_Otriple__valid(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ). % 164.98/164.95 % 164.98/164.95 fof(fact_finite__range__map__of,axiom, % 164.98/164.95 ! [V_xys_2,T_b,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_a)),hAPP(c_Set_Oimage(T_b,tc_Option_Ooption(T_a),hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ). % 164.98/164.95 % 164.98/164.95 fof(fact_convex__bound__le,axiom, % 164.98/164.95 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__1(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 164.98/164.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 164.98/164.95 => 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)) ) ) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod_Oinsert__remove,axiom, % 164.98/164.95 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__Un__disjoint,axiom, % 164.98/164.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod_Ounion__disjoint,axiom, % 164.98/164.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_card__gt__0__iff,axiom, % 164.98/164.95 ! [V_A_2,T_a] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))) % 164.98/164.95 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.95 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_finite__UNIV__card__ge__0,axiom, % 164.98/164.95 ! [T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum_Oeq__fold,axiom, % 164.98/164.95 ! [V_g_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum_OF__eq,axiom, % 164.98/164.95 ! [V_g_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Oplus__class_Oplus(T_b)),V_g_2),c_Groups_Ozero__class_Ozero(T_b)),V_A_2) ) % 164.98/164.95 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_Suc__pred_H,axiom, % 164.98/164.95 ! [V_n] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.95 => 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))) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_Suc__diff__1,axiom, % 164.98/164.95 ! [V_n] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.95 => 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 ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_add__eq__if,axiom, % 164.98/164.95 ! [V_n,V_m] : % 164.98/164.95 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 164.98/164.95 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 => 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)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_mult__eq__if,axiom, % 164.98/164.95 ! [V_n,V_m] : % 164.98/164.95 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 164.98/164.95 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 => 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)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__restrict__set,axiom, % 164.98/164.95 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_card_Oeq__fold__g,axiom, % 164.98/164.95 ! [V_A_2,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_card__def,axiom, % 164.98/164.95 ! [V_A_2,T_a] : % 164.98/164.95 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) % 164.98/164.95 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_convex__bound__lt,axiom, % 164.98/164.95 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 164.98/164.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 164.98/164.95 => 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)) ) ) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_triple_Osize_I1_J,axiom, % 164.98/164.95 ! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_a] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_a,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.95 % 164.98/164.95 fof(fact_even__less__0__iff,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_triple_Osize_I2_J,axiom, % 164.98/164.95 ! [V_fun2_2,V_com_2,V_fun1_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.95 % 164.98/164.95 fof(fact_card_Ounion__inter__neutral,axiom, % 164.98/164.95 ! [V_B_2,V_A_2,T_a] : % 164.98/164.95 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.98/164.95 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 164.98/164.95 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_a),V_B_2)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__mono2,axiom, % 164.98/164.95 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Oordered__comm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.98/164.95 => ( ! [B_b] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) ) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__Un__one,axiom, % 164.98/164.95 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 164.98/164.95 => ( ! [B_x] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) % 164.98/164.95 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod_Ounion__inter__neutral,axiom, % 164.98/164.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => ( ! [B_x] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.98/164.95 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_diff__Suc,axiom, % 164.98/164.95 ! [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)) ). % 164.98/164.95 % 164.98/164.95 fof(fact_double__eq__0__iff,axiom, % 164.98/164.95 ! [V_a_2,T_a] : % 164.98/164.95 ( class_Groups_Olinordered__ab__group__add(T_a) % 164.98/164.95 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.95 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_arith__series__nat,axiom, % 164.98/164.95 ! [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)))) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum_Ounion__inter__neutral,axiom, % 164.98/164.95 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => ( ! [B_x] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.98/164.95 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_B_2)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__Un__zero,axiom, % 164.98/164.95 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 164.98/164.95 => ( ! [B_x] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) % 164.98/164.95 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_card__Suc__eq,axiom, % 164.98/164.95 ! [V_k_2,V_A_2,T_a] : % 164.98/164.95 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 164.98/164.95 <=> ? [B_b,B_B] : % 164.98/164.95 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) % 164.98/164.95 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B)) % 164.98/164.95 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2 % 164.98/164.95 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.95 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__mono3,axiom, % 164.98/164.95 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 164.98/164.95 ( ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.95 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.98/164.95 => ( ! [B_x] : % 164.98/164.95 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2))) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 164.98/164.95 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2))) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__gen__delta,axiom, % 164.98/164.95 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 164.98/164.95 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 164.98/164.95 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ca_2),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)) ) ) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_option_Osize_I2_J,axiom, % 164.98/164.95 ! [V_a_2,V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,hAPP(c_Option_Ooption_OSome(T_a),V_a_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 164.98/164.95 % 164.98/164.95 fof(fact_finite__lessThan,axiom, % 164.98/164.95 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 164.98/164.95 % 164.98/164.95 fof(fact_card__lessThan,axiom, % 164.98/164.95 ! [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 ). % 164.98/164.95 % 164.98/164.95 fof(fact_lessThan__eq__iff,axiom, % 164.98/164.95 ! [V_y_2,V_x_2,T_a] : % 164.98/164.95 ( class_Orderings_Olinorder(T_a) % 164.98/164.95 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2) % 164.98/164.95 <=> V_x_2 = V_y_2 ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 164.98/164.95 ! [V_q,V_y,V_x,T_a] : % 164.98/164.95 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zpower__zadd__distrib,axiom, % 164.98/164.95 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 164.98/164.95 ! [V_q,V_p,V_x,T_a] : % 164.98/164.95 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_zpower__zpower,axiom, % 164.98/164.95 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 164.98/164.95 ! [V_x,T_a] : % 164.98/164.95 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_lessThan__0,axiom, % 164.98/164.95 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)) ). % 164.98/164.95 % 164.98/164.95 fof(fact_lessThan__Suc,axiom, % 164.98/164.95 ! [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)) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 164.98/164.95 ! [V_q,V_x,T_a] : % 164.98/164.95 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 164.98/164.95 ! [V_q,V_x,T_a] : % 164.98/164.95 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 164.98/164.95 ! [V_q,V_x,T_a] : % 164.98/164.95 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 164.98/164.95 ! [V_x,T_a] : % 164.98/164.95 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.95 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 164.98/164.95 ! [V_q,V_p,V_x,T_a] : % 164.98/164.95 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.95 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 164.98/164.95 ! [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))) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setsum__lessThan__Suc,axiom, % 164.98/164.95 ! [V_n_2,V_f_2,T_a] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_lessThan__iff,axiom, % 164.98/164.95 ! [V_k_2,V_i_2,T_a] : % 164.98/164.95 ( class_Orderings_Oord(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_lessThan__subset__iff,axiom, % 164.98/164.95 ! [V_y_2,V_x_2,T_a] : % 164.98/164.95 ( class_Orderings_Olinorder(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_lessThan__strict__subset__iff,axiom, % 164.98/164.95 ! [V_n_2,V_m_2,T_a] : % 164.98/164.95 ( class_Orderings_Olinorder(T_a) % 164.98/164.95 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_n_2))) % 164.98/164.95 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ). % 164.98/164.95 % 164.98/164.95 fof(fact_setprod__constant,axiom, % 164.98/164.95 ! [V_y_2,V_A_2,T_a,T_b] : % 164.98/164.95 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.95 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.95 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_COMBK(T_b,T_a),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ) ). % 164.98/164.95 % 164.98/164.96 fof(fact_option_Osize_I1_J,axiom, % 164.98/164.96 ! [V_fa_2,T_a] : c_Option_Ooption_Ooption__size(T_a,V_fa_2,c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__eq__if,axiom, % 164.98/164.96 ! [V_p,V_m] : % 164.98/164.96 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 164.98/164.96 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.96 => 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)))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_single__Diff__lessThan,axiom, % 164.98/164.96 ! [V_k_2,T_a] : % 164.98/164.96 ( class_Orderings_Oorder(T_a) % 164.98/164.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__strict__mono,axiom, % 164.98/164.96 ! [V_n,V_b,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_one__less__power,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__le__imp__le__exp,axiom, % 164.98/164.96 ! [V_n,V_m,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 164.98/164.96 => ( 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))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__increasing__iff,axiom, % 164.98/164.96 ! [V_y_2,V_x_2,V_b_2,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__decreasing,axiom, % 164.98/164.96 ! [V_a,V_N,V_n,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__strict__decreasing,axiom, % 164.98/164.96 ! [V_a,V_N,V_n,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zadd__zmult__distrib2,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zadd__zmult__distrib,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiff__zmult__distrib2,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiff__zmult__distrib,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zmult__assoc,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zmult__commute,axiom, % 164.98/164.96 ! [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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zmult__zminus,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zmult__1__right,axiom, % 164.98/164.96 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 164.98/164.96 % 164.98/164.96 fof(fact_zmult__1,axiom, % 164.98/164.96 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 164.98/164.96 % 164.98/164.96 fof(fact_pos__zmult__eq__1__iff,axiom, % 164.98/164.96 ! [V_n_2,V_m_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 164.98/164.96 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 164.98/164.96 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 164.98/164.96 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zmult__zless__mono2,axiom, % 164.98/164.96 ! [V_k,V_j,V_i] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 164.98/164.96 => 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))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_field__power__not__zero,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 164.98/164.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 164.98/164.96 ! [V_m_2,V_x_2] : % 164.98/164.96 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 164.98/164.96 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.96 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__Suc__0,axiom, % 164.98/164.96 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nat__power__less__imp__less,axiom, % 164.98/164.96 ! [V_n,V_m,V_i] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nat__zero__less__power__iff,axiom, % 164.98/164.96 ! [V_n_2,V_x_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))) % 164.98/164.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 164.98/164.96 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__commutes,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Groups_Omonoid__mult(T_a) % 164.98/164.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__mult__distrib,axiom, % 164.98/164.96 ! [V_n,V_b,V_a,T_a] : % 164.98/164.96 ( class_Groups_Ocomm__monoid__mult(T_a) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__one,axiom, % 164.98/164.96 ! [V_n,T_a] : % 164.98/164.96 ( class_Groups_Omonoid__mult(T_a) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__mult,axiom, % 164.98/164.96 ! [V_n,V_m,V_a,T_a] : % 164.98/164.96 ( class_Groups_Omonoid__mult(T_a) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__one__right,axiom, % 164.98/164.96 ! [V_a,T_a] : % 164.98/164.96 ( class_Groups_Omonoid__mult(T_a) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__mono,axiom, % 164.98/164.96 ! [V_n,V_b,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zero__le__power,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zero__less__power,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__eq__0__iff,axiom, % 164.98/164.96 ! [V_n_2,V_a_2,T_a] : % 164.98/164.96 ( ( class_Power_Opower(T_a) % 164.98/164.96 & class_Rings_Omult__zero(T_a) % 164.98/164.96 & class_Rings_Ono__zero__divisors(T_a) % 164.98/164.96 & class_Rings_Ozero__neq__one(T_a) ) % 164.98/164.96 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_one__le__power,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__0__Suc,axiom, % 164.98/164.96 ! [V_n,T_a] : % 164.98/164.96 ( ( class_Power_Opower(T_a) % 164.98/164.96 & class_Rings_Osemiring__0(T_a) ) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__inject__exp,axiom, % 164.98/164.96 ! [V_n_2,V_m_2,V_a_2,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)) % 164.98/164.96 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) % 164.98/164.96 <=> V_m_2 = V_n_2 ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__Suc2,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Groups_Omonoid__mult(T_a) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__Suc,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Power_Opower(T_a) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nat__one__le__power,axiom, % 164.98/164.96 ! [V_n,V_i] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__0,axiom, % 164.98/164.96 ! [V_a,T_a] : % 164.98/164.96 ( class_Power_Opower(T_a) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__add,axiom, % 164.98/164.96 ! [V_n,V_m,V_a,T_a] : % 164.98/164.96 ( class_Groups_Omonoid__mult(T_a) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__less__imp__less__base,axiom, % 164.98/164.96 ! [V_b,V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__le__imp__le__base,axiom, % 164.98/164.96 ! [V_b,V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__inject__base,axiom, % 164.98/164.96 ! [V_b,V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.96 => V_a = V_b ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__less__power__Suc,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__gt1__lemma,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__0__left,axiom, % 164.98/164.96 ! [V_n,T_a] : % 164.98/164.96 ( ( class_Power_Opower(T_a) % 164.98/164.96 & class_Rings_Osemiring__0(T_a) ) % 164.98/164.96 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) % 164.98/164.96 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__gt1,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__strict__increasing__iff,axiom, % 164.98/164.96 ! [V_y_2,V_x_2,V_b_2,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__less__imp__less__exp,axiom, % 164.98/164.96 ! [V_n,V_m,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__strict__increasing,axiom, % 164.98/164.96 ! [V_a,V_N,V_n,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__increasing,axiom, % 164.98/164.96 ! [V_a,V_N,V_n,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__minus,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Oring__1(T_a) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__Suc__less,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__eq__imp__eq__base,axiom, % 164.98/164.96 ! [V_b,V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.96 => V_a = V_b ) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__Suc__less__one,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nat_Osize_I2_J,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__power__power,axiom, % 164.98/164.96 ! [T_a] : % 164.98/164.96 ( class_Power_Opower(T_a) % 164.98/164.96 => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_arith__series__general,axiom, % 164.98/164.96 ! [V_n_2,V_d_2,V_a_2,T_a] : % 164.98/164.96 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_a)),c_Nat_Osemiring__1__class_Oof__nat(T_a))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nat_Osize_I4_J,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_option_Osize_I4_J,axiom, % 164.98/164.96 ! [V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),hAPP(c_Option_Ooption_OSome(T_a),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.96 % 164.98/164.96 fof(fact_option_Osize_I3_J,axiom, % 164.98/164.96 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.96 % 164.98/164.96 fof(fact_negative__zle,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_negative__zless,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_less__bin__lemma,axiom, % 164.98/164.96 ! [V_l_2,V_k_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 164.98/164.96 <=> 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_negative__zle__0,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zero__zle__int,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zminus__0,axiom, % 164.98/164.96 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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__less__0__conv,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__0__neq__1,axiom, % 164.98/164.96 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__one__le__iff__zero__less,axiom, % 164.98/164.96 ! [V_z_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__0__less__1,axiom, % 164.98/164.96 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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zadd__0__right,axiom, % 164.98/164.96 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 164.98/164.96 % 164.98/164.96 fof(fact_zadd__0,axiom, % 164.98/164.96 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 164.98/164.96 % 164.98/164.96 fof(fact_zadd__zminus__inverse2,axiom, % 164.98/164.96 ! [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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_odd__nonzero,axiom, % 164.98/164.96 ! [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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_le__imp__0__less,axiom, % 164.98/164.96 ! [V_z] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 164.98/164.96 => 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_odd__less__0,axiom, % 164.98/164.96 ! [V_z_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_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))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zless__add1__eq,axiom, % 164.98/164.96 ! [V_z_2,V_w_2] : % 164.98/164.96 ( 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)))) % 164.98/164.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 164.98/164.96 | V_w_2 = V_z_2 ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zless__imp__add1__zle,axiom, % 164.98/164.96 ! [V_z,V_w] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 164.98/164.96 => 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)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_add1__zle__eq,axiom, % 164.98/164.96 ! [V_z_2,V_w_2] : % 164.98/164.96 ( 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)) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zle__add1__eq__le,axiom, % 164.98/164.96 ! [V_z_2,V_w_2] : % 164.98/164.96 ( 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)))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zadd__strict__right__mono,axiom, % 164.98/164.96 ! [V_k,V_j,V_i] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 164.98/164.96 => 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zminus__zadd__distrib,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zadd__commute,axiom, % 164.98/164.96 ! [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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zadd__left__commute,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zadd__assoc,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zadd__left__mono,axiom, % 164.98/164.96 ! [V_k,V_j,V_i] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 164.98/164.96 => 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zle__iff__zadd,axiom, % 164.98/164.96 ! [V_z_2,V_w_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 164.98/164.96 <=> ? [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)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zadd__zless__mono,axiom, % 164.98/164.96 ! [V_z,V_z_H,V_w,V_w_H] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 164.98/164.96 => 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))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_diff__int__def__symmetric,axiom, % 164.98/164.96 ! [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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_diff__int__def,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zle__diff1__eq,axiom, % 164.98/164.96 ! [V_z_2,V_w_2] : % 164.98/164.96 ( 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)))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zless__linear,axiom, % 164.98/164.96 ! [V_y,V_x] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 164.98/164.96 | V_x = V_y % 164.98/164.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_not__int__zless__negative,axiom, % 164.98/164.96 ! [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)))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zminus__zminus,axiom, % 164.98/164.96 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 164.98/164.96 % 164.98/164.96 fof(fact_zless__le,axiom, % 164.98/164.96 ! [V_w_2,V_z_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 164.98/164.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 164.98/164.96 & V_z_2 != V_w_2 ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__eq__iff,axiom, % 164.98/164.96 ! [V_n_2,V_m_2,T_a] : % 164.98/164.96 ( class_Nat_Osemiring__char__0(T_a) % 164.98/164.96 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) % 164.98/164.96 <=> V_m_2 = V_n_2 ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nat__size,axiom, % 164.98/164.96 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 164.98/164.96 % 164.98/164.96 fof(fact_negative__eq__positive,axiom, % 164.98/164.96 ! [V_m_2,V_n_2] : % 164.98/164.96 ( 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) % 164.98/164.96 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.96 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__0,axiom, % 164.98/164.96 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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__eq__0__conv,axiom, % 164.98/164.96 ! [V_n_2] : % 164.98/164.96 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.96 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__le__0__conv,axiom, % 164.98/164.96 ! [V_n_2] : % 164.98/164.96 ( 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))) % 164.98/164.96 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__zle__neg,axiom, % 164.98/164.96 ! [V_m_2,V_n_2] : % 164.98/164.96 ( 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)))) % 164.98/164.96 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.96 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zless__iff__Suc__zadd,axiom, % 164.98/164.96 ! [V_z_2,V_w_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 164.98/164.96 <=> ? [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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__Suc,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_not__zle__0__negative,axiom, % 164.98/164.96 ! [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))))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_negative__zless__0,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zless__int,axiom, % 164.98/164.96 ! [V_n_2,V_m_2] : % 164.98/164.96 ( 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))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zadd__int__left,axiom, % 164.98/164.96 ! [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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zadd__int,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zle__int,axiom, % 164.98/164.96 ! [V_n_2,V_m_2] : % 164.98/164.96 ( 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))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__1,axiom, % 164.98/164.96 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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_inj__int,axiom, % 164.98/164.96 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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__setsum,axiom, % 164.98/164.96 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__setprod,axiom, % 164.98/164.96 ! [V_A_2,V_f_2,T_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__Suc0__eq__1,axiom, % 164.98/164.96 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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zero__less__int__conv,axiom, % 164.98/164.96 ! [V_n_2] : % 164.98/164.96 ( 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))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__0__le__iff,axiom, % 164.98/164.96 ! [V_n,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zero__le__imp__of__nat,axiom, % 164.98/164.96 ! [V_m,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiff__int,axiom, % 164.98/164.96 ! [V_m,V_n] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 164.98/164.96 => 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)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__less__0__iff,axiom, % 164.98/164.96 ! [V_m,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ~ 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zmult__int,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__mult,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__0,axiom, % 164.98/164.96 ! [T_a] : % 164.98/164.96 ( class_Rings_Osemiring__1(T_a) % 164.98/164.96 => 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) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__less__imp__less,axiom, % 164.98/164.96 ! [V_n,V_m,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( 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))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_less__imp__of__nat__less,axiom, % 164.98/164.96 ! [V_n,V_m,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.98/164.96 => 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))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__less__iff,axiom, % 164.98/164.96 ! [V_n_2,V_m_2,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__le__iff,axiom, % 164.98/164.96 ! [V_n_2,V_m_2,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__add,axiom, % 164.98/164.96 ! [V_n,V_m,T_a] : % 164.98/164.96 ( class_Rings_Osemiring__1(T_a) % 164.98/164.96 => 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)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__mult,axiom, % 164.98/164.96 ! [V_n,V_m,T_a] : % 164.98/164.96 ( class_Rings_Osemiring__1(T_a) % 164.98/164.96 => 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)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__1,axiom, % 164.98/164.96 ! [T_a] : % 164.98/164.96 ( class_Rings_Osemiring__1(T_a) % 164.98/164.96 => 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) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__power,axiom, % 164.98/164.96 ! [V_n,V_m,T_a] : % 164.98/164.96 ( class_Rings_Osemiring__1(T_a) % 164.98/164.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zpower__int,axiom, % 164.98/164.96 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__power,axiom, % 164.98/164.96 ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__setsum,axiom, % 164.98/164.96 ! [V_A_2,V_f_2,T_b,T_a] : % 164.98/164.96 ( class_Rings_Osemiring__1(T_a) % 164.98/164.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_inj__of__nat,axiom, % 164.98/164.96 ! [T_a] : % 164.98/164.96 ( class_Nat_Osemiring__char__0(T_a) % 164.98/164.96 => c_Fun_Oinj__on(tc_Nat_Onat,T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nat_Osize_I3_J,axiom, % 164.98/164.96 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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zmult__zless__mono2__lemma,axiom, % 164.98/164.96 ! [V_k,V_j,V_i] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 164.98/164.96 => 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))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__setprod,axiom, % 164.98/164.96 ! [V_A_2,V_f_2,T_b,T_a] : % 164.98/164.96 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 164.98/164.96 & class_Rings_Osemiring__1(T_a) ) % 164.98/164.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_a)),V_f_2)),V_A_2) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power_Opower_Opower__0,axiom, % 164.98/164.96 ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__Suc,axiom, % 164.98/164.96 ! [V_m,T_a] : % 164.98/164.96 ( class_Rings_Osemiring__1(T_a) % 164.98/164.96 => 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)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power_Opower_Opower__Suc,axiom, % 164.98/164.96 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__diff,axiom, % 164.98/164.96 ! [V_m,V_n,T_a] : % 164.98/164.96 ( class_Rings_Oring__1(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 164.98/164.96 => 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)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_setsum__constant,axiom, % 164.98/164.96 ! [V_A_2,V_y_2,T_b,T_a] : % 164.98/164.96 ( class_Rings_Osemiring__1(T_a) % 164.98/164.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_y_2) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nat_Osize_I1_J,axiom, % 164.98/164.96 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__0__less__iff,axiom, % 164.98/164.96 ! [V_n_2,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__semidom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_self__quotient__aux1,axiom, % 164.98/164.96 ! [V_q,V_r,V_a] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 164.98/164.96 => ( 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)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_self__quotient__aux2,axiom, % 164.98/164.96 ! [V_q,V_r,V_a] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 164.98/164.96 => ( 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)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiff__int__split,axiom, % 164.98/164.96 ! [V_y_2,V_x_2,V_P_2] : % 164.98/164.96 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2)))) % 164.98/164.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 164.98/164.96 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) ) % 164.98/164.96 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 164.98/164.96 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_q__pos__lemma,axiom, % 164.98/164.96 ! [V_r_H,V_q_H,V_b_H] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_q__neg__lemma,axiom, % 164.98/164.96 ! [V_r_H,V_q_H,V_b_H] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_unique__quotient__lemma,axiom, % 164.98/164.96 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),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))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__int__eq,axiom, % 164.98/164.96 ! [V_n_2,V_m_2] : % 164.98/164.96 ( 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) % 164.98/164.96 <=> V_m_2 = V_n_2 ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zle__refl,axiom, % 164.98/164.96 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zle__linear,axiom, % 164.98/164.96 ! [V_w,V_z] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 164.98/164.96 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zle__trans,axiom, % 164.98/164.96 ! [V_k,V_j,V_i] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zle__antisym,axiom, % 164.98/164.96 ! [V_w,V_z] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 164.98/164.96 => V_z = V_w ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiv__mono2__neg__lemma,axiom, % 164.98/164.96 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 164.98/164.96 ( 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) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_unique__quotient__lemma__neg,axiom, % 164.98/164.96 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),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))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiv__mono2__lemma,axiom, % 164.98/164.96 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 164.98/164.96 ( 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) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 164.98/164.96 ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 164.98/164.96 ! [V_n,V_x] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.96 => 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 164.98/164.96 ! [V_n_2,T_a] : % 164.98/164.96 ( class_Rings_Osemiring__1(T_a) % 164.98/164.96 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_Groups_Oone__class_Oone(T_a)),V_n_2,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 164.98/164.96 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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 164.98/164.96 ! [V_i_2,V_inc_2,T_a] : % 164.98/164.96 ( class_Rings_Osemiring__1(T_a) % 164.98/164.96 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 164.98/164.96 ! [V_i_2,V_n_2,V_inc_2,T_a] : % 164.98/164.96 ( class_Rings_Osemiring__1(T_a) % 164.98/164.96 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 164.98/164.96 ! [V_y_2,V_x_2] : % 164.98/164.96 ( 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) % 164.98/164.96 <=> V_x_2 = V_y_2 ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 164.98/164.96 ! [V_B_2,V_A_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.98/164.96 <=> 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 164.98/164.96 ! [V_B_2,V_A_2] : % 164.98/164.96 ( V_A_2 = V_B_2 % 164.98/164.96 <=> 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) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 164.98/164.96 ! [V_A_2,V_x_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 164.98/164.96 <=> 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 164.98/164.96 ! [V_B_2,V_A_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.98/164.96 <=> 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 164.98/164.96 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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 164.98/164.96 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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 164.98/164.96 ! [V_A_2] : % 164.98/164.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 164.98/164.96 <=> 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 164.98/164.96 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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 164.98/164.96 ! [V_y,V_x] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 164.98/164.96 ! [V_P_2] : % 164.98/164.96 ( ? [B_x] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 164.98/164.96 & hBOOL(hAPP(V_P_2,B_x)) ) % 164.98/164.96 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 164.98/164.96 ! [V_P_2] : % 164.98/164.96 ( ! [B_x] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 164.98/164.96 => hBOOL(hAPP(V_P_2,B_x)) ) % 164.98/164.96 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 164.98/164.96 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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 164.98/164.96 ! [V_y,V_x] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 164.98/164.96 ! [V_y_2,V_x_2] : % 164.98/164.96 ( 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))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 164.98/164.96 ! [V_y_2,V_x_2] : % 164.98/164.96 ( 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))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_small_H_Osimps,axiom, % 164.98/164.96 ! [V_f_2,V_i_2,V_d_2] : % 164.98/164.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 164.98/164.96 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 164.98/164.96 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_setsum__bounded,axiom, % 164.98/164.96 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] : % 164.98/164.96 ( ( class_Groups_Oordered__ab__semigroup__add(T_b) % 164.98/164.96 & class_Rings_Osemiring__1(T_b) ) % 164.98/164.96 => ( ! [B_i] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) ) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_a),V_A_2))),V_K_2))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_tsub__def,axiom, % 164.98/164.96 ! [V_x,V_y] : % 164.98/164.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 164.98/164.96 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 164.98/164.96 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 164.98/164.96 ! [V_x_2,V_y_2,V_ca_2] : % 164.98/164.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 164.98/164.96 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2)) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 164.98/164.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 164.98/164.96 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 164.98/164.96 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Ints__odd__less__0,axiom, % 164.98/164.96 ! [V_a_2,T_a] : % 164.98/164.96 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__power__div__base,axiom, % 164.98/164.96 ! [V_k,V_m] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_finite__atLeastLessThan,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_infinite__UNIV__int,axiom, % 164.98/164.96 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiv__zero,axiom, % 164.98/164.96 ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiv__zminus__zminus,axiom, % 164.98/164.96 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiv__zminus2,axiom, % 164.98/164.96 ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__by__0,axiom, % 164.98/164.96 ! [V_a,T_a] : % 164.98/164.96 ( class_Divides_Osemiring__div(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__0,axiom, % 164.98/164.96 ! [V_a,T_a] : % 164.98/164.96 ( class_Divides_Osemiring__div(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__by__1,axiom, % 164.98/164.96 ! [V_a,T_a] : % 164.98/164.96 ( class_Divides_Osemiring__div(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeastLessThan__eq__iff,axiom, % 164.98/164.96 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 164.98/164.96 ( class_Orderings_Olinorder(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 164.98/164.96 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2) % 164.98/164.96 <=> ( V_a_2 = V_ca_2 % 164.98/164.96 & V_b_2 = V_d_2 ) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 164.98/164.96 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 164.98/164.96 ( class_Orderings_Olinorder(T_a) % 164.98/164.96 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 164.98/164.96 => V_a_2 = V_ca_2 ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 164.98/164.96 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 164.98/164.96 ( class_Orderings_Olinorder(T_a) % 164.98/164.96 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 164.98/164.96 => V_b_2 = V_d_2 ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 164.98/164.96 ! [V_y,V_x] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__neg__pos__less0,axiom, % 164.98/164.96 ! [V_b,V_a] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 164.98/164.96 ! [V_a_2,V_b_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 164.98/164.96 ! [V_a_2,V_b_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeastLessThan__add__Un,axiom, % 164.98/164.96 ! [V_k_2,V_j_2,V_i_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 164.98/164.96 => 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiv__self,axiom, % 164.98/164.96 ! [V_a] : % 164.98/164.96 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeastLessThan0,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeast0LessThan,axiom, % 164.98/164.96 ! [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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__mult__mult1__if,axiom, % 164.98/164.96 ! [V_b,V_a,V_c,T_a] : % 164.98/164.96 ( class_Divides_Osemiring__div(T_a) % 164.98/164.96 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) ) % 164.98/164.96 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__mult__self2__is__id,axiom, % 164.98/164.96 ! [V_a,V_b,T_a] : % 164.98/164.96 ( class_Divides_Osemiring__div(T_a) % 164.98/164.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__mult__self1__is__id,axiom, % 164.98/164.96 ! [V_a,V_b,T_a] : % 164.98/164.96 ( class_Divides_Osemiring__div(T_a) % 164.98/164.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__mult__mult2,axiom, % 164.98/164.96 ! [V_b,V_a,V_c,T_a] : % 164.98/164.96 ( class_Divides_Osemiring__div(T_a) % 164.98/164.96 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__mult__mult1,axiom, % 164.98/164.96 ! [V_b,V_a,V_c,T_a] : % 164.98/164.96 ( class_Divides_Osemiring__div(T_a) % 164.98/164.96 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__self,axiom, % 164.98/164.96 ! [V_a,T_a] : % 164.98/164.96 ( class_Divides_Osemiring__div(T_a) % 164.98/164.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_subset__card__intvl__is__intvl,axiom, % 164.98/164.96 ! [V_k_2,V_A_2] : % 164.98/164.96 ( 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))))) % 164.98/164.96 => 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))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_card__atLeastLessThan,axiom, % 164.98/164.96 ! [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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_image__Suc__atLeastLessThan,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeastLessThan__empty,axiom, % 164.98/164.96 ! [V_a_2,V_b_2,T_a] : % 164.98/164.96 ( class_Orderings_Oorder(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 164.98/164.96 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeastLessThan__empty__iff,axiom, % 164.98/164.96 ! [V_b_2,V_a_2,T_a] : % 164.98/164.96 ( class_Orderings_Oorder(T_a) % 164.98/164.96 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.96 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeastLessThan__empty__iff2,axiom, % 164.98/164.96 ! [V_b_2,V_a_2,T_a] : % 164.98/164.96 ( class_Orderings_Oorder(T_a) % 164.98/164.96 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) % 164.98/164.96 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeastLessThan__subset__iff,axiom, % 164.98/164.96 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 164.98/164.96 ( class_Orderings_Olinorder(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 164.98/164.96 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 164.98/164.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 164.98/164.96 ! [V_n_2,V_m_2,V_f_2,T_a] : % 164.98/164.96 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ivl__disj__un_I17_J,axiom, % 164.98/164.96 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Olinorder(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 164.98/164.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 164.98/164.96 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 164.98/164.96 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ivl__diff,axiom, % 164.98/164.96 ! [V_m_2,V_n_2,V_i_2,T_a] : % 164.98/164.96 ( class_Orderings_Olinorder(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2)) % 164.98/164.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_n_2),V_m_2) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ivl__disj__int_I11_J,axiom, % 164.98/164.96 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Oorder(T_a) % 164.98/164.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_image__add__atLeastLessThan,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Ints__0,axiom, % 164.98/164.96 ! [T_a] : % 164.98/164.96 ( class_Rings_Oring__1(T_a) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiv__eq__0__iff,axiom, % 164.98/164.96 ! [V_k_2,V_i_2] : % 164.98/164.96 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.96 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.96 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 164.98/164.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 164.98/164.96 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 164.98/164.96 ! [V_a_2,V_b_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 164.98/164.96 ! [V_i_2,V_k_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 164.98/164.96 ! [V_b_2,V_a_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 164.98/164.96 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 164.98/164.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiv__mono2,axiom, % 164.98/164.96 ! [V_b,V_b_H,V_a] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__nonneg__neg__le0,axiom, % 164.98/164.96 ! [V_b,V_a] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__pos__pos__trivial,axiom, % 164.98/164.96 ! [V_b,V_a] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 164.98/164.96 ! [V_a_2,V_b_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__nonpos__pos__le0,axiom, % 164.98/164.96 ! [V_b,V_a] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiv__mono2__neg,axiom, % 164.98/164.96 ! [V_b,V_b_H,V_a] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__neg__neg__trivial,axiom, % 164.98/164.96 ! [V_b,V_a] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiv__mono1,axiom, % 164.98/164.96 ! [V_b,V_a_H,V_a] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiv__mono1__neg,axiom, % 164.98/164.96 ! [V_b,V_a_H,V_a] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Ints__add,axiom, % 164.98/164.96 ! [V_b_2,V_a_2,T_a] : % 164.98/164.96 ( class_Rings_Oring__1(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Ints__mult,axiom, % 164.98/164.96 ! [V_b_2,V_a_2,T_a] : % 164.98/164.96 ( class_Rings_Oring__1(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Ints__diff,axiom, % 164.98/164.96 ! [V_b_2,V_a_2,T_a] : % 164.98/164.96 ( class_Rings_Oring__1(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_int__div__less__self,axiom, % 164.98/164.96 ! [V_k,V_x] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiv__zmult2__eq,axiom, % 164.98/164.96 ! [V_b,V_a,V_c] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Ints__1,axiom, % 164.98/164.96 ! [T_a] : % 164.98/164.96 ( class_Rings_Oring__1(T_a) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Ints__minus,axiom, % 164.98/164.96 ! [V_a_2,T_a] : % 164.98/164.96 ( class_Rings_Oring__1(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Ints__power,axiom, % 164.98/164.96 ! [V_n_2,V_a_2,T_a] : % 164.98/164.96 ( class_Rings_Oring__1(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Ints__of__nat,axiom, % 164.98/164.96 ! [V_n_2,T_a] : % 164.98/164.96 ( class_Rings_Oring__1(T_a) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_setsum__add__nat__ivl,axiom, % 164.98/164.96 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 164.98/164.96 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 164.98/164.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_setsum__diff__nat__ivl,axiom, % 164.98/164.96 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 164.98/164.96 ( class_Groups_Oab__group__add(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 164.98/164.96 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__mult__self2,axiom, % 164.98/164.96 ! [V_c,V_a,V_b,T_a] : % 164.98/164.96 ( class_Divides_Osemiring__div(T_a) % 164.98/164.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__mult__self1,axiom, % 164.98/164.96 ! [V_c,V_a,V_b,T_a] : % 164.98/164.96 ( class_Divides_Osemiring__div(T_a) % 164.98/164.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__add__self1,axiom, % 164.98/164.96 ! [V_a,V_b,T_a] : % 164.98/164.96 ( class_Divides_Osemiring__div(T_a) % 164.98/164.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__add__self2,axiom, % 164.98/164.96 ! [V_a,V_b,T_a] : % 164.98/164.96 ( class_Divides_Osemiring__div(T_a) % 164.98/164.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeastLessThan__singleton,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ivl__disj__un_I8_J,axiom, % 164.98/164.96 ! [V_u_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Olinorder(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 164.98/164.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ivl__disj__int_I2_J,axiom, % 164.98/164.96 ! [V_u_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Oorder(T_a) % 164.98/164.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 164.98/164.96 ! [V_k_2,V_f_2,T_a] : % 164.98/164.96 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.96 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_setsum__head__upt__Suc,axiom, % 164.98/164.96 ! [V_f_2,V_n_2,V_m_2,T_a] : % 164.98/164.96 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 164.98/164.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Ints__double__eq__0__iff,axiom, % 164.98/164.96 ! [V_a_2,T_a] : % 164.98/164.96 ( class_Int_Oring__char__0(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 164.98/164.96 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeastLessThanSuc,axiom, % 164.98/164.96 ! [V_n_2,V_m_2] : % 164.98/164.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.98/164.96 => 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)) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.98/164.96 => 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)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_setsum__op__ivl__Suc,axiom, % 164.98/164.96 ! [V_f_2,V_m_2,V_n_2,T_a] : % 164.98/164.96 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 164.98/164.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_a) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 164.98/164.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_split__zdiv,axiom, % 164.98/164.96 ! [V_k_2,V_n_2,V_P_2] : % 164.98/164.96 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 164.98/164.96 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.96 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 164.98/164.96 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 164.98/164.96 => ! [B_i] : % 164.98/164.96 ( ? [B_j] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 164.98/164.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 164.98/164.96 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 164.98/164.96 => hBOOL(hAPP(V_P_2,B_i)) ) ) % 164.98/164.96 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 => ! [B_i] : % 164.98/164.96 ( ? [B_j] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 164.98/164.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.96 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) ) % 164.98/164.96 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_divmod__int__rel__div__eq,axiom, % 164.98/164.96 ! [V_r_1,V_y,V_b_1,V_a_1] : % 164.98/164.96 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1) % 164.98/164.96 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 164.98/164.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 164.98/164.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 164.98/164.96 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 164.98/164.96 ! [V_y,V_x] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 164.98/164.96 => 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))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_tsub__eq,axiom, % 164.98/164.96 ! [V_x,V_y] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 164.98/164.96 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Ints__odd__nonzero,axiom, % 164.98/164.96 ! [V_a_2,T_a] : % 164.98/164.96 ( class_Int_Oring__char__0(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 164.98/164.96 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_all__nat__less__eq,axiom, % 164.98/164.96 ! [V_P_2,V_n_2] : % 164.98/164.96 ( ! [B_m] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 164.98/164.96 => hBOOL(hAPP(V_P_2,B_m)) ) % 164.98/164.96 <=> ! [B_x] : % 164.98/164.96 ( 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))) % 164.98/164.96 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ex__nat__less__eq,axiom, % 164.98/164.96 ! [V_P_2,V_n_2] : % 164.98/164.96 ( ? [B_m] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 164.98/164.96 & hBOOL(hAPP(V_P_2,B_m)) ) % 164.98/164.96 <=> ? [B_x] : % 164.98/164.96 ( 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))) % 164.98/164.96 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_z3div__def,axiom, % 164.98/164.96 ! [V_k,V_l] : % 164.98/164.96 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 164.98/164.96 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 164.98/164.96 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ivl__disj__un_I3_J,axiom, % 164.98/164.96 ! [V_u_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Olinorder(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 164.98/164.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_com_Osize_I4_J,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_card__Plus__conv__if,axiom, % 164.98/164.96 ! [V_B_2,T_b,V_A_2,T_a] : % 164.98/164.96 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.96 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 164.98/164.96 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) % 164.98/164.96 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.96 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 164.98/164.96 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_finite__greaterThanLessThan,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_finite__atLeastLessThan__int,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_finite__greaterThanLessThan__int,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__le__dividend,axiom, % 164.98/164.96 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__le__mono,axiom, % 164.98/164.96 ! [V_k,V_n,V_m] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__mult2__eq,axiom, % 164.98/164.96 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 164.98/164.96 ! [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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__1,axiom, % 164.98/164.96 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__less,axiom, % 164.98/164.96 ! [V_n,V_m] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nat__mult__div__cancel__disj,axiom, % 164.98/164.96 ! [V_n,V_m,V_k] : % 164.98/164.96 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 164.98/164.96 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 164.98/164.96 ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_zdiv__int,axiom, % 164.98/164.96 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_greaterThanLessThan__empty,axiom, % 164.98/164.96 ! [V_k_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Oorder(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 164.98/164.96 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__le__mono2,axiom, % 164.98/164.96 ! [V_k,V_n,V_m] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nat__mult__div__cancel1,axiom, % 164.98/164.96 ! [V_n,V_m,V_k] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__mult__self__is__m,axiom, % 164.98/164.96 ! [V_m,V_n] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__mult__self1__is__m,axiom, % 164.98/164.96 ! [V_m,V_n] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__less__dividend,axiom, % 164.98/164.96 ! [V_m,V_n] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 164.98/164.96 ! [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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_image__uminus__greaterThanLessThan,axiom, % 164.98/164.96 ! [V_y_2,V_x_2,T_a] : % 164.98/164.96 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.96 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_com_Osize_I7_J,axiom, % 164.98/164.96 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.96 % 164.98/164.96 fof(fact_com_Osize_I8_J,axiom, % 164.98/164.96 ! [V_fun_2,V_pname_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.96 % 164.98/164.96 fof(fact_com_Osize_I1_J,axiom, % 164.98/164.96 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__if,axiom, % 164.98/164.96 ! [V_m,V_n] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_div__geq,axiom, % 164.98/164.96 ! [V_m,V_n] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.96 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_split__div,axiom, % 164.98/164.96 ! [V_k_2,V_n_2,V_P_2] : % 164.98/164.96 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 164.98/164.96 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.96 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 164.98/164.96 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.96 => ! [B_i,B_j] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 164.98/164.96 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j) % 164.98/164.96 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_image__add__int__atLeastLessThan,axiom, % 164.98/164.96 ! [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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ivl__disj__int_I9_J,axiom, % 164.98/164.96 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Oorder(T_a) % 164.98/164.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_card__greaterThanLessThan,axiom, % 164.98/164.96 ! [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)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_finite__PlusD_I2_J,axiom, % 164.98/164.96 ! [V_B_2,V_A_2,T_b,T_a] : % 164.98/164.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) % 164.98/164.96 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_finite__PlusD_I1_J,axiom, % 164.98/164.96 ! [V_B_2,V_A_2,T_b,T_a] : % 164.98/164.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) % 164.98/164.96 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_finite__Plus,axiom, % 164.98/164.96 ! [V_B_2,T_b,V_A_2,T_a] : % 164.98/164.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 164.98/164.96 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_finite__Plus__iff,axiom, % 164.98/164.96 ! [V_B_2,V_A_2,T_b,T_a] : % 164.98/164.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))) % 164.98/164.96 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.96 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_le__div__geq,axiom, % 164.98/164.96 ! [V_m,V_n] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 164.98/164.96 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_split__div__lemma,axiom, % 164.98/164.96 ! [V_m_2,V_q_2,V_n_2] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 164.98/164.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) % 164.98/164.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2)))) ) % 164.98/164.96 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_split__div_H,axiom, % 164.98/164.96 ! [V_n_2,V_m_2,V_P_2] : % 164.98/164.96 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 164.98/164.96 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.96 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 164.98/164.96 | ? [B_q] : % 164.98/164.96 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) % 164.98/164.96 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q)))) % 164.98/164.96 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_card__Plus,axiom, % 164.98/164.96 ! [V_B_2,T_b,V_A_2,T_a] : % 164.98/164.96 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 164.98/164.96 => hAPP(c_Finite__Set_Ocard(tc_sum(T_a,T_b)),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ivl__disj__un_I15_J,axiom, % 164.98/164.96 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Olinorder(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 164.98/164.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_com_Osize_I6_J,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_UNIV__Plus__UNIV,axiom, % 164.98/164.96 ! [T_b,T_a] : c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) ). % 164.98/164.96 % 164.98/164.96 fof(fact_Plus__eq__empty__conv,axiom, % 164.98/164.96 ! [V_B_2,V_A_2,T_b,T_a] : % 164.98/164.96 ( c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) % 164.98/164.96 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.96 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ivl__disj__un_I4_J,axiom, % 164.98/164.96 ! [V_u_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Olinorder(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 164.98/164.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_com_Osize_I12_J,axiom, % 164.98/164.96 ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_setprod__diff1,axiom, % 164.98/164.96 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] : % 164.98/164.96 ( class_Fields_Ofield(T_b) % 164.98/164.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.96 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) % 164.98/164.96 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2) ) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_com_Osize_I14_J,axiom, % 164.98/164.96 ! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_finite__greaterThanAtMost,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_finite__greaterThanAtMost__int,axiom, % 164.98/164.96 ! [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))) ). % 164.98/164.96 % 164.98/164.96 fof(fact_divide__zero,axiom, % 164.98/164.96 ! [V_a,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_divide__zero__left,axiom, % 164.98/164.96 ! [V_a,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_add__divide__distrib,axiom, % 164.98/164.96 ! [V_c,V_b,V_a,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_times__divide__eq__right,axiom, % 164.98/164.96 ! [V_c,V_b,V_a,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_diff__divide__distrib,axiom, % 164.98/164.96 ! [V_c,V_b,V_a,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_divide__1,axiom, % 164.98/164.96 ! [V_a,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_minus__divide__left,axiom, % 164.98/164.96 ! [V_b,V_a,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__divide,axiom, % 164.98/164.96 ! [V_n,V_b,V_a,T_a] : % 164.98/164.96 ( class_Fields_Ofield__inverse__zero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_setsum__divide__distrib,axiom, % 164.98/164.96 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 164.98/164.96 ( class_Fields_Ofield(T_a) % 164.98/164.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Rings_Oinverse__class_Odivide(T_a)),V_f_2)),V_r_2)),V_A_2) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nonzero__eq__divide__eq,axiom, % 164.98/164.96 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 164.98/164.96 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nonzero__divide__eq__eq,axiom, % 164.98/164.96 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 164.98/164.96 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_divide__eq__imp,axiom, % 164.98/164.96 ! [V_a,V_b,V_c,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 164.98/164.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_eq__divide__imp,axiom, % 164.98/164.96 ! [V_b,V_a,V_c,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 164.98/164.96 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_right__inverse__eq,axiom, % 164.98/164.96 ! [V_a_2,V_b_2,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a) % 164.98/164.96 <=> V_a_2 = V_b_2 ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_divide__self,axiom, % 164.98/164.96 ! [V_a,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_divide__self__if,axiom, % 164.98/164.96 ! [V_a,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 164.98/164.96 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 164.98/164.96 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nonzero__minus__divide__divide,axiom, % 164.98/164.96 ! [V_a,V_b,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nonzero__minus__divide__right,axiom, % 164.98/164.96 ! [V_a,V_b,T_a] : % 164.98/164.96 ( class_Rings_Odivision__ring(T_a) % 164.98/164.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_nonzero__power__divide,axiom, % 164.98/164.96 ! [V_n,V_a,V_b,T_a] : % 164.98/164.96 ( class_Fields_Ofield(T_a) % 164.98/164.96 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__one__over,axiom, % 164.98/164.96 ! [V_n,V_a,T_a] : % 164.98/164.96 ( class_Fields_Ofield__inverse__zero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_setprod__dividef,axiom, % 164.98/164.96 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 164.98/164.96 ( class_Fields_Ofield__inverse__zero(T_b) % 164.98/164.96 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),V_A_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_greaterThanAtMost__empty,axiom, % 164.98/164.96 ! [V_k_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Oorder(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 164.98/164.96 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_greaterThanAtMost__empty__iff,axiom, % 164.98/164.96 ! [V_l_2,V_k_2,T_a] : % 164.98/164.96 ( class_Orderings_Oorder(T_a) % 164.98/164.96 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.96 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 164.98/164.96 ! [V_l_2,V_k_2,T_a] : % 164.98/164.96 ( class_Orderings_Oorder(T_a) % 164.98/164.96 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2) % 164.98/164.96 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ivl__disj__un_I20_J,axiom, % 164.98/164.96 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Olinorder(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 164.98/164.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ivl__disj__int_I14_J,axiom, % 164.98/164.96 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Oorder(T_a) % 164.98/164.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_card__greaterThanAtMost,axiom, % 164.98/164.96 ! [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) ). % 164.98/164.96 % 164.98/164.96 fof(fact_com_Osize_I15_J,axiom, % 164.98/164.96 ! [V_pname] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.96 % 164.98/164.96 fof(fact_com_Osize_I16_J,axiom, % 164.98/164.96 ! [V_fun_2,V_pname_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.96 % 164.98/164.96 fof(fact_com_Osize_I9_J,axiom, % 164.98/164.96 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.96 % 164.98/164.96 fof(fact_power__diff,axiom, % 164.98/164.96 ! [V_m,V_n,V_a,T_a] : % 164.98/164.96 ( class_Fields_Ofield(T_a) % 164.98/164.96 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 164.98/164.96 => 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)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_image__uminus__greaterThanAtMost,axiom, % 164.98/164.96 ! [V_y_2,V_x_2,T_a] : % 164.98/164.96 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.96 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_image__uminus__atLeastLessThan,axiom, % 164.98/164.96 ! [V_y_2,V_x_2,T_a] : % 164.98/164.96 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.96 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ivl__disj__int_I10_J,axiom, % 164.98/164.96 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Oorder(T_a) % 164.98/164.96 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_ivl__disj__un_I16_J,axiom, % 164.98/164.96 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.96 ( class_Orderings_Olinorder(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 164.98/164.96 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_geometric__sum,axiom, % 164.98/164.96 ! [V_n_2,V_x_2,T_a] : % 164.98/164.96 ( class_Fields_Ofield(T_a) % 164.98/164.96 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a) % 164.98/164.96 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_Power_Opower__class_Opower(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x_2),c_Groups_Oone__class_Oone(T_a))) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_le__divide__eq,axiom, % 164.98/164.96 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 164.98/164.96 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 164.98/164.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_divide__le__eq,axiom, % 164.98/164.96 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 164.98/164.96 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 164.98/164.96 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.96 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 164.98/164.96 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.96 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_pos__le__divide__eq,axiom, % 164.98/164.96 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 164.98/164.96 ( class_Fields_Olinordered__field(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_pos__divide__le__eq,axiom, % 164.98/164.96 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 164.98/164.96 ( class_Fields_Olinordered__field(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 164.98/164.96 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_mult__imp__div__pos__le,axiom, % 164.98/164.96 ! [V_z,V_x,V_y,T_a] : % 164.98/164.96 ( class_Fields_Olinordered__field(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 164.98/164.96 => ( 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))) % 164.98/164.96 => 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)) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_mult__imp__le__div__pos,axiom, % 164.98/164.96 ! [V_x,V_z,V_y,T_a] : % 164.98/164.96 ( class_Fields_Olinordered__field(T_a) % 164.98/164.96 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 164.98/164.96 => ( 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)) % 164.98/164.96 => 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))) ) ) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_times__divide__times__eq,axiom, % 164.98/164.96 ! [V_w,V_z,V_y,V_x,T_a] : % 164.98/164.96 ( class_Fields_Ofield__inverse__zero(T_a) % 164.98/164.96 => 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)) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_minus__divide__divide,axiom, % 164.98/164.96 ! [V_b,V_a,T_a] : % 164.98/164.96 ( class_Fields_Ofield__inverse__zero(T_a) % 164.98/164.96 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ). % 164.98/164.96 % 164.98/164.96 fof(fact_minus__divide__right,axiom, % 164.98/164.97 ! [V_b,V_a,T_a] : % 164.98/164.97 ( class_Fields_Ofield__inverse__zero(T_a) % 164.98/164.97 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_zero__le__divide__iff,axiom, % 164.98/164.97 ! [V_b_2,V_a_2,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2))) % 164.98/164.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 164.98/164.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__le__0__iff,axiom, % 164.98/164.97 ! [V_b_2,V_a_2,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 164.98/164.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__right__mono,axiom, % 164.98/164.97 ! [V_c,V_b,V_a,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__right__mono__neg,axiom, % 164.98/164.97 ! [V_c,V_b,V_a,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_zero__less__divide__iff,axiom, % 164.98/164.97 ! [V_b_2,V_a_2,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2))) % 164.98/164.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 164.98/164.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__less__0__iff,axiom, % 164.98/164.97 ! [V_b_2,V_a_2,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 164.98/164.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__pos__pos,axiom, % 164.98/164.97 ! [V_y,V_x,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__pos__neg,axiom, % 164.98/164.97 ! [V_y,V_x,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__neg__pos,axiom, % 164.98/164.97 ! [V_y,V_x,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__neg__neg,axiom, % 164.98/164.97 ! [V_y,V_x,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__strict__right__mono,axiom, % 164.98/164.97 ! [V_c,V_b,V_a,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__strict__right__mono__neg,axiom, % 164.98/164.97 ! [V_c,V_a,V_b,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_frac__eq__eq,axiom, % 164.98/164.97 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] : % 164.98/164.97 ( class_Fields_Ofield(T_a) % 164.98/164.97 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w_2),V_z_2) % 164.98/164.97 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mult__divide__mult__cancel__left,axiom, % 164.98/164.97 ! [V_b,V_a,V_c,T_a] : % 164.98/164.97 ( class_Fields_Ofield__inverse__zero(T_a) % 164.98/164.97 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mult__divide__mult__cancel__right,axiom, % 164.98/164.97 ! [V_b,V_a,V_c,T_a] : % 164.98/164.97 ( class_Fields_Ofield__inverse__zero(T_a) % 164.98/164.97 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__eq__eq,axiom, % 164.98/164.97 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 164.98/164.97 ( class_Fields_Ofield__inverse__zero(T_a) % 164.98/164.97 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 164.98/164.97 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) % 164.98/164.97 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_eq__divide__eq,axiom, % 164.98/164.97 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 164.98/164.97 ( class_Fields_Ofield__inverse__zero(T_a) % 164.98/164.97 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 164.98/164.97 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) % 164.98/164.97 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__nonneg__pos,axiom, % 164.98/164.97 ! [V_y,V_x,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__nonneg__neg,axiom, % 164.98/164.97 ! [V_y,V_x,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_frac__less2,axiom, % 164.98/164.97 ! [V_z,V_w,V_y,V_x,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_frac__less,axiom, % 164.98/164.97 ! [V_z,V_w,V_y,V_x,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_frac__le,axiom, % 164.98/164.97 ! [V_z,V_w,V_y,V_x,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__nonpos__pos,axiom, % 164.98/164.97 ! [V_y,V_x,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__nonpos__neg,axiom, % 164.98/164.97 ! [V_y,V_x,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_less__divide__eq,axiom, % 164.98/164.97 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 164.98/164.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 164.98/164.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) % 164.98/164.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__less__eq,axiom, % 164.98/164.97 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 164.98/164.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) % 164.98/164.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 164.98/164.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_pos__less__divide__eq,axiom, % 164.98/164.97 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_pos__divide__less__eq,axiom, % 164.98/164.97 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mult__imp__div__pos__less,axiom, % 164.98/164.97 ! [V_z,V_x,V_y,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mult__imp__less__div__pos,axiom, % 164.98/164.97 ! [V_x,V_z,V_y,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_neg__less__divide__eq,axiom, % 164.98/164.97 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_neg__divide__less__eq,axiom, % 164.98/164.97 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__strict__left__mono,axiom, % 164.98/164.97 ! [V_c,V_a,V_b,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__strict__left__mono__neg,axiom, % 164.98/164.97 ! [V_c,V_b,V_a,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_add__num__frac,axiom, % 164.98/164.97 ! [V_x,V_z,V_y,T_a] : % 164.98/164.97 ( class_Fields_Ofield__inverse__zero(T_a) % 164.98/164.97 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_add__divide__eq__iff,axiom, % 164.98/164.97 ! [V_y,V_x,V_z,T_a] : % 164.98/164.97 ( class_Fields_Ofield(T_a) % 164.98/164.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_add__frac__num,axiom, % 164.98/164.97 ! [V_z,V_x,V_y,T_a] : % 164.98/164.97 ( class_Fields_Ofield__inverse__zero(T_a) % 164.98/164.97 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__add__eq__iff,axiom, % 164.98/164.97 ! [V_y,V_x,V_z,T_a] : % 164.98/164.97 ( class_Fields_Ofield(T_a) % 164.98/164.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_add__frac__eq,axiom, % 164.98/164.97 ! [V_w,V_x,V_z,V_y,T_a] : % 164.98/164.97 ( class_Fields_Ofield(T_a) % 164.98/164.97 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_diff__divide__eq__iff,axiom, % 164.98/164.97 ! [V_y,V_x,V_z,T_a] : % 164.98/164.97 ( class_Fields_Ofield(T_a) % 164.98/164.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__diff__eq__iff,axiom, % 164.98/164.97 ! [V_y,V_x,V_z,T_a] : % 164.98/164.97 ( class_Fields_Ofield(T_a) % 164.98/164.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_diff__frac__eq,axiom, % 164.98/164.97 ! [V_w,V_x,V_z,V_y,T_a] : % 164.98/164.97 ( class_Fields_Ofield(T_a) % 164.98/164.97 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_less__half__sum,axiom, % 164.98/164.97 ! [V_b,V_a,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_gt__half__sum,axiom, % 164.98/164.97 ! [V_b,V_a,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))),V_b)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__left__mono__neg,axiom, % 164.98/164.97 ! [V_c,V_b,V_a,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_divide__left__mono,axiom, % 164.98/164.97 ! [V_c,V_a,V_b,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_neg__divide__le__eq,axiom, % 164.98/164.97 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_neg__le__divide__eq,axiom, % 164.98/164.97 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setprod__Un,axiom, % 164.98/164.97 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 164.98/164.97 ( class_Fields_Ofield(T_b) % 164.98/164.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.97 => ( ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 164.98/164.97 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) ) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_image__atLeastZeroLessThan__int,axiom, % 164.98/164.97 ! [V_u_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 164.98/164.97 => 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))) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setsum__nonneg__0,axiom, % 164.98/164.97 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] : % 164.98/164.97 ( class_Groups_Oordered__ab__group__add(T_b) % 164.98/164.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 164.98/164.97 => ( ! [B_i] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 164.98/164.97 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_b) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 164.98/164.97 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setsum__nonneg__leq__bound,axiom, % 164.98/164.97 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] : % 164.98/164.97 ( class_Groups_Oordered__ab__group__add(T_b) % 164.98/164.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 164.98/164.97 => ( ! [B_i] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 164.98/164.97 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2 % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_greaterThan__0,axiom, % 164.98/164.97 hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_greaterThan__eq__iff,axiom, % 164.98/164.97 ! [V_y_2,V_x_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2) % 164.98/164.97 <=> V_x_2 = V_y_2 ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__int,axiom, % 164.98/164.97 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__0,axiom, % 164.98/164.97 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 164.98/164.97 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_eq__nat__nat__iff,axiom, % 164.98/164.97 ! [V_z_H_2,V_z_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 164.98/164.97 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 164.98/164.97 <=> V_z_2 = V_z_H_2 ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ex__nat,axiom, % 164.98/164.97 ! [V_P_2] : % 164.98/164.97 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 164.98/164.97 <=> ? [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 164.98/164.97 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_all__nat,axiom, % 164.98/164.97 ! [V_P_2] : % 164.98/164.97 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 164.98/164.97 <=> ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 164.98/164.97 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 164.98/164.97 ! [V_y_2,V_x_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 164.98/164.97 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 164.98/164.97 <=> V_x_2 = V_y_2 ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 164.98/164.97 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 164.98/164.97 ! [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))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__int__nat__set__return__embed,axiom, % 164.98/164.97 ! [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 ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 164.98/164.97 ! [V_A_2,V_f_2,T_a] : % 164.98/164.97 ( ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.97 & class_Groups_Ocomm__monoid__mult(T_a) ) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 164.98/164.97 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))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__0__iff,axiom, % 164.98/164.97 ! [V_i_2] : % 164.98/164.97 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__le__0,axiom, % 164.98/164.97 ! [V_z] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.97 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_zless__nat__conj,axiom, % 164.98/164.97 ! [V_z_2,V_w_2] : % 164.98/164.97 ( 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))) % 164.98/164.97 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__mono__iff,axiom, % 164.98/164.97 ! [V_w_2,V_z_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 164.98/164.97 => ( 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))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 164.98/164.97 ! [V_y_2,V_x_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 164.98/164.97 => ( 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))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__1,axiom, % 164.98/164.97 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__0__le,axiom, % 164.98/164.97 ! [V_z] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 164.98/164.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_int__eq__iff,axiom, % 164.98/164.97 ! [V_z_2,V_m_2] : % 164.98/164.97 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 164.98/164.97 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_int__nat__eq,axiom, % 164.98/164.97 ! [V_z] : % 164.98/164.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 164.98/164.97 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 164.98/164.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 164.98/164.97 => 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) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_zless__nat__eq__int__zless,axiom, % 164.98/164.97 ! [V_z_2,V_m_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 164.98/164.97 <=> 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)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__zminus__int,axiom, % 164.98/164.97 ! [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) ). % 164.98/164.97 % 164.98/164.97 fof(fact_greaterThan__iff,axiom, % 164.98/164.97 ! [V_k_2,V_i_2,T_a] : % 164.98/164.97 ( class_Orderings_Oord(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_greaterThan__subset__iff,axiom, % 164.98/164.97 ! [V_y_2,V_x_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 164.98/164.97 ! [V_A_2,V_f_2,T_a] : % 164.98/164.97 ( ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.97 & class_Groups_Ocomm__monoid__mult(T_a) ) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_card__atLeastZeroLessThan__int,axiom, % 164.98/164.97 ! [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) ). % 164.98/164.97 % 164.98/164.97 fof(fact_card__atLeastLessThan__int,axiom, % 164.98/164.97 ! [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)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_zero__less__nat__eq,axiom, % 164.98/164.97 ! [V_z_2] : % 164.98/164.97 ( 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))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__less__eq__zless,axiom, % 164.98/164.97 ! [V_z_2,V_w_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 164.98/164.97 => ( 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))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 164.98/164.97 ! [V_y_2,V_x_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 164.98/164.97 => ( 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))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__eq__iff,axiom, % 164.98/164.97 ! [V_m_2,V_w_2] : % 164.98/164.97 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 164.98/164.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 164.98/164.97 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 164.98/164.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 164.98/164.97 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__eq__iff2,axiom, % 164.98/164.97 ! [V_w_2,V_m_2] : % 164.98/164.97 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 164.98/164.97 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 164.98/164.97 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 164.98/164.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 164.98/164.97 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__le__eq__zle,axiom, % 164.98/164.97 ! [V_z_2,V_w_2] : % 164.98/164.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 164.98/164.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 164.98/164.97 => ( 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))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_split__nat,axiom, % 164.98/164.97 ! [V_i_2,V_P_2] : % 164.98/164.97 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) % 164.98/164.97 <=> ( ! [B_n] : % 164.98/164.97 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 164.98/164.97 => hBOOL(hAPP(V_P_2,B_n)) ) % 164.98/164.97 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.97 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__add__distrib,axiom, % 164.98/164.97 ! [V_z_H,V_z] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 164.98/164.97 => 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)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 164.98/164.97 ! [V_y,V_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 164.98/164.97 => 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)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__mult__distrib,axiom, % 164.98/164.97 ! [V_z_H,V_z] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 164.98/164.97 => 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)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 164.98/164.97 ! [V_y,V_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 164.98/164.97 => 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)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 164.98/164.97 ! [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))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__diff__distrib,axiom, % 164.98/164.97 ! [V_z,V_z_H] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 164.98/164.97 => 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)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 164.98/164.97 ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 164.98/164.97 ! [V_y,V_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 164.98/164.97 => 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)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__div__distrib,axiom, % 164.98/164.97 ! [V_y,V_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.97 => 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)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_card__greaterThanAtMost__int,axiom, % 164.98/164.97 ! [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)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 164.98/164.97 ! [V_n,V_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.97 => 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)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__power__eq,axiom, % 164.98/164.97 ! [V_n,V_z] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 164.98/164.97 => 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) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 164.98/164.97 ! [V_A_2,V_f_2,T_a] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_a),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 164.98/164.97 ! [V_y,V_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 164.98/164.97 => 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)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_one__less__nat__eq,axiom, % 164.98/164.97 ! [V_z_2] : % 164.98/164.97 ( 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))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__less__iff,axiom, % 164.98/164.97 ! [V_m_2,V_w_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 164.98/164.97 <=> 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))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 164.98/164.97 ! [V_z] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 164.98/164.97 => 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)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__mult__distrib__neg,axiom, % 164.98/164.97 ! [V_z_H,V_z] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.97 => 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))) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I11_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_image__uminus__greaterThan,axiom, % 164.98/164.97 ! [V_x_2,T_a] : % 164.98/164.97 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.97 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_image__uminus__lessThan,axiom, % 164.98/164.97 ! [V_x_2,T_a] : % 164.98/164.97 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.97 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__int_I5_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_greaterThan__Suc,axiom, % 164.98/164.97 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_card__greaterThanLessThan__int,axiom, % 164.98/164.97 ! [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)))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__aux__def,axiom, % 164.98/164.97 ! [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) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__morphism__nat__int,axiom, % 164.98/164.97 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))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__of__nat,axiom, % 164.98/164.97 ! [V_k,T_a] : % 164.98/164.97 ( class_Rings_Oring__1(T_a) % 164.98/164.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.97 => 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)))) ) % 164.98/164.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.97 => 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)) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 164.98/164.97 ! [V_B_2,V_A_2] : % 164.98/164.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 164.98/164.97 => 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))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_sum__diff__distrib,axiom, % 164.98/164.97 ! [V_n_2,V_P_2,V_Q_2] : % 164.98/164.97 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x))) % 164.98/164.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__eq__iff,axiom, % 164.98/164.97 ! [V_z_2,V_w_2,T_a] : % 164.98/164.97 ( class_Int_Oring__char__0(T_a) % 164.98/164.97 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 164.98/164.97 <=> V_w_2 = V_z_2 ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 164.98/164.97 ! [V_B_2,V_A_2] : % 164.98/164.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 164.98/164.97 => 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)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 164.98/164.97 ! [V_B_2,V_A_2] : % 164.98/164.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 164.98/164.97 => 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)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__int__eq,axiom, % 164.98/164.97 ! [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) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 164.98/164.97 ! [V_B_2,V_A_2] : % 164.98/164.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 164.98/164.97 => ( V_A_2 = V_B_2 % 164.98/164.97 <=> 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) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__0,axiom, % 164.98/164.97 ! [T_a] : % 164.98/164.97 ( class_Rings_Oring__1(T_a) % 164.98/164.97 => 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) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__0__eq__iff,axiom, % 164.98/164.97 ! [V_z_2,T_a] : % 164.98/164.97 ( class_Int_Oring__char__0(T_a) % 164.98/164.97 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 164.98/164.97 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__eq__0__iff,axiom, % 164.98/164.97 ! [V_z_2,T_a] : % 164.98/164.97 ( class_Int_Oring__char__0(T_a) % 164.98/164.97 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.97 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 164.98/164.97 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__le__iff,axiom, % 164.98/164.97 ! [V_z_2,V_w_2,T_a] : % 164.98/164.97 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__less__iff,axiom, % 164.98/164.97 ! [V_z_2,V_w_2,T_a] : % 164.98/164.97 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__add,axiom, % 164.98/164.97 ! [V_z,V_w,T_a] : % 164.98/164.97 ( class_Rings_Oring__1(T_a) % 164.98/164.97 => 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)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__mult,axiom, % 164.98/164.97 ! [V_z,V_w,T_a] : % 164.98/164.97 ( class_Rings_Oring__1(T_a) % 164.98/164.97 => 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)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__1,axiom, % 164.98/164.97 ! [T_a] : % 164.98/164.97 ( class_Rings_Oring__1(T_a) % 164.98/164.97 => 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) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__diff,axiom, % 164.98/164.97 ! [V_z,V_w,T_a] : % 164.98/164.97 ( class_Rings_Oring__1(T_a) % 164.98/164.97 => 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)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__of__nat__eq,axiom, % 164.98/164.97 ! [V_n,T_a] : % 164.98/164.97 ( class_Rings_Oring__1(T_a) % 164.98/164.97 => 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) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__minus,axiom, % 164.98/164.97 ! [V_z,T_a] : % 164.98/164.97 ( class_Rings_Oring__1(T_a) % 164.98/164.97 => 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)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Ints__of__int,axiom, % 164.98/164.97 ! [V_z_2,T_a] : % 164.98/164.97 ( class_Rings_Oring__1(T_a) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__power,axiom, % 164.98/164.97 ! [V_n,V_z,T_a] : % 164.98/164.97 ( class_Rings_Oring__1(T_a) % 164.98/164.97 => 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) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_nat__set__def,axiom, % 164.98/164.97 ! [V_S_2] : % 164.98/164.97 ( c_Nat__Transfer_Onat__set(V_S_2) % 164.98/164.97 <=> ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 164.98/164.97 ! [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)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 164.98/164.97 ! [V_f_2,V_A_2,T_a] : % 164.98/164.97 ( ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.97 & class_Groups_Ocomm__monoid__mult(T_a) ) % 164.98/164.97 => ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__setsum,axiom, % 164.98/164.97 ! [V_A_2,V_f_2,T_b,T_a] : % 164.98/164.97 ( class_Rings_Oring__1(T_a) % 164.98/164.97 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__setprod,axiom, % 164.98/164.97 ! [V_A_2,V_f_2,T_b,T_a] : % 164.98/164.97 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 164.98/164.97 & class_Rings_Oring__1(T_a) ) % 164.98/164.97 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,T_b),c_Int_Oring__1__class_Oof__int(T_a)),V_f_2)),V_A_2) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 164.98/164.97 ! [V_B_2,V_A_2] : % 164.98/164.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 164.98/164.97 => 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))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__nat__int__set__return__embed,axiom, % 164.98/164.97 ! [V_A_2] : % 164.98/164.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => 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 ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 164.98/164.97 ! [V_x_2,V_A_2] : % 164.98/164.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__0__le__iff,axiom, % 164.98/164.97 ! [V_z_2,T_a] : % 164.98/164.97 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__le__0__iff,axiom, % 164.98/164.97 ! [V_z_2,T_a] : % 164.98/164.97 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__0__less__iff,axiom, % 164.98/164.97 ! [V_z_2,T_a] : % 164.98/164.97 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__int__less__0__iff,axiom, % 164.98/164.97 ! [V_z_2,T_a] : % 164.98/164.97 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2)),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_of__nat__nat,axiom, % 164.98/164.97 ! [V_z,T_a] : % 164.98/164.97 ( class_Rings_Oring__1(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 164.98/164.97 => 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) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 164.98/164.97 ! [V_f_2,V_A_2,T_a] : % 164.98/164.97 ( ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.97 & class_Groups_Ocomm__monoid__mult(T_a) ) % 164.98/164.97 => ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_a,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 164.98/164.97 ! [V_A_2] : % 164.98/164.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 164.98/164.97 <=> 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))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 164.98/164.97 ! [V_A_2] : % 164.98/164.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => 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)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 164.98/164.97 ! [V_B_2,V_A_2] : % 164.98/164.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.98/164.97 <=> 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))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 164.98/164.97 ! [V_B_2,V_A_2] : % 164.98/164.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.98/164.97 <=> 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))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 164.98/164.97 ! [V_A_2,V_x_2] : % 164.98/164.97 ( c_Nat__Transfer_Ois__nat(V_x_2) % 164.98/164.97 => ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 164.98/164.97 <=> 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))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeast__Suc,axiom, % 164.98/164.97 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setsum__natinterval__difff,axiom, % 164.98/164.97 ! [V_f_2,V_n_2,V_m_2,T_a] : % 164.98/164.97 ( class_Groups_Oab__group__add(T_a) % 164.98/164.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 164.98/164.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_gauss__sum,axiom, % 164.98/164.97 ! [V_n_2,T_a] : % 164.98/164.97 ( class_Rings_Ocomm__semiring__1(T_a) % 164.98/164.97 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Groups_Oone__class_Oone(T_a))) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I12_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_finite__atLeastAtMost,axiom, % 164.98/164.97 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeast__eq__iff,axiom, % 164.98/164.97 ! [V_y_2,V_x_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2) % 164.98/164.97 <=> V_x_2 = V_y_2 ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 164.98/164.97 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 164.98/164.97 ! [V_y,V_x] : % 164.98/164.97 ( c_Nat__Transfer_Ois__nat(V_x) % 164.98/164.97 => ( c_Nat__Transfer_Ois__nat(V_y) % 164.98/164.97 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 164.98/164.97 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 164.98/164.97 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 164.98/164.97 ! [V_y,V_x] : % 164.98/164.97 ( c_Nat__Transfer_Ois__nat(V_x) % 164.98/164.97 => ( c_Nat__Transfer_Ois__nat(V_y) % 164.98/164.97 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 164.98/164.97 ! [V_y,V_x] : % 164.98/164.97 ( c_Nat__Transfer_Ois__nat(V_x) % 164.98/164.97 => ( c_Nat__Transfer_Ois__nat(V_y) % 164.98/164.97 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 164.98/164.97 ! [V_n,V_x] : % 164.98/164.97 ( c_Nat__Transfer_Ois__nat(V_x) % 164.98/164.97 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I13_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_all__nat__less,axiom, % 164.98/164.97 ! [V_P_2,V_n_2] : % 164.98/164.97 ( ! [B_m] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 164.98/164.97 => hBOOL(hAPP(V_P_2,B_m)) ) % 164.98/164.97 <=> ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) % 164.98/164.97 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ex__nat__less,axiom, % 164.98/164.97 ! [V_P_2,V_n_2] : % 164.98/164.97 ( ? [B_m] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 164.98/164.97 & hBOOL(hAPP(V_P_2,B_m)) ) % 164.98/164.97 <=> ? [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) % 164.98/164.97 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 164.98/164.97 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 164.98/164.97 ! [V_y,V_x] : % 164.98/164.97 ( c_Nat__Transfer_Ois__nat(V_x) % 164.98/164.97 => ( c_Nat__Transfer_Ois__nat(V_y) % 164.98/164.97 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeastatMost__empty__iff2,axiom, % 164.98/164.97 ! [V_b_2,V_a_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) % 164.98/164.97 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeastatMost__empty__iff,axiom, % 164.98/164.97 ! [V_b_2,V_a_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.97 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeastatMost__empty,axiom, % 164.98/164.97 ! [V_a_2,V_b_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) % 164.98/164.97 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeastatMost__subset__iff,axiom, % 164.98/164.97 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2))) % 164.98/164.97 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 164.98/164.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeastAtMost__singleton,axiom, % 164.98/164.97 ! [V_a_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeastAtMost__singleton__iff,axiom, % 164.98/164.97 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 164.98/164.97 <=> ( V_a_2 = V_b_2 % 164.98/164.97 & V_b_2 = V_ca_2 ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeastAtMost__singleton_H,axiom, % 164.98/164.97 ! [V_b_2,V_a_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => ( V_a_2 = V_b_2 % 164.98/164.97 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_image__uminus__atLeastAtMost,axiom, % 164.98/164.97 ! [V_y_2,V_x_2,T_a] : % 164.98/164.97 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.97 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_image__Suc__atLeastAtMost,axiom, % 164.98/164.97 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 164.98/164.97 ! [V_n_2,V_m_2,V_f_2,T_a] : % 164.98/164.97 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 164.98/164.97 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 164.98/164.97 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 164.98/164.97 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2) ). % 164.98/164.97 % 164.98/164.97 fof(fact_is__nat__def,axiom, % 164.98/164.97 ! [V_x_2] : % 164.98/164.97 ( c_Nat__Transfer_Ois__nat(V_x_2) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_image__add__atLeastAtMost,axiom, % 164.98/164.97 ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeast__iff,axiom, % 164.98/164.97 ! [V_k_2,V_i_2,T_a] : % 164.98/164.97 ( class_Orderings_Oord(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeast__subset__iff,axiom, % 164.98/164.97 ! [V_y_2,V_x_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeast__0,axiom, % 164.98/164.97 hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_card__atLeastAtMost,axiom, % 164.98/164.97 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeastAtMostSuc__conv,axiom, % 164.98/164.97 ! [V_n_2,V_m_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 164.98/164.97 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Compl__lessThan,axiom, % 164.98/164.97 ! [V_k_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Compl__atLeast,axiom, % 164.98/164.97 ! [V_k_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 164.98/164.97 ! [V_x_2,V_A_2] : % 164.98/164.97 ( c_Nat__Transfer_Onat__set(V_A_2) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 164.98/164.97 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 164.98/164.97 ! [V_k_2,V_f_2] : % 164.98/164.97 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeast__Suc__greaterThan,axiom, % 164.98/164.97 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I21_J,axiom, % 164.98/164.97 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__int_I15_J,axiom, % 164.98/164.97 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeastatMost__psubset__iff,axiom, % 164.98/164.97 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2))) % 164.98/164.97 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 164.98/164.97 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) % 164.98/164.97 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_a_2)) % 164.98/164.97 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) ) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I22_J,axiom, % 164.98/164.97 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__int_I4_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__int_I16_J,axiom, % 164.98/164.97 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__int_I13_J,axiom, % 164.98/164.97 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__int_I12_J,axiom, % 164.98/164.97 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__int_I7_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setsum__head__Suc,axiom, % 164.98/164.97 ! [V_f_2,V_n_2,V_m_2,T_a] : % 164.98/164.97 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I14_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__int_I8_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__int_I6_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setsum__cl__ivl__Suc,axiom, % 164.98/164.97 ! [V_f_2,V_m_2,V_n_2,T_a] : % 164.98/164.97 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.97 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_a) ) % 164.98/164.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setsum__head,axiom, % 164.98/164.97 ! [V_P_2,V_n_2,V_m_2,T_a] : % 164.98/164.97 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setsum__ub__add__nat,axiom, % 164.98/164.97 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] : % 164.98/164.97 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2)))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I6_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I5_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I18_J,axiom, % 164.98/164.97 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2),V_u_2) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I1_J,axiom, % 164.98/164.97 ! [V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_l_2) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I19_J,axiom, % 164.98/164.97 ! [V_u_2,V_m_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 164.98/164.97 ! [V_f_2,V_A_2,T_a] : % 164.98/164.97 ( ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.98/164.97 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 164.98/164.97 ! [V_f_2,V_A_2,T_a] : % 164.98/164.97 ( ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 164.98/164.97 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_a),c_Int_Onat),V_f_2)),V_A_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_decr__mult__lemma,axiom, % 164.98/164.97 ! [V_k_2,V_P_2,V_d_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 164.98/164.97 => ( ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(V_P_2,B_x)) % 164.98/164.97 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 164.98/164.97 => ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(V_P_2,B_x)) % 164.98/164.97 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_negD,axiom, % 164.98/164.97 ! [V_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.97 => ? [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))) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_incr__mult__lemma,axiom, % 164.98/164.97 ! [V_k_2,V_P_2,V_d_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 164.98/164.97 => ( ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(V_P_2,B_x)) % 164.98/164.97 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 164.98/164.97 => ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(V_P_2,B_x)) % 164.98/164.97 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_finite__atLeastAtMost__int,axiom, % 164.98/164.97 ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 164.98/164.97 ! [V_y_2,V_x_2] : % 164.98/164.97 ( c_Nat__Transfer_Ois__nat(V_x_2) % 164.98/164.97 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 164.98/164.97 ! [V_y_2,V_x_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 164.98/164.97 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 164.98/164.97 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 164.98/164.97 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2) ). % 164.98/164.97 % 164.98/164.97 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 164.98/164.97 ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_simp__from__to,axiom, % 164.98/164.97 ! [V_i_2,V_j_2] : % 164.98/164.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 164.98/164.97 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) ) % 164.98/164.97 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 164.98/164.97 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_card__atLeastAtMost__int,axiom, % 164.98/164.97 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 164.98/164.97 ! [V_n_2,V_m_2] : % 164.98/164.97 ( c_Nat__Transfer_Ois__nat(V_m_2) % 164.98/164.97 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 164.98/164.97 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2))) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_bset_I8_J,axiom, % 164.98/164.97 ! [V_B_2,V_t_2,V_D_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) % 164.98/164.97 => ! [B_x] : % 164.98/164.97 ( ! [B_xa] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 164.98/164.97 => ! [B_xb] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 164.98/164.97 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_aset_I6_J,axiom, % 164.98/164.97 ! [V_A_2,V_t_2,V_D_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) % 164.98/164.97 => ! [B_x] : % 164.98/164.97 ( ! [B_xa] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 164.98/164.97 => ! [B_xb] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 164.98/164.97 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_bset_I3_J,axiom, % 164.98/164.97 ! [V_B_2,V_t_2,V_D_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2)) % 164.98/164.97 => ( ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 164.98/164.97 => ! [B_xa] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 164.98/164.97 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 164.98/164.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_aset_I3_J,axiom, % 164.98/164.97 ! [V_A_2,V_t_2,V_D_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2)) % 164.98/164.97 => ( ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 164.98/164.97 => ! [B_xa] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 164.98/164.97 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 164.98/164.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_aset_I5_J,axiom, % 164.98/164.97 ! [V_A_2,V_t_2,V_D_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 164.98/164.97 => ! [B_x] : % 164.98/164.97 ( ! [B_xa] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 164.98/164.97 => ! [B_xb] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 164.98/164.97 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_aset_I4_J,axiom, % 164.98/164.97 ! [V_A_2,V_t_2,V_D_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 164.98/164.97 => ! [B_x] : % 164.98/164.97 ( ! [B_xa] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 164.98/164.97 => ! [B_xb] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 164.98/164.97 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 164.98/164.97 => ( B_x != V_t_2 % 164.98/164.97 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_bset_I4_J,axiom, % 164.98/164.97 ! [V_B_2,V_t_2,V_D_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 164.98/164.97 => ! [B_x] : % 164.98/164.97 ( ! [B_xa] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 164.98/164.97 => ! [B_xb] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 164.98/164.97 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 164.98/164.97 => ( B_x != V_t_2 % 164.98/164.97 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_bset_I7_J,axiom, % 164.98/164.97 ! [V_B_2,V_t_2,V_D_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 164.98/164.97 => ! [B_x] : % 164.98/164.97 ( ! [B_xa] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 164.98/164.97 => ! [B_xb] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 164.98/164.97 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_aset_I8_J,axiom, % 164.98/164.97 ! [V_t_2,V_A_2,V_D_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 164.98/164.97 => ! [B_x] : % 164.98/164.97 ( ! [B_xa] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 164.98/164.97 => ! [B_xb] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 164.98/164.97 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 164.98/164.97 => 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))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_bset_I6_J,axiom, % 164.98/164.97 ! [V_t_2,V_B_2,V_D_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 164.98/164.97 => ! [B_x] : % 164.98/164.97 ( ! [B_xa] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 164.98/164.97 => ! [B_xb] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 164.98/164.97 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 164.98/164.97 => 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)) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_periodic__finite__ex,axiom, % 164.98/164.97 ! [V_P_2,V_d_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 164.98/164.97 => ( ! [B_x,B_k] : % 164.98/164.97 ( hBOOL(hAPP(V_P_2,B_x)) % 164.98/164.97 <=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) ) % 164.98/164.97 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 164.98/164.97 <=> ? [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) % 164.98/164.97 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_bset_I5_J,axiom, % 164.98/164.97 ! [V_t_2,V_B_2,V_D_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 164.98/164.97 => ! [B_x] : % 164.98/164.97 ( ! [B_xa] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 164.98/164.97 => ! [B_xb] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 164.98/164.97 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 164.98/164.97 => 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)) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_aset_I7_J,axiom, % 164.98/164.97 ! [V_t_2,V_A_2,V_D_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 164.98/164.97 => ! [B_x] : % 164.98/164.97 ( ! [B_xa] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) % 164.98/164.97 => ! [B_xb] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 164.98/164.97 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 164.98/164.97 => 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))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 164.98/164.97 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ex__least__nat__less,axiom, % 164.98/164.97 ! [V_n_2,V_P_2] : % 164.98/164.97 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 164.98/164.97 => ( hBOOL(hAPP(V_P_2,V_n_2)) % 164.98/164.97 => ? [B_k] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 164.98/164.97 & ! [B_i] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 164.98/164.97 => ~ hBOOL(hAPP(V_P_2,B_i)) ) % 164.98/164.97 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_finite__atMost,axiom, % 164.98/164.97 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atMost__eq__iff,axiom, % 164.98/164.97 ! [V_y_2,V_x_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2) % 164.98/164.97 <=> V_x_2 = V_y_2 ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atLeast0AtMost,axiom, % 164.98/164.97 ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) ). % 164.98/164.97 % 164.98/164.97 fof(fact_lessThan__Suc__atMost,axiom, % 164.98/164.97 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2) ). % 164.98/164.97 % 164.98/164.97 fof(fact_card__atMost,axiom, % 164.98/164.97 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atMost__Suc,axiom, % 164.98/164.97 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atMost__iff,axiom, % 164.98/164.97 ! [V_k_2,V_i_2,T_a] : % 164.98/164.97 ( class_Orderings_Oord(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atMost__subset__iff,axiom, % 164.98/164.97 ! [V_y_2,V_x_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2))) % 164.98/164.97 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Compl__atMost,axiom, % 164.98/164.97 ! [V_k_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Compl__greaterThan,axiom, % 164.98/164.97 ! [V_k_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setsum__atMost__Suc,axiom, % 164.98/164.97 ! [V_n_2,V_f_2,T_a] : % 164.98/164.97 ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atMost__0,axiom, % 164.98/164.97 hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I9_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__int_I3_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__int_I1_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_image__uminus__atLeast,axiom, % 164.98/164.97 ! [V_x_2,T_a] : % 164.98/164.97 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.97 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_image__uminus__atMost,axiom, % 164.98/164.97 ! [V_x_2,T_a] : % 164.98/164.97 ( class_Groups_Oordered__ab__group__add(T_a) % 164.98/164.97 => hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I2_J,axiom, % 164.98/164.97 ! [V_u_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I10_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_u_2) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_atMost__Int__atLeast,axiom, % 164.98/164.97 ! [V_n_2,T_a] : % 164.98/164.97 ( class_Orderings_Oorder(T_a) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_ivl__disj__un_I7_J,axiom, % 164.98/164.97 ! [V_u_2,V_l_2,T_a] : % 164.98/164.97 ( class_Orderings_Olinorder(T_a) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 164.98/164.97 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_u_2) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setprod__mono__one__right,axiom, % 164.98/164.97 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 164.98/164.97 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 164.98/164.97 => ( ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 164.98/164.97 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setprod__mono__one__left,axiom, % 164.98/164.97 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 164.98/164.97 ( class_Groups_Ocomm__monoid__mult(T_b) % 164.98/164.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 164.98/164.97 => ( ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 164.98/164.97 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_zero__less__imp__eq__int,axiom, % 164.98/164.97 ! [V_k] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 164.98/164.97 => ? [B_n] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 164.98/164.97 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setsum__mono__zero__right,axiom, % 164.98/164.97 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 164.98/164.97 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 164.98/164.97 => ( ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 164.98/164.97 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_setsum__mono__zero__left,axiom, % 164.98/164.97 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 164.98/164.97 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.97 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 164.98/164.97 => ( ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 164.98/164.97 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_T_2) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_card__Pow,axiom, % 164.98/164.97 ! [V_A_2,T_a] : % 164.98/164.97 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.97 => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_body__def,axiom, % 164.98/164.97 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ). % 164.98/164.97 % 164.98/164.97 fof(fact_field__le__mult__one__interval,axiom, % 164.98/164.97 ! [V_y,V_x,T_a] : % 164.98/164.97 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.97 => ( ! [B_z] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 164.98/164.97 => 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)) ) ) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 164.98/164.97 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 164.98/164.97 ( ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.97 & class_Groups_Ocomm__monoid__mult(T_a) ) % 164.98/164.97 => ( V_A_2 = V_B_2 % 164.98/164.97 => ( c_Nat__Transfer_Onat__set(V_B_2) % 164.98/164.97 => ( ! [B_x] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 164.98/164.97 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 164.98/164.97 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_split__neg__lemma,axiom, % 164.98/164.97 ! [V_n_2,V_P_2,V_k_2] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.97 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 164.98/164.97 <=> ! [B_i,B_j] : % 164.98/164.97 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 164.98/164.97 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.97 & 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) ) % 164.98/164.97 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_PowI,axiom, % 164.98/164.97 ! [V_B_2,V_A_2,T_a] : % 164.98/164.97 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.98/164.97 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_zdiff__zmod__left,axiom, % 164.98/164.97 ! [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) ). % 164.98/164.97 % 164.98/164.97 fof(fact_zdiff__zmod__right,axiom, % 164.98/164.97 ! [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) ). % 164.98/164.97 % 164.98/164.97 fof(fact_zmod__zminus2,axiom, % 164.98/164.97 ! [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)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_zmod__zminus__zminus,axiom, % 164.98/164.97 ! [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)) ). % 164.98/164.97 % 164.98/164.97 fof(fact_zminus__zmod,axiom, % 164.98/164.97 ! [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) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Cantors__paradox,axiom, % 164.98/164.97 ! [V_A_2,T_a] : % 164.98/164.97 ~ ? [B_f] : hAPP(c_Set_Oimage(T_a,tc_fun(T_a,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_a),V_A_2) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__diff__right__eq,axiom, % 164.98/164.97 ! [V_c,V_b,V_a,T_a] : % 164.98/164.97 ( class_Divides_Oring__div(T_a) % 164.98/164.97 => 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) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__diff__left__eq,axiom, % 164.98/164.97 ! [V_c,V_b,V_a,T_a] : % 164.98/164.97 ( class_Divides_Oring__div(T_a) % 164.98/164.97 => 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) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__diff__eq,axiom, % 164.98/164.97 ! [V_c,V_b,V_a,T_a] : % 164.98/164.97 ( class_Divides_Oring__div(T_a) % 164.98/164.97 => 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) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__diff__cong,axiom, % 164.98/164.97 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 164.98/164.97 ( class_Divides_Oring__div(T_a) % 164.98/164.97 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 164.98/164.97 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 164.98/164.97 => 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) ) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_zmod__zero,axiom, % 164.98/164.97 ! [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) ). % 164.98/164.97 % 164.98/164.97 fof(fact_zmod__self,axiom, % 164.98/164.97 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__minus__cong,axiom, % 164.98/164.97 ! [V_a_H,V_b,V_a,T_a] : % 164.98/164.97 ( class_Divides_Oring__div(T_a) % 164.98/164.97 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 164.98/164.97 => 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) ) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__minus__eq,axiom, % 164.98/164.97 ! [V_b,V_a,T_a] : % 164.98/164.97 ( class_Divides_Oring__div(T_a) % 164.98/164.97 => 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) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__0,axiom, % 164.98/164.97 ! [V_a,T_a] : % 164.98/164.97 ( class_Divides_Osemiring__div(T_a) % 164.98/164.97 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__by__0,axiom, % 164.98/164.97 ! [V_a,T_a] : % 164.98/164.97 ( class_Divides_Osemiring__div(T_a) % 164.98/164.97 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__self,axiom, % 164.98/164.97 ! [V_a,T_a] : % 164.98/164.97 ( class_Divides_Osemiring__div(T_a) % 164.98/164.97 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__mod__trivial,axiom, % 164.98/164.97 ! [V_b,V_a,T_a] : % 164.98/164.97 ( class_Divides_Osemiring__div(T_a) % 164.98/164.97 => 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) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_Pow__top,axiom, % 164.98/164.97 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_A_2))) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__mult__right__eq,axiom, % 164.98/164.97 ! [V_c,V_b,V_a,T_a] : % 164.98/164.97 ( class_Divides_Osemiring__div(T_a) % 164.98/164.97 => 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) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__mult__left__eq,axiom, % 164.98/164.97 ! [V_c,V_b,V_a,T_a] : % 164.98/164.97 ( class_Divides_Osemiring__div(T_a) % 164.98/164.97 => 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) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__mult__eq,axiom, % 164.98/164.97 ! [V_c,V_b,V_a,T_a] : % 164.98/164.97 ( class_Divides_Osemiring__div(T_a) % 164.98/164.97 => 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) ) ). % 164.98/164.97 % 164.98/164.97 fof(fact_mod__mult__mult1,axiom, % 164.98/164.97 ! [V_b,V_a,V_c,T_a] : % 164.98/164.97 ( class_Divides_Osemiring__div(T_a) % 164.98/164.97 => 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)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__mult__mult2,axiom, % 164.98/164.98 ! [V_b,V_c,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__simps_I4_J,axiom, % 164.98/164.98 ! [V_b,V_c,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__mult__cong,axiom, % 164.98/164.98 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 164.98/164.98 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 164.98/164.98 => 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) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__add__self2,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__add__self1,axiom, % 164.98/164.98 ! [V_a,V_b,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__add__right__eq,axiom, % 164.98/164.98 ! [V_c,V_b,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__add__left__eq,axiom, % 164.98/164.98 ! [V_c,V_b,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__add__eq,axiom, % 164.98/164.98 ! [V_c,V_b,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__simps_I2_J,axiom, % 164.98/164.98 ! [V_c,V_b,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__simps_I1_J,axiom, % 164.98/164.98 ! [V_b,V_c,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__add__cong,axiom, % 164.98/164.98 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 164.98/164.98 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 164.98/164.98 => 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) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Pow__not__empty,axiom, % 164.98/164.98 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__zmult1__eq,axiom, % 164.98/164.98 ! [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) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__simps_I3_J,axiom, % 164.98/164.98 ! [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) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 164.98/164.98 ! [V_y,V_x] : % 164.98/164.98 ( c_Nat__Transfer_Ois__nat(V_x) % 164.98/164.98 => ( c_Nat__Transfer_Ois__nat(V_y) % 164.98/164.98 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zpower__zmod,axiom, % 164.98/164.98 ! [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) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Pow__bottom,axiom, % 164.98/164.98 ! [V_B_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Set_OPow(T_a),V_B_2))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Pow__empty,axiom, % 164.98/164.98 ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_finite__Pow__iff,axiom, % 164.98/164.98 ! [V_A_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2))) % 164.98/164.98 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Pow__insert,axiom, % 164.98/164.98 ! [V_A_2,V_a_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_a),V_a_2)),hAPP(c_Set_OPow(T_a),V_A_2))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Pow__mono,axiom, % 164.98/164.98 ! [V_B_2,V_A_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Pow__iff,axiom, % 164.98/164.98 ! [V_B_2,V_A_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 164.98/164.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_PowD,axiom, % 164.98/164.98 ! [V_B_2,V_A_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_image__Pow__surj,axiom, % 164.98/164.98 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 164.98/164.98 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2 % 164.98/164.98 => hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(c_Set_OPow(T_a),V_B_2) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Pow__UNIV,axiom, % 164.98/164.98 ! [T_a] : hAPP(c_Set_OPow(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Un__Pow__subset,axiom, % 164.98/164.98 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Pow__Int__eq,axiom, % 164.98/164.98 ! [V_B_2,V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2)),hAPP(c_Set_OPow(T_a),V_B_2)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__mult__self2__is__0,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__mult__self1__is__0,axiom, % 164.98/164.98 ! [V_a,V_b,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__mult__self1,axiom, % 164.98/164.98 ! [V_b,V_c,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__mult__self2,axiom, % 164.98/164.98 ! [V_c,V_b,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__by__1,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__div__trivial,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__le__nonneg__dividend,axiom, % 164.98/164.98 ! [V_k,V_m] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 164.98/164.98 => 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)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 164.98/164.98 ! [V_y,V_x] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 164.98/164.98 => 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))) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_neg__mod__bound,axiom, % 164.98/164.98 ! [V_a,V_b] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.98 => 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))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_pos__mod__bound,axiom, % 164.98/164.98 ! [V_a,V_b] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 164.98/164.98 => 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)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__eq__0__iff,axiom, % 164.98/164.98 ! [V_d_2,V_m_2] : % 164.98/164.98 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__zminus2__not__zero,axiom, % 164.98/164.98 ! [V_l,V_k] : % 164.98/164.98 ( 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) % 164.98/164.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__zminus1__not__zero,axiom, % 164.98/164.98 ! [V_l,V_k] : % 164.98/164.98 ( 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) % 164.98/164.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_DIVISION__BY__ZERO,axiom, % 164.98/164.98 ! [V_a] : % 164.98/164.98 ( 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) % 164.98/164.98 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__zdiv__trivial,axiom, % 164.98/164.98 ! [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) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zdiv__zadd1__eq,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_image__Pow__mono,axiom, % 164.98/164.98 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2)),V_B_2)) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_f_2)),hAPP(c_Set_OPow(T_b),V_A_2))),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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 ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__div__equality2,axiom, % 164.98/164.98 ! [V_a,V_b,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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 ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__div__equality,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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 ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_div__mod__equality2,axiom, % 164.98/164.98 ! [V_c,V_a,V_b,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_div__mod__equality,axiom, % 164.98/164.98 ! [V_c,V_b,V_a,T_a] : % 164.98/164.98 ( class_Divides_Osemiring__div(T_a) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_pos__mod__sign,axiom, % 164.98/164.98 ! [V_a,V_b] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 164.98/164.98 => 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))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_pos__mod__conj,axiom, % 164.98/164.98 ! [V_a,V_b] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 164.98/164.98 => ( 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))) % 164.98/164.98 & 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)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__pos__pos__trivial,axiom, % 164.98/164.98 ! [V_b,V_a] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 164.98/164.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_neg__mod__sign,axiom, % 164.98/164.98 ! [V_a,V_b] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.98 => 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))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_neg__mod__conj,axiom, % 164.98/164.98 ! [V_a,V_b] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.98 => ( 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))) % 164.98/164.98 & 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))) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__neg__neg__trivial,axiom, % 164.98/164.98 ! [V_b,V_a] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 164.98/164.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__zminus1__eq__if,axiom, % 164.98/164.98 ! [V_b,V_a] : % 164.98/164.98 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => 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) ) % 164.98/164.98 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => 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)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__zminus2__eq__if,axiom, % 164.98/164.98 ! [V_b,V_a] : % 164.98/164.98 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => 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) ) % 164.98/164.98 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => 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) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__zdiv__equality,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zdiv__zmult1__eq,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zdiv__zmod__equality,axiom, % 164.98/164.98 ! [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) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zdiv__zmod__equality2,axiom, % 164.98/164.98 ! [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) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmult__div__cancel,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__zdiv__equality_H,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__pos__neg__trivial,axiom, % 164.98/164.98 ! [V_b,V_a] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 164.98/164.98 => ( 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))) % 164.98/164.98 => 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) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_split__zmod,axiom, % 164.98/164.98 ! [V_k_2,V_n_2,V_P_2] : % 164.98/164.98 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 164.98/164.98 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 164.98/164.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 164.98/164.98 => ! [B_i,B_j] : % 164.98/164.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 164.98/164.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 164.98/164.98 & 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) ) % 164.98/164.98 => hBOOL(hAPP(V_P_2,B_j)) ) ) % 164.98/164.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.98 => ! [B_i,B_j] : % 164.98/164.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 164.98/164.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.98 & 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) ) % 164.98/164.98 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmult2__lemma__aux3,axiom, % 164.98/164.98 ! [V_q,V_b,V_r,V_c] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 164.98/164.98 => 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))) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmult2__lemma__aux4,axiom, % 164.98/164.98 ! [V_q,V_b,V_r,V_c] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 164.98/164.98 => 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))) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmult2__lemma__aux1,axiom, % 164.98/164.98 ! [V_q,V_r,V_b,V_c] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.98 => 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))) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmult2__lemma__aux2,axiom, % 164.98/164.98 ! [V_q,V_r,V_b,V_c] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.98 => 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))) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_divmod__int__rel__mod__eq,axiom, % 164.98/164.98 ! [V_y,V_q_1,V_b_1,V_a_1] : % 164.98/164.98 ( 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) % 164.98/164.98 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 164.98/164.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 164.98/164.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 164.98/164.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 164.98/164.98 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__zmult2__eq,axiom, % 164.98/164.98 ! [V_b,V_a,V_c] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 164.98/164.98 => 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)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zdiv__zminus2__eq__if,axiom, % 164.98/164.98 ! [V_a,V_b] : % 164.98/164.98 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => 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)) ) % 164.98/164.98 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => 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)) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zdiv__zminus1__eq__if,axiom, % 164.98/164.98 ! [V_a,V_b] : % 164.98/164.98 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => 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)) ) % 164.98/164.98 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => 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)) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_split__pos__lemma,axiom, % 164.98/164.98 ! [V_n_2,V_P_2,V_k_2] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 164.98/164.98 <=> ! [B_i,B_j] : % 164.98/164.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 164.98/164.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 164.98/164.98 & 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) ) % 164.98/164.98 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_z3mod__def,axiom, % 164.98/164.98 ! [V_k,V_l] : % 164.98/164.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 164.98/164.98 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 164.98/164.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 164.98/164.98 => 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)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Powp__Pow__eq,axiom, % 164.98/164.98 ! [V_x_2,V_A_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2)) % 164.98/164.98 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_sgn__if,axiom, % 164.98/164.98 ! [V_x,T_a] : % 164.98/164.98 ( class_Groups_Osgn__if(T_a) % 164.98/164.98 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.98 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 164.98/164.98 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 164.98/164.98 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 164.98/164.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 164.98/164.98 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_sgn__neg,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.98 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_sgn__1__neg,axiom, % 164.98/164.98 ! [V_a_2,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) % 164.98/164.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__less,axiom, % 164.98/164.98 ! [V_n,V_m] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.98/164.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__less__eq__dividend,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 164.98/164.98 ! [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) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__mult__distrib2,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__mult__distrib,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_sgn__sgn,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_sgn0,axiom, % 164.98/164.98 ! [T_a] : % 164.98/164.98 ( class_Groups_Osgn__if(T_a) % 164.98/164.98 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_sgn__0__0,axiom, % 164.98/164.98 ! [V_a_2,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.98 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_sgn__times,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__1,axiom, % 164.98/164.98 ! [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) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__Suc,axiom, % 164.98/164.98 ! [V_n,V_m] : % 164.98/164.98 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 164.98/164.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 164.98/164.98 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 164.98/164.98 => 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)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__less__divisor,axiom, % 164.98/164.98 ! [V_m,V_n] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.98 => 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)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__eq__0__iff,axiom, % 164.98/164.98 ! [V_d_2,V_m_2] : % 164.98/164.98 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.98 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__if,axiom, % 164.98/164.98 ! [V_n,V_m] : % 164.98/164.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.98/164.98 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 164.98/164.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.98/164.98 => 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) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__geq,axiom, % 164.98/164.98 ! [V_n,V_m] : % 164.98/164.98 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__mult__self3,axiom, % 164.98/164.98 ! [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) ). % 164.98/164.98 % 164.98/164.98 fof(fact_le__mod__geq,axiom, % 164.98/164.98 ! [V_m,V_n] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zmod__int,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_div__add1__eq,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__le__divisor,axiom, % 164.98/164.98 ! [V_m,V_n] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 164.98/164.98 => 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)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__mult__self4,axiom, % 164.98/164.98 ! [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) ). % 164.98/164.98 % 164.98/164.98 fof(fact_sgn__less,axiom, % 164.98/164.98 ! [V_a_2,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_sgn__greater,axiom, % 164.98/164.98 ! [V_a_2,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2))) % 164.98/164.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__mult2__eq,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_div__mult1__eq,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Divides_Omod__div__equality_H,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mult__div__cancel,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_div__mod__equality_H,axiom, % 164.98/164.98 ! [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)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Powp__mono,axiom, % 164.98/164.98 ! [V_B_2,V_A_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_a,V_A_2)),c_Predicate_OPowp(T_a,V_B_2))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mod__lemma,axiom, % 164.98/164.98 ! [V_q,V_b,V_r,V_c] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 164.98/164.98 => 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))) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_split__mod,axiom, % 164.98/164.98 ! [V_k_2,V_n_2,V_P_2] : % 164.98/164.98 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 164.98/164.98 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.98 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 164.98/164.98 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 164.98/164.98 => ! [B_i,B_j] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 164.98/164.98 => ( 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) % 164.98/164.98 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Suc__times__mod__eq,axiom, % 164.98/164.98 ! [V_m,V_k] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 164.98/164.98 ! [V_y,V_x] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 164.98/164.98 => 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)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_nat__mod__distrib,axiom, % 164.98/164.98 ! [V_y,V_x] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 164.98/164.98 => 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)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_sgn__1__pos,axiom, % 164.98/164.98 ! [V_a_2,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) % 164.98/164.98 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_sgn__pos,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.98 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zsgn__def,axiom, % 164.98/164.98 ! [V_i] : % 164.98/164.98 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 164.98/164.98 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 164.98/164.98 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 164.98/164.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 164.98/164.98 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_decr__lemma,axiom, % 164.98/164.98 ! [V_z,V_x,V_d] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_incr__lemma,axiom, % 164.98/164.98 ! [V_x,V_z,V_d] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 164.98/164.98 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 164.98/164.98 ( ( class_Groups_Ocomm__monoid__add(T_a) % 164.98/164.98 & class_Groups_Ocomm__monoid__mult(T_a) ) % 164.98/164.98 => ( V_A_2 = V_B_2 % 164.98/164.98 => ( c_Nat__Transfer_Onat__set(V_B_2) % 164.98/164.98 => ( ! [B_x] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 164.98/164.98 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 164.98/164.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_g_2),V_B_2) ) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_setprod__pos__nat,axiom, % 164.98/164.98 ! [V_f_2,V_S_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 164.98/164.98 => ( ! [B_x] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_card__less__Suc,axiom, % 164.98/164.98 ! [V_i_2,V_M_2] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 164.98/164.98 => 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))))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_CollectI,axiom, % 164.98/164.98 ! [T_a,V_a_2,V_P_2] : % 164.98/164.98 ( hBOOL(hAPP(V_P_2,V_a_2)) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_finite__Collect__conjI,axiom, % 164.98/164.98 ! [V_Q_2,V_P_2,T_a] : % 164.98/164.98 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 164.98/164.98 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) % 164.98/164.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_setsum__abs,axiom, % 164.98/164.98 ! [V_A_2,V_f_2,T_b,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_finite__Collect__less__nat,axiom, % 164.98/164.98 ! [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)))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_finite__Collect__le__nat,axiom, % 164.98/164.98 ! [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)))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_setsum__abs__ge__zero,axiom, % 164.98/164.98 ! [V_A_2,V_f_2,T_b,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__ge__self,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__le__D1,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Collect__empty__eq,axiom, % 164.98/164.98 ! [V_P_2,T_a] : % 164.98/164.98 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.98 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_empty__Collect__eq,axiom, % 164.98/164.98 ! [V_P_2,T_a] : % 164.98/164.98 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2) % 164.98/164.98 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__minus__commute,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__divide,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__int__eq,axiom, % 164.98/164.98 ! [V_m] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__one,axiom, % 164.98/164.98 ! [T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__minus__cancel,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__zero,axiom, % 164.98/164.98 ! [T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__eq__0,axiom, % 164.98/164.98 ! [V_a_2,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.98 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__idempotent,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Collect__def,axiom, % 164.98/164.98 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__mult__self,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__mult,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__add__abs,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__of__nat,axiom, % 164.98/164.98 ! [V_n,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_power__abs,axiom, % 164.98/164.98 ! [V_n,V_a,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_CollectE,axiom, % 164.98/164.98 ! [V_P_2,V_a_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 164.98/164.98 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_CollectD,axiom, % 164.98/164.98 ! [V_P_2,V_a_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 164.98/164.98 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mem__Collect__eq,axiom, % 164.98/164.98 ! [V_P_2,V_a_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 164.98/164.98 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Collect__mem__eq,axiom, % 164.98/164.98 ! [V_A_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)) = V_A_2 ). % 164.98/164.98 % 164.98/164.98 fof(fact_empty__def,axiom, % 164.98/164.98 ! [T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_finite__Collect__disjI,axiom, % 164.98/164.98 ! [V_Q_2,V_P_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2)))) % 164.98/164.98 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 164.98/164.98 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_insert__Collect,axiom, % 164.98/164.98 ! [V_P_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__setsum__abs,axiom, % 164.98/164.98 ! [V_A_2,V_f_2,T_b,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_UNIV__def,axiom, % 164.98/164.98 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fTrue)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Collect__disj__eq,axiom, % 164.98/164.98 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Collect__conj__eq,axiom, % 164.98/164.98 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_Set_OCollect(T_a),V_Q_2)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__setprod,axiom, % 164.98/164.98 ! [V_A_2,V_f_2,T_b,T_a] : % 164.98/164.98 ( class_Fields_Olinordered__field(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),c_Groups_Oabs__class_Oabs(T_a)),V_f_2)),V_A_2) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Collect__neg__eq,axiom, % 164.98/164.98 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_vimage__Collect__eq,axiom, % 164.98/164.98 ! [V_P_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),V_P_2),V_f_2)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__ge__zero,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__le__zero__iff,axiom, % 164.98/164.98 ! [V_a_2,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.98 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__of__nonneg,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__of__pos,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zero__less__abs__iff,axiom, % 164.98/164.98 ! [V_a_2,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2))) % 164.98/164.98 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__not__less__zero,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__triangle__ineq,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__mult__less,axiom, % 164.98/164.98 ! [V_d,V_b,V_c,V_a,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__triangle__ineq3,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__triangle__ineq2,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__triangle__ineq2__sym,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__le__D2,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__leI,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__le__iff,axiom, % 164.98/164.98 ! [V_b_2,V_a_2,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 164.98/164.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 164.98/164.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__ge__minus__self,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__less__iff,axiom, % 164.98/164.98 ! [V_b_2,V_a_2,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 164.98/164.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 164.98/164.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_nonzero__abs__divide,axiom, % 164.98/164.98 ! [V_a,V_b,T_a] : % 164.98/164.98 ( class_Fields_Olinordered__field(T_a) % 164.98/164.98 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__power__minus,axiom, % 164.98/164.98 ! [V_n,V_a,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__zmult__eq__1,axiom, % 164.98/164.98 ! [V_n,V_m] : % 164.98/164.98 ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_mult__sgn__abs,axiom, % 164.98/164.98 ! [V_x,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__sgn,axiom, % 164.98/164.98 ! [V_k,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_insert__compr,axiom, % 164.98/164.98 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_insert__compr__raw,axiom, % 164.98/164.98 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Un__def,axiom, % 164.98/164.98 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Int__Collect,axiom, % 164.98/164.98 ! [V_P_2,V_A_2,V_x_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))) % 164.98/164.98 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 164.98/164.98 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Int__def,axiom, % 164.98/164.98 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Collect__conv__if,axiom, % 164.98/164.98 ! [T_a,V_a_2,V_P_2] : % 164.98/164.98 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 164.98/164.98 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) % 164.98/164.98 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 164.98/164.98 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Collect__conv__if2,axiom, % 164.98/164.98 ! [T_a,V_a_2,V_P_2] : % 164.98/164.98 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 164.98/164.98 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) % 164.98/164.98 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 164.98/164.98 => hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_singleton__conv,axiom, % 164.98/164.98 ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_singleton__conv2,axiom, % 164.98/164.98 ! [V_a_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_set__diff__eq,axiom, % 164.98/164.98 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_finite__Collect__not,axiom, % 164.98/164.98 ! [V_P_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 164.98/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)))) % 164.98/164.98 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_insert__def,axiom, % 164.98/164.98 ! [V_B_2,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Compl__eq,axiom, % 164.98/164.98 ! [V_A_2,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_vimage__def,axiom, % 164.98/164.98 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(T_b)),V_f_2)),V_B_2)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Collect__imp__eq,axiom, % 164.98/164.98 ! [V_Q_2,V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(c_Set_OCollect(T_a),V_Q_2)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_dom__def,axiom, % 164.98/164.98 ! [V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,tc_Option_Ooption(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),V_m_2)),c_Option_Ooption_ONone(T_b)))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_finite__M__bounded__by__nat,axiom, % 164.98/164.98 ! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__eq__mult,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Rings_Oordered__ring__abs(T_a) % 164.98/164.98 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 164.98/164.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 164.98/164.98 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 164.98/164.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__mult__pos,axiom, % 164.98/164.98 ! [V_y,V_x,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 164.98/164.98 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__triangle__ineq4,axiom, % 164.98/164.98 ! [V_b,V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__diff__triangle__ineq,axiom, % 164.98/164.98 ! [V_d,V_c,V_b,V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d))))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__of__nonpos,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__minus__le__zero,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__of__neg,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__if,axiom, % 164.98/164.98 ! [V_a,T_a] : % 164.98/164.98 ( class_Groups_Oabs__if(T_a) % 164.98/164.98 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 164.98/164.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zero__le__power__abs,axiom, % 164.98/164.98 ! [V_n,V_a,T_a] : % 164.98/164.98 ( class_Rings_Olinordered__idom(T_a) % 164.98/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_abs__div__pos,axiom, % 164.98/164.98 ! [V_x,V_y,T_a] : % 164.98/164.98 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 164.98/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 164.98/164.98 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zabs__less__one__iff,axiom, % 164.98/164.98 ! [V_z_2] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) % 164.98/164.98 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zabs__def,axiom, % 164.98/164.98 ! [V_i] : % 164.98/164.98 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 164.98/164.98 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 164.98/164.98 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_nat__abs__mult__distrib,axiom, % 164.98/164.98 ! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zero__le__zpower__abs,axiom, % 164.98/164.98 ! [V_n,V_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_setsum__setsum__restrict,axiom, % 164.98/164.98 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] : % 164.98/164.98 ( class_Groups_Ocomm__monoid__add(T_c) % 164.98/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 164.98/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 164.98/164.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,T_c),tc_fun(tc_fun(T_a,tc_HOL_Obool),T_c),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c)),hAPP(c_COMBC(T_a,T_b,T_c),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_if__image__distrib,axiom, % 164.98/164.98 ! [V_S_2,V_g_2,V_f_2,V_P_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(c_Set_Oimage(T_b,T_a,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_dom__if,axiom, % 164.98/164.98 ! [V_g_2,V_f_2,V_P_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_a,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_a),c_If(tc_Option_Ooption(T_b))),V_P_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_g_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_nat__seg__image__imp__finite,axiom, % 164.98/164.98 ! [V_n_2,V_f_2,T_a,V_A_2] : % 164.98/164.98 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2))) % 164.98/164.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_zero__less__zpower__abs__iff,axiom, % 164.98/164.98 ! [V_n_2,V_x_2] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2))) % 164.98/164.98 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 164.98/164.98 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_setsum__restrict__set_H,axiom, % 164.98/164.98 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 164.98/164.98 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_setsum__image__gen,axiom, % 164.98/164.98 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] : % 164.98/164.98 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 164.98/164.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),T_b,T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_OCollect(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))),hAPP(c_COMBC(T_a,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_a),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_S_2)) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_setsum__cases,axiom, % 164.98/164.98 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] : % 164.98/164.98 ( class_Groups_Ocomm__monoid__add(T_b) % 164.98/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_a),V_P_2))))) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_card__less__Suc2,axiom, % 164.98/164.98 ! [V_i_2,V_M_2] : % 164.98/164.98 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 164.98/164.98 => 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))))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_card__less,axiom, % 164.98/164.98 ! [V_i_2,V_M_2] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 164.98/164.98 => 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) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_dom__override__on,axiom, % 164.98/164.98 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Fun_Ooverride__on(T_a,tc_Option_Ooption(T_b),V_f_2,V_g_2,V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),c_Map_Odom(T_a,T_b,V_f_2)),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2)))))),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Map_Odom(T_a,T_b,V_g_2))))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_setsum__multicount,axiom, % 164.98/164.98 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 164.98/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 164.98/164.98 => ( ! [B_x] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2)) % 164.98/164.98 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 ) % 164.98/164.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_T_2)) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_setsum__multicount__gen,axiom, % 164.98/164.98 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 164.98/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2)) % 164.98/164.98 => ( ! [B_x] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2)) % 164.98/164.98 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_s_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) ) % 164.98/164.98 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Nitpick_Oint__lcm__def,axiom, % 164.98/164.98 ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_inf__Sup2__distrib,axiom, % 164.98/164.98 ! [V_B_2,V_A_2,T_a] : % 164.98/164.98 ( class_Lattices_Odistrib__lattice(T_a) % 164.98/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 164.98/164.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_finite__Collect__subsets,axiom, % 164.98/164.98 ! [V_A_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Pow__Compl,axiom, % 164.98/164.98 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_a))))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Pow__def,axiom, % 164.98/164.98 ! [V_A_2,T_a] : hAPP(c_Set_OPow(T_a),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 164.98/164.98 % 164.98/164.98 fof(fact_finite__Collect__bounded__ex,axiom, % 164.98/164.98 ! [V_Q_2,T_b,V_P_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 164.98/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2))))) % 164.98/164.98 <=> ! [B_y] : % 164.98/164.98 ( hBOOL(hAPP(V_P_2,B_y)) % 164.98/164.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_finite__image__set,axiom, % 164.98/164.98 ! [V_f_2,T_b,V_P_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 164.98/164.98 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_a)),c_fequal)),V_f_2)))),V_P_2))))) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_override__on__apply__in,axiom, % 164.98/164.98 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 164.98/164.98 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.98 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_override__on__apply__notin,axiom, % 164.98/164.98 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 164.98/164.98 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.98 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_override__on__emptyset,axiom, % 164.98/164.98 ! [V_g_2,V_f_2,T_b,T_a] : c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = V_f_2 ). % 164.98/164.98 % 164.98/164.98 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 164.98/164.98 ! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_override__on__def,axiom, % 164.98/164.98 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 164.98/164.98 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.98 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) % 164.98/164.98 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 164.98/164.98 => hAPP(c_Fun_Ooverride__on(T_a,T_b,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ). % 164.98/164.98 % 164.98/164.98 fof(fact_ran__def,axiom, % 164.98/164.98 ! [V_m_2,T_a,T_b] : c_Map_Oran(T_b,T_a,V_m_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_m_2))),c_Option_Ooption_OSome(T_a)))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 164.98/164.98 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 164.98/164.98 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))) ). % 164.98/164.98 % 164.98/164.98 fof(fact_sup__Inf1__distrib,axiom, % 164.98/164.98 ! [V_x_2,V_A_2,T_a] : % 164.98/164.98 ( class_Lattices_Odistrib__lattice(T_a) % 164.98/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 164.98/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 164.98/164.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_sup__Inf2__distrib,axiom, % 165.14/164.98 ! [V_B_2,V_A_2,T_a] : % 165.14/164.98 ( class_Lattices_Odistrib__lattice(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_inf__Sup1__distrib,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Lattices_Odistrib__lattice(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Nitpick_Onat__lcm__def,axiom, % 165.14/164.98 ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)) ). % 165.14/164.98 % 165.14/164.98 fof(fact_add__Max__commute,axiom, % 165.14/164.98 ! [V_k_2,V_N_2,T_a] : % 165.14/164.98 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 165.14/164.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_add__Min__commute,axiom, % 165.14/164.98 ! [V_k_2,V_N_2,T_a] : % 165.14/164.98 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 165.14/164.98 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_a),V_k_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_N_2))))) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_finite__conv__nat__seg__image,axiom, % 165.14/164.98 ! [V_A_2,T_a] : % 165.14/164.98 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_a,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_minus__Min__eq__Max,axiom, % 165.14/164.98 ! [V_S_2,T_a] : % 165.14/164.98 ( class_Groups_Olinordered__ab__group__add(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 165.14/164.98 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_minus__Max__eq__Min,axiom, % 165.14/164.98 ! [V_S_2,T_a] : % 165.14/164.98 ( class_Groups_Olinordered__ab__group__add(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 165.14/164.98 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a)),V_S_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Max_Osingleton,axiom, % 165.14/164.98 ! [V_x_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Min_Osingleton,axiom, % 165.14/164.98 ! [V_x_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Min__le,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_x_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Max__ge,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2))) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Min__in,axiom, % 165.14/164.98 ! [V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Max__in,axiom, % 165.14/164.98 ! [V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Max__mono,axiom, % 165.14/164.98 ! [V_N_2,V_M_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 165.14/164.98 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 165.14/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2))) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Min__antimono,axiom, % 165.14/164.98 ! [V_N_2,V_M_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 165.14/164.98 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 165.14/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_M_2))) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_nat__gcd_Osimps,axiom, % 165.14/164.98 ! [V_x,V_y] : % 165.14/164.98 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/164.98 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 165.14/164.98 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/164.98 => c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Nitpick_Oint__gcd__def,axiom, % 165.14/164.98 ! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Min_Oremove,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) % 165.14/164.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Max_Oremove,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.98 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) % 165.14/164.98 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_int__val__lemma,axiom, % 165.14/164.98 ! [V_k_2,V_f_2,V_n_2] : % 165.14/164.98 ( ! [B_i] : % 165.14/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 165.14/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 165.14/164.98 => ? [B_i] : % 165.14/164.98 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 165.14/164.98 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__diff,axiom, % 165.14/164.98 ! [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) ). % 165.14/164.98 % 165.14/164.98 fof(fact_max__add__distrib__left,axiom, % 165.14/164.98 ! [V_z,V_y,V_x,T_a] : % 165.14/164.98 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__add__distrib__left,axiom, % 165.14/164.98 ! [V_z,V_y,V_x,T_a] : % 165.14/164.98 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_max__0R,axiom, % 165.14/164.98 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 165.14/164.98 % 165.14/164.98 fof(fact_max__0L,axiom, % 165.14/164.98 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup_Oidem,axiom, % 165.14/164.98 ! [V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf_Oidem,axiom, % 165.14/164.98 ! [V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup_Ocommute,axiom, % 165.14/164.98 ! [V_b,V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup__commute,axiom, % 165.14/164.98 ! [V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf_Ocommute,axiom, % 165.14/164.98 ! [V_b,V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf__commute,axiom, % 165.14/164.98 ! [V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup__inf__absorb,axiom, % 165.14/164.98 ! [V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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 ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf__sup__absorb,axiom, % 165.14/164.98 ! [V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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 ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup_Oleft__idem,axiom, % 165.14/164.98 ! [V_b,V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup__left__idem,axiom, % 165.14/164.98 ! [V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 165.14/164.98 ! [V_b,V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf__left__idem,axiom, % 165.14/164.98 ! [V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup_Oleft__commute,axiom, % 165.14/164.98 ! [V_c,V_a,V_b,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup__left__commute,axiom, % 165.14/164.98 ! [V_z,V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 165.14/164.98 ! [V_c,V_a,V_b,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf__left__commute,axiom, % 165.14/164.98 ! [V_z,V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup__inf__distrib1,axiom, % 165.14/164.98 ! [V_z,V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 165.14/164.98 ! [V_z,V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup_Oassoc,axiom, % 165.14/164.98 ! [V_c,V_b,V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup__assoc,axiom, % 165.14/164.98 ! [V_z,V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf_Oassoc,axiom, % 165.14/164.98 ! [V_c,V_b,V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf__assoc,axiom, % 165.14/164.98 ! [V_z,V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup__inf__distrib2,axiom, % 165.14/164.98 ! [V_x,V_z,V_y,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 165.14/164.98 ! [V_x,V_z,V_y,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Max_Oidem,axiom, % 165.14/164.98 ! [V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Min_Oidem,axiom, % 165.14/164.98 ! [V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_minus__min__eq__max,axiom, % 165.14/164.98 ! [V_y,V_x,T_a] : % 165.14/164.98 ( class_Groups_Olinordered__ab__group__add(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_minus__max__eq__min,axiom, % 165.14/164.98 ! [V_y,V_x,T_a] : % 165.14/164.98 ( class_Groups_Olinordered__ab__group__add(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__less__iff__disj,axiom, % 165.14/164.98 ! [V_z_2,V_y_2,V_x_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2)) % 165.14/164.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 165.14/164.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__less__iff__conj,axiom, % 165.14/164.98 ! [V_y_2,V_x_2,V_z_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2))) % 165.14/164.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 165.14/164.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oless__infI2,axiom, % 165.14/164.98 ! [V_a,V_x,V_b,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 165.14/164.98 => 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)) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oless__infI1,axiom, % 165.14/164.98 ! [V_b,V_x,V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 165.14/164.98 => 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)) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_max__less__iff__conj,axiom, % 165.14/164.98 ! [V_z_2,V_y_2,V_x_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2)) % 165.14/164.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 165.14/164.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_less__max__iff__disj,axiom, % 165.14/164.98 ! [V_y_2,V_x_2,V_z_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2))) % 165.14/164.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 165.14/164.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oless__supI2,axiom, % 165.14/164.98 ! [V_a,V_b,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 165.14/164.98 => 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))) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oless__supI1,axiom, % 165.14/164.98 ! [V_b,V_a,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 165.14/164.98 => 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))) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__Suc__Suc,axiom, % 165.14/164.98 ! [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)) ). % 165.14/164.98 % 165.14/164.98 fof(fact_max__Suc__Suc,axiom, % 165.14/164.98 ! [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)) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__0R,axiom, % 165.14/164.98 ! [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) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__0L,axiom, % 165.14/164.98 ! [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) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__diff__distrib__left,axiom, % 165.14/164.98 ! [V_z,V_y,V_x,T_a] : % 165.14/164.98 ( class_Groups_Oordered__ab__group__add(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_max__diff__distrib__left,axiom, % 165.14/164.98 ! [V_z,V_y,V_x,T_a] : % 165.14/164.98 ( class_Groups_Oordered__ab__group__add(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_sup__max,axiom, % 165.14/164.98 ! [T_a] : % 165.14/164.98 ( ( class_Lattices_Osemilattice__sup(T_a) % 165.14/164.98 & class_Orderings_Olinorder(T_a) ) % 165.14/164.98 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_inf__min,axiom, % 165.14/164.98 ! [T_a] : % 165.14/164.98 ( ( class_Lattices_Osemilattice__inf(T_a) % 165.14/164.98 & class_Orderings_Olinorder(T_a) ) % 165.14/164.98 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Int__atLeastLessThan,axiom, % 165.14/164.98 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Int__greaterThanLessThan,axiom, % 165.14/164.98 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Int__greaterThanAtMost,axiom, % 165.14/164.98 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_le__max__iff__disj,axiom, % 165.14/164.98 ! [V_y_2,V_x_2,V_z_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2))) % 165.14/164.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2)) % 165.14/164.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ole__supE,axiom, % 165.14/164.98 ! [V_x,V_b,V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( 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)) % 165.14/164.98 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 165.14/164.98 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup__mono,axiom, % 165.14/164.98 ! [V_d,V_b,V_c,V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 165.14/164.98 => 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))) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup__least,axiom, % 165.14/164.98 ! [V_z,V_x,V_y,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 165.14/164.98 => 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)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ole__supI,axiom, % 165.14/164.98 ! [V_b,V_x,V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 165.14/164.98 => 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)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup__absorb1,axiom, % 165.14/164.98 ! [V_x,V_y,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 165.14/164.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Osup__absorb2,axiom, % 165.14/164.98 ! [V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 165.14/164.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ole__supI2,axiom, % 165.14/164.98 ! [V_a,V_b,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 165.14/164.98 => 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))) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ole__supI1,axiom, % 165.14/164.98 ! [V_b,V_a,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 165.14/164.98 => 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))) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ole__sup__iff,axiom, % 165.14/164.98 ! [V_z_2,V_y_2,V_x_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2)) % 165.14/164.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 165.14/164.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ole__iff__sup,axiom, % 165.14/164.98 ! [V_y_2,V_x_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 165.14/164.98 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_le__maxI2,axiom, % 165.14/164.98 ! [V_x,V_y,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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))) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_le__maxI1,axiom, % 165.14/164.98 ! [V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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))) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__le__iff__disj,axiom, % 165.14/164.98 ! [V_z_2,V_y_2,V_x_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2)),V_z_2)) % 165.14/164.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 165.14/164.98 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ole__infE,axiom, % 165.14/164.98 ! [V_b,V_a,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( 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))) % 165.14/164.98 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 165.14/164.98 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf__mono,axiom, % 165.14/164.98 ! [V_d,V_b,V_c,V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 165.14/164.98 => 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))) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf__greatest,axiom, % 165.14/164.98 ! [V_z,V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 165.14/164.98 => 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))) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ole__infI,axiom, % 165.14/164.98 ! [V_b,V_a,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 165.14/164.98 => 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))) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf__absorb2,axiom, % 165.14/164.98 ! [V_x,V_y,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 165.14/164.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf__absorb1,axiom, % 165.14/164.98 ! [V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 165.14/164.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ole__infI2,axiom, % 165.14/164.98 ! [V_a,V_x,V_b,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 165.14/164.98 => 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)) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ole__infI1,axiom, % 165.14/164.98 ! [V_b,V_x,V_a,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 165.14/164.98 => 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)) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ole__inf__iff,axiom, % 165.14/164.98 ! [V_z_2,V_y_2,V_x_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y_2),V_z_2))) % 165.14/164.98 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 165.14/164.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ole__iff__inf,axiom, % 165.14/164.98 ! [V_y_2,V_x_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 165.14/164.98 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf__le2,axiom, % 165.14/164.98 ! [V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Oinf__le1,axiom, % 165.14/164.98 ! [V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Odistrib__sup__le,axiom, % 165.14/164.98 ! [V_z,V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)))) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Odistrib__inf__le,axiom, % 165.14/164.98 ! [V_z,V_y,V_x,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => 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)))) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Int__atLeastAtMost,axiom, % 165.14/164.98 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 165.14/164.98 ! [T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 165.14/164.98 ! [T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_nat__minus__add__max,axiom, % 165.14/164.98 ! [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) ). % 165.14/164.98 % 165.14/164.98 fof(fact_max__Suc2,axiom, % 165.14/164.98 ! [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) ). % 165.14/164.98 % 165.14/164.98 fof(fact_max__Suc1,axiom, % 165.14/164.98 ! [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) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Max_Oin__idem,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Min_Oin__idem,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Int__atLeastAtMostR1,axiom, % 165.14/164.98 ! [V_d_2,V_ca_2,V_b_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Int__atLeastAtMostL1,axiom, % 165.14/164.98 ! [V_d_2,V_b_2,V_a_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Int__atLeastAtMostR2,axiom, % 165.14/164.98 ! [V_d_2,V_ca_2,V_a_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),V_d_2) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Int__atLeastAtMostL2,axiom, % 165.14/164.98 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),V_b_2) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Max_OF__eq,axiom, % 165.14/164.98 ! [V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Min_OF__eq,axiom, % 165.14/164.98 ! [V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__Suc2,axiom, % 165.14/164.98 ! [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) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__Suc1,axiom, % 165.14/164.98 ! [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) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Ofold1__belowI,axiom, % 165.14/164.98 ! [V_a_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_a_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_fold1__below__iff,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2)) % 165.14/164.98 <=> ? [B_x] : % 165.14/164.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/164.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_min__max_Obelow__fold1__iff,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) % 165.14/164.98 <=> ! [B_x] : % 165.14/164.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_fold1__strict__below__iff,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2)),V_x_2)) % 165.14/164.98 <=> ? [B_x] : % 165.14/164.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/164.98 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_strict__below__fold1__iff,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) % 165.14/164.98 <=> ! [B_x] : % 165.14/164.98 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/164.98 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Max__insert,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Min__insert,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Max_Osubset__idem,axiom, % 165.14/164.98 ! [V_B_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 165.14/164.98 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Min_Osubset__idem,axiom, % 165.14/164.98 ! [V_B_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 165.14/164.98 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Max__Un,axiom, % 165.14/164.98 ! [V_B_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Min__Un,axiom, % 165.14/164.98 ! [V_B_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.98 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Max_Oinsert,axiom, % 165.14/164.98 ! [V_x_2,V_A_2,T_a] : % 165.14/164.98 ( class_Orderings_Olinorder(T_a) % 165.14/164.98 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.98 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.98 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.98 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)) ) ) ) ) ). % 165.14/164.98 % 165.14/164.98 fof(fact_Min_Oinsert,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_fold1__antimono,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2))) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Max_Oinsert__remove,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 165.14/164.99 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Max_Ounion__inter,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.99 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Max_Ounion__disjoint,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_a,V_B_2)) ) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Min_Oinsert__remove,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 165.14/164.99 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Min_Ounion__inter,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.99 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Min_Ounion__disjoint,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_a,V_B_2)) ) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_dual__min,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => c_Orderings_Oord_Omin(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omax(T_a) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_dual__max,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => c_Orderings_Oord_Omax(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a))) = c_Orderings_Oord__class_Omin(T_a) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_max__ord__max,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Orderings_Oord(T_a) % 165.14/164.99 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__ord__min,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Orderings_Oord(T_a) % 165.14/164.99 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_inf__nat__def,axiom, % 165.14/164.99 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 165.14/164.99 % 165.14/164.99 fof(fact_sup__nat__def,axiom, % 165.14/164.99 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))))) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omax(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBS(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal))),c_Orderings_Oord__class_Omin(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))))))) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__le__Sup,axiom, % 165.14/164.99 ! [V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2))) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 165.14/164.99 ! [V_x_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 165.14/164.99 ! [V_x_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 165.14/164.99 ! [V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omin(T_a)),V_A_2) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 165.14/164.99 ! [V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,c_Orderings_Oord__class_Omax(T_a)),V_A_2) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_Osup__Inf__absorb,axiom, % 165.14/164.99 ! [V_a_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) = V_a_2 ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 165.14/164.99 ! [V_a_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) = V_a_2 ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 165.14/164.99 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 165.14/164.99 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.99 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_B_2)) ) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.99 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/164.99 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_B_2)) ) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__fin_Oremove,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.99 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 ) % 165.14/164.99 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OSup__fin_Oremove,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.99 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 ) % 165.14/164.99 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 165.14/164.99 ! [V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2)),V_A_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 165.14/164.99 ! [V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2)),V_A_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Max_Oclosed,axiom, % 165.14/164.99 ! [V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Min_Oclosed,axiom, % 165.14/164.99 ! [V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),hAPP(hAPP(c_Set_Oinsert(T_a),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 165.14/164.99 ! [V_N_2,V_h_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 165.14/164.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 165.14/164.99 ! [V_N_2,V_h_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 165.14/164.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Max_Ohom__commute,axiom, % 165.14/164.99 ! [V_N_2,V_h_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 165.14/164.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Min_Ohom__commute,axiom, % 165.14/164.99 ! [V_N_2,V_h_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 165.14/164.99 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_a,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_N_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat0__intermed__int__val,axiom, % 165.14/164.99 ! [V_k_2,V_f_2,V_n_2] : % 165.14/164.99 ( ! [B_i] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 165.14/164.99 => 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))) ) % 165.14/164.99 => ( 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)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 165.14/164.99 => ? [B_i] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 165.14/164.99 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_pigeonhole__infinite,axiom, % 165.14/164.99 ! [V_f_2,T_b,V_A_2,T_a] : % 165.14/164.99 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 165.14/164.99 => ? [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/164.99 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_card__quotient__disjoint,axiom, % 165.14/164.99 ! [V_r_2,V_A_2,T_a] : % 165.14/164.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2) % 165.14/164.99 => hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_a),V_A_2) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__le__eq__Un0,axiom, % 165.14/164.99 ! [V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_SUP1__I,axiom, % 165.14/164.99 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_finite__UN,axiom, % 165.14/164.99 ! [V_B_2,T_b,V_A_2,T_a] : % 165.14/164.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) % 165.14/164.99 <=> ! [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/164.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_SUP1__iff,axiom, % 165.14/164.99 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 165.14/164.99 <=> ? [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/164.99 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_quotient__empty,axiom, % 165.14/164.99 ! [V_r_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_quotient__is__empty2,axiom, % 165.14/164.99 ! [V_r_2,V_A_2,T_a] : % 165.14/164.99 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) % 165.14/164.99 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_quotient__is__empty,axiom, % 165.14/164.99 ! [V_r_2,V_A_2,T_a] : % 165.14/164.99 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 165.14/164.99 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_SUP__UN__eq,axiom, % 165.14/164.99 ! [V_x_2,V_r_2,T_b,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2)) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__lessThan__UNIV,axiom, % 165.14/164.99 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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__atMost__UNIV,axiom, % 165.14/164.99 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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__atLeast__UNIV,axiom, % 165.14/164.99 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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__UN__finite__eq,axiom, % 165.14/164.99 ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__le__add__shift,axiom, % 165.14/164.99 ! [V_k_2,V_M_2,V_n_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_quotient__diff1,axiom, % 165.14/164.99 ! [V_a_2,V_A_2,V_r_2,T_a] : % 165.14/164.99 ( c_Fun_Oinj__on(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Equiv__Relations_Oquotient(T_a)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2),V_A_2) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/164.99 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__I,axiom, % 165.14/164.99 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_vimage__eq__UN,axiom, % 165.14/164.99 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_Ovimage(T_a,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_image__eq__UN,axiom, % 165.14/164.99 ! [V_A_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__Pow__subset,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2))),hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_ball__UN,axiom, % 165.14/164.99 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] : % 165.14/164.99 ( ! [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 165.14/164.99 => hBOOL(hAPP(V_P_2,B_x)) ) % 165.14/164.99 <=> ! [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 165.14/164.99 => ! [B_xa] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x))) % 165.14/164.99 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_SUP__commute,axiom, % 165.14/164.99 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 165.14/164.99 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__extend__simps_I9_J,axiom, % 165.14/164.99 ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__simps_I9_J,axiom, % 165.14/164.99 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__UN__flatten,axiom, % 165.14/164.99 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_SUP__le__iff,axiom, % 165.14/164.99 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] : % 165.14/164.99 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_M_2)),V_u_2)) % 165.14/164.99 <=> ! [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__SUP__iff,axiom, % 165.14/164.99 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] : % 165.14/164.99 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/164.99 & class_Orderings_Olinorder(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),V_f_2))) % 165.14/164.99 <=> ? [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 165.14/164.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__iff,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 165.14/164.99 <=> ? [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 165.14/164.99 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_SUP__const,axiom, % 165.14/164.99 ! [V_M_2,T_a,V_A_2,T_b] : % 165.14/164.99 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 165.14/164.99 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UNION__empty__conv_I2_J,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_a,T_b] : % 165.14/164.99 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 <=> ! [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 165.14/164.99 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__constant,axiom, % 165.14/164.99 ! [V_ca_2,T_b,T_a,V_A_2] : % 165.14/164.99 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 165.14/164.99 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = V_ca_2 ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__empty2,axiom, % 165.14/164.99 ! [V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UNION__empty__conv_I1_J,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_b,T_a] : % 165.14/164.99 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) % 165.14/164.99 <=> ! [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 165.14/164.99 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__subset__iff,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) % 165.14/164.99 <=> ! [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__simps_I10_J,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_image__UN,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_c,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Oimage(T_b,T_a,V_f_2)),V_B_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__extend__simps_I10_J,axiom, % 165.14/164.99 ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__Un__distrib,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__Un,axiom, % 165.14/164.99 ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Int__UN__distrib2,axiom, % 165.14/164.99 ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__extend__simps_I4_J,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Int__UN__distrib,axiom, % 165.14/164.99 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__extend__simps_I5_J,axiom, % 165.14/164.99 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__simps_I4_J,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__simps_I5_J,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_SUPR__apply,axiom, % 165.14/164.99 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 165.14/164.99 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/164.99 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__simps_I6_J,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__extend__simps_I6_J,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_vimage__UN,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_SUP__subset,axiom, % 165.14/164.99 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 165.14/164.99 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_B_2),V_f_2))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_le__SUPI,axiom, % 165.14/164.99 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 165.14/164.99 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_M_2))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__insert__distrib,axiom, % 165.14/164.99 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__upper,axiom, % 165.14/164.99 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__absorb,axiom, % 165.14/164.99 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 165.14/164.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__simps_I1_J,axiom, % 165.14/164.99 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 165.14/164.99 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 165.14/164.99 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__singleton,axiom, % 165.14/164.99 ! [V_A_2,T_a] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_A_2 ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__extend__simps_I1_J,axiom, % 165.14/164.99 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 165.14/164.99 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) % 165.14/164.99 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__simps_I3_J,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 165.14/164.99 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 165.14/164.99 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__simps_I2_J,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 165.14/164.99 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 165.14/164.99 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__extend__simps_I3_J,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 165.14/164.99 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 165.14/164.99 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__extend__simps_I2_J,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 165.14/164.99 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 165.14/164.99 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/164.99 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__insert,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__finite2__subset,axiom, % 165.14/164.99 ! [V_B_2,V_k_2,V_A_2,T_a] : % 165.14/164.99 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_quotient__def,axiom, % 165.14/164.99 ! [V_r_2,V_A_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),c_Relation_OImage(T_a,T_a,V_r_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__finite2__eq,axiom, % 165.14/164.99 ! [V_B_2,V_k_2,V_A_2,T_a] : % 165.14/164.99 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__finite__subset,axiom, % 165.14/164.99 ! [V_C_2,V_A_2,T_a] : % 165.14/164.99 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_SUP2__I,axiom, % 165.14/164.99 ! [T_c,T_b,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_quotientI,axiom, % 165.14/164.99 ! [V_r_2,V_A_2,V_x_2,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_singleton__quotient,axiom, % 165.14/164.99 ! [V_r_2,V_x_2,T_a] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Image__eq__UN,axiom, % 165.14/164.99 ! [V_B_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_a,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Image__Int__subset,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Image__UN,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,T_c,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_quotientE,axiom, % 165.14/164.99 ! [V_r_2,V_A_2,V_X_2,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 165.14/164.99 => ~ ! [B_x] : % 165.14/164.99 ( V_X_2 = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 165.14/164.99 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_SUP2__iff,axiom, % 165.14/164.99 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 165.14/164.99 <=> ? [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/164.99 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Image__empty,axiom, % 165.14/164.99 ! [V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Image__mono,axiom, % 165.14/164.99 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Image__Un,axiom, % 165.14/164.99 ! [V_B_2,V_A_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Un__Image,axiom, % 165.14/164.99 ! [V_A_2,V_S_2,V_R_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_S_2),V_A_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_finite__UN__I,axiom, % 165.14/164.99 ! [V_B_2,T_b,V_A_2,T_a] : % 165.14/164.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( ! [B_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 165.14/164.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 165.14/164.99 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_diff__nat__eq__if,axiom, % 165.14/164.99 ! [V_z_2,V_z_H_2] : % 165.14/164.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 165.14/164.99 => 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)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_setsum__SucD,axiom, % 165.14/164.99 ! [V_n_2,V_A_2,V_f_2,T_a] : % 165.14/164.99 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2) % 165.14/164.99 => ? [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/164.99 & 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))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__mod__eq__lemma,axiom, % 165.14/164.99 ! [V_y,V_n,V_x] : % 165.14/164.99 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 165.14/164.99 => ? [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)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_not__neg__0,axiom, % 165.14/164.99 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__by__empty,axiom, % 165.14/164.99 ! [V_B_2,T_a,V_A_2] : % 165.14/164.99 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_not__neg__1,axiom, % 165.14/164.99 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_not__neg__int,axiom, % 165.14/164.99 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_not__neg__eq__ge__0,axiom, % 165.14/164.99 ! [V_x_2] : % 165.14/164.99 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_neg__def,axiom, % 165.14/164.99 ! [V_Z_2] : % 165.14/164.99 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_neg__nat,axiom, % 165.14/164.99 ! [V_z] : % 165.14/164.99 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 165.14/164.99 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_not__neg__nat,axiom, % 165.14/164.99 ! [V_z] : % 165.14/164.99 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 165.14/164.99 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_neg__zminus__int,axiom, % 165.14/164.99 ! [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))))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osize_I13_J,axiom, % 165.14/164.99 ! [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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osize_I5_J,axiom, % 165.14/164.99 ! [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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_fold__image__1,axiom, % 165.14/164.99 ! [V_f_2,V_S_2,T_a,T_b] : % 165.14/164.99 ( class_Groups_Ocomm__monoid__mult(T_b) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 165.14/164.99 => ( ! [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 165.14/164.99 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 165.14/164.99 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_f_2),c_Groups_Oone__class_Oone(T_b)),V_S_2) = c_Groups_Oone__class_Oone(T_b) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_card_Oneutral,axiom, % 165.14/164.99 ! [V_A_2,T_a] : % 165.14/164.99 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/164.99 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 165.14/164.99 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_WTs__elim__cases_I5_J,axiom, % 165.14/164.99 ! [V_c2_2,V_c1_2,V_b_2] : % 165.14/164.99 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2))) % 165.14/164.99 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 165.14/164.99 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I4_J,axiom, % 165.14/164.99 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 165.14/164.99 ( 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) % 165.14/164.99 <=> ( V_fun_2 = V_fun_H_2 % 165.14/164.99 & V_com1_2 = V_com1_H_2 % 165.14/164.99 & V_com2_2 = V_com2_H_2 ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I55_J,axiom, % 165.14/164.99 ! [V_com2_2,V_com1_2,V_fun_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I54_J,axiom, % 165.14/164.99 ! [V_pname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_WT_Oequations_I5_J,axiom, % 165.14/164.99 ! [V_a2_2,V_a1_2,V_a3_2] : % 165.14/164.99 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2))) % 165.14/164.99 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 165.14/164.99 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_WT_OIf,axiom, % 165.14/164.99 ! [V_b_2,V_c1_2,V_c0_2] : % 165.14/164.99 ( hBOOL(hAPP(c_Com_OWT,V_c0_2)) % 165.14/164.99 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 165.14/164.99 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I53_J,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I52_J,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I57_J,axiom, % 165.14/164.99 ! [V_com2_2,V_com1_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I56_J,axiom, % 165.14/164.99 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I44_J,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I45_J,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I14_J,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I15_J,axiom, % 165.14/164.99 ! [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 ). % 165.14/164.99 % 165.14/164.99 fof(fact_mod__induct__0,axiom, % 165.14/164.99 ! [V_i_2,V_P_2,V_p_2] : % 165.14/164.99 ( ! [B_i] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 165.14/164.99 => ( hBOOL(hAPP(V_P_2,B_i)) % 165.14/164.99 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 165.14/164.99 => ( hBOOL(hAPP(V_P_2,V_i_2)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 165.14/164.99 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_fold__image__cong,axiom, % 165.14/164.99 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] : % 165.14/164.99 ( class_Groups_Oab__semigroup__mult(T_b) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( ! [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/164.99 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 165.14/164.99 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_a,c_Groups_Otimes__class_Otimes(T_b)),V_h_2),V_z_2),V_A_2) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Min__eqI,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( ! [B_y] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.99 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Max__eqI,axiom, % 165.14/164.99 ! [V_x_2,V_A_2,T_a] : % 165.14/164.99 ( class_Orderings_Olinorder(T_a) % 165.14/164.99 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/164.99 => ( ! [B_y] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/164.99 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_expand__Suc,axiom, % 165.14/164.99 ! [V_v] : % 165.14/164.99 ( 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))) % 165.14/164.99 => 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))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_quotient__disj,axiom, % 165.14/164.99 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 165.14/164.99 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 165.14/164.99 => ( V_X_2 = V_Y_2 % 165.14/164.99 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osize_I11_J,axiom, % 165.14/164.99 ! [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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osize_I3_J,axiom, % 165.14/164.99 ! [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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_WTs__elim__cases_I3_J,axiom, % 165.14/164.99 ! [V_ca_2,V_a_2,V_Y_2] : % 165.14/164.99 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) % 165.14/164.99 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I38_J,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I39_J,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_of__nat__number__of__lemma,axiom, % 165.14/164.99 ! [V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => ( ( 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))) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ 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))) % 165.14/164.99 => 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) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_of__nat__number__of__eq,axiom, % 165.14/164.99 ! [V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I40_J,axiom, % 165.14/164.99 ! [V_pname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != hAPP(c_Com_Ocom_OBODY,V_pname_H_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I41_J,axiom, % 165.14/164.99 ! [V_com_2,V_fun_2,V_loc_2,V_pname_H_2] : hAPP(c_Com_Ocom_OBODY,V_pname_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_WT_OLocal,axiom, % 165.14/164.99 ! [V_a_2,V_Y_2,V_ca_2] : % 165.14/164.99 ( hBOOL(hAPP(c_Com_OWT,V_ca_2)) % 165.14/164.99 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_WT_Oequations_I3_J,axiom, % 165.14/164.99 ! [V_a1_2,V_a3_2,V_a2_2] : % 165.14/164.99 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2))) % 165.14/164.99 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_of__int__number__of__eq,axiom, % 165.14/164.99 ! [V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of__reorient,axiom, % 165.14/164.99 ! [V_x_2,V_w_2,T_a] : % 165.14/164.99 ( class_Int_Onumber(T_a) % 165.14/164.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2 % 165.14/164.99 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_eq__number__of,axiom, % 165.14/164.99 ! [V_y_2,V_x_2,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Int_Oring__char__0(T_a) ) % 165.14/164.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 165.14/164.99 <=> V_x_2 = V_y_2 ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I2_J,axiom, % 165.14/164.99 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 165.14/164.99 ( 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) % 165.14/164.99 <=> ( V_loc_2 = V_loc_H_2 % 165.14/164.99 & V_fun_2 = V_fun_H_2 % 165.14/164.99 & V_com_2 = V_com_H_2 ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of__eq,axiom, % 165.14/164.99 ! [V_k,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I37_J,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I36_J,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I43_J,axiom, % 165.14/164.99 ! [V_com_2,V_fun_2,V_loc_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I42_J,axiom, % 165.14/164.99 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I35_J,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I34_J,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I10_J,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_com_Osimps_I11_J,axiom, % 165.14/164.99 ! [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 ). % 165.14/164.99 % 165.14/164.99 fof(fact_le__number__of__eq__not__less,axiom, % 165.14/164.99 ! [V_w_2,V_v_2,T_a] : % 165.14/164.99 ( ( class_Int_Onumber(T_a) % 165.14/164.99 & class_Orderings_Olinorder(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 165.14/164.99 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_right__distrib__number__of,axiom, % 165.14/164.99 ! [V_c,V_b,V_v,T_b] : % 165.14/164.99 ( ( class_Int_Onumber(T_b) % 165.14/164.99 & class_Rings_Osemiring(T_b) ) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_left__distrib__number__of,axiom, % 165.14/164.99 ! [V_v,V_b,V_a,T_b] : % 165.14/164.99 ( ( class_Int_Onumber(T_b) % 165.14/164.99 & class_Rings_Osemiring(T_b) ) % 165.14/164.99 => 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))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_right__diff__distrib__number__of,axiom, % 165.14/164.99 ! [V_c,V_b,V_v,T_b] : % 165.14/164.99 ( ( class_Int_Onumber(T_b) % 165.14/164.99 & class_Rings_Oring(T_b) ) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_left__diff__distrib__number__of,axiom, % 165.14/164.99 ! [V_v,V_b,V_a,T_b] : % 165.14/164.99 ( ( class_Int_Onumber(T_b) % 165.14/164.99 & class_Rings_Oring(T_b) ) % 165.14/164.99 => 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))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_le__number__of,axiom, % 165.14/164.99 ! [V_y_2,V_x_2,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Rings_Olinordered__idom(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__number__of,axiom, % 165.14/164.99 ! [V_y_2,V_x_2,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Rings_Olinordered__idom(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__number__of,axiom, % 165.14/164.99 ! [V_v,V_u,T_b] : % 165.14/164.99 ( ( class_Int_Onumber(T_b) % 165.14/164.99 & class_Orderings_Oord(T_b) ) % 165.14/164.99 => ( ( 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))) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ 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))) % 165.14/164.99 => 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) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_max__number__of,axiom, % 165.14/164.99 ! [V_v,V_u,T_b] : % 165.14/164.99 ( ( class_Int_Onumber(T_b) % 165.14/164.99 & class_Orderings_Oord(T_b) ) % 165.14/164.99 => ( ( 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))) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ 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))) % 165.14/164.99 => 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) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__number__of__left,axiom, % 165.14/164.99 ! [V_z,V_w,V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__number__of__eq,axiom, % 165.14/164.99 ! [V_w,V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of__add,axiom, % 165.14/164.99 ! [V_w,V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_mult__number__of__left,axiom, % 165.14/164.99 ! [V_z,V_w,V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_arith__simps_I32_J,axiom, % 165.14/164.99 ! [V_w,V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of__mult,axiom, % 165.14/164.99 ! [V_w,V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of__diff,axiom, % 165.14/164.99 ! [V_w,V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_arith__simps_I30_J,axiom, % 165.14/164.99 ! [V_w,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of__minus,axiom, % 165.14/164.99 ! [V_w,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Ints__number__of,axiom, % 165.14/164.99 ! [V_w_2,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_eq__divide__eq__number__of1,axiom, % 165.14/164.99 ! [V_w_2,V_b_2,V_a_2,T_a] : % 165.14/164.99 ( ( class_Fields_Ofield__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber(T_a) ) % 165.14/164.99 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) % 165.14/164.99 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 165.14/164.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_b_2 ) % 165.14/164.99 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 165.14/164.99 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_eq__divide__eq__number__of,axiom, % 165.14/164.99 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 165.14/164.99 ( ( class_Fields_Ofield__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber(T_a) ) % 165.14/164.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 165.14/164.99 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 165.14/164.99 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2) = V_b_2 ) % 165.14/164.99 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 165.14/164.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_divide__eq__eq__number__of,axiom, % 165.14/164.99 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 165.14/164.99 ( ( class_Fields_Ofield__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber(T_a) ) % 165.14/164.99 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) % 165.14/164.99 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 165.14/164.99 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2) ) % 165.14/164.99 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 165.14/164.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_divide__eq__eq__number__of1,axiom, % 165.14/164.99 ! [V_a_2,V_w_2,V_b_2,T_a] : % 165.14/164.99 ( ( class_Fields_Ofield__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber(T_a) ) % 165.14/164.99 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) = V_a_2 % 165.14/164.99 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 165.14/164.99 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) % 165.14/164.99 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 165.14/164.99 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__number__of__diff1,axiom, % 165.14/164.99 ! [V_c,V_w,V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_minus__number__of__mult,axiom, % 165.14/164.99 ! [V_z,V_w,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_diff__number__of__eq,axiom, % 165.14/164.99 ! [V_w,V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__divide__eq__number__of1,axiom, % 165.14/164.99 ! [V_w_2,V_b_2,V_a_2,T_a] : % 165.14/164.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) % 165.14/164.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 165.14/164.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__divide__eq__number__of,axiom, % 165.14/164.99 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 165.14/164.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 165.14/164.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 165.14/164.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_divide__less__eq__number__of,axiom, % 165.14/164.99 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 165.14/164.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 165.14/164.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 165.14/164.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_divide__less__eq__number__of1,axiom, % 165.14/164.99 ! [V_a_2,V_w_2,V_b_2,T_a] : % 165.14/164.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2)) % 165.14/164.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 165.14/164.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_abs__number__of,axiom, % 165.14/164.99 ! [V_x,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Rings_Olinordered__idom(T_a) ) % 165.14/164.99 => ( ( 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))) % 165.14/164.99 => 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)) ) % 165.14/164.99 & ( ~ 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))) % 165.14/164.99 => 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) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__number__of__diff2,axiom, % 165.14/164.99 ! [V_w,V_c,V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_divide__le__eq__number__of1,axiom, % 165.14/164.99 ! [V_a_2,V_w_2,V_b_2,T_a] : % 165.14/164.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_a_2)) % 165.14/164.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 165.14/164.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_divide__le__eq__number__of,axiom, % 165.14/164.99 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 165.14/164.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 165.14/164.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 165.14/164.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) ) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_le__divide__eq__number__of,axiom, % 165.14/164.99 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 165.14/164.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 165.14/164.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 165.14/164.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_le__divide__eq__number__of1,axiom, % 165.14/164.99 ! [V_w_2,V_b_2,V_a_2,T_a] : % 165.14/164.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) % 165.14/164.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))),V_b_2)) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 165.14/164.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)))) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_equiv__class__self,axiom, % 165.14/164.99 ! [V_a_2,V_r_2,V_A_2,T_a] : % 165.14/164.99 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__equiv__class2,axiom, % 165.14/164.99 ! [V_a2_2,V_a1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 165.14/164.99 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 165.14/164.99 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 165.14/164.99 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2)) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__equiv__class,axiom, % 165.14/164.99 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 165.14/164.99 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/164.99 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/164.99 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_one__mod__nat__number__of,axiom, % 165.14/164.99 ! [V_v_H] : % 165.14/164.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 165.14/164.99 => 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)) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 165.14/164.99 => 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))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_one__div__nat__number__of,axiom, % 165.14/164.99 ! [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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__eq__number__of__int__code,axiom, % 165.14/164.99 ! [V_l_2,V_k_2] : % 165.14/164.99 ( 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))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_times__numeral__code_I5_J,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of__is__id,axiom, % 165.14/164.99 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 165.14/164.99 % 165.14/164.99 fof(fact_plus__numeral__code_I9_J,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__number__of__int__code,axiom, % 165.14/164.99 ! [V_l_2,V_k_2] : % 165.14/164.99 ( 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))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_minus__numeral__code_I5_J,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_int__number__of__def,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__number__of__def,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__number__of,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_congruent2__implies__congruent,axiom, % 165.14/164.99 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] : % 165.14/164.99 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2) % 165.14/164.99 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/164.99 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_minus__numeral__code_I6_J,axiom, % 165.14/164.99 ! [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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_neg__imp__number__of__eq__0,axiom, % 165.14/164.99 ! [V_v] : % 165.14/164.99 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_int__eq__iff__number__of,axiom, % 165.14/164.99 ! [V_v_2,V_m_2] : % 165.14/164.99 ( 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) % 165.14/164.99 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 165.14/164.99 & 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))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_eq__nat__number__of,axiom, % 165.14/164.99 ! [V_v_H_2,V_v_2] : % 165.14/164.99 ( 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) % 165.14/164.99 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 165.14/164.99 => 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))) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 165.14/164.99 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 165.14/164.99 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 165.14/164.99 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__number__of__add__left,axiom, % 165.14/164.99 ! [V_k,V_v_H,V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 165.14/164.99 => 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) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_int__nat__number__of,axiom, % 165.14/164.99 ! [V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_mod__nat__number__of,axiom, % 165.14/164.99 ! [V_v_H,V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 165.14/164.99 => 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))) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_congruent2__implies__congruent__UN,axiom, % 165.14/164.99 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 165.14/164.99 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 165.14/164.99 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 165.14/164.99 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2)) % 165.14/164.99 => c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_c,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_f_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_div__nat__number__of,axiom, % 165.14/164.99 ! [V_v_H,V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power__nat__number__of__number__of,axiom, % 165.14/164.99 ! [V_w,V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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)) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power__nat__number__of,axiom, % 165.14/164.99 ! [V_n,V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Suc__nat__number__of__add,axiom, % 165.14/164.99 ! [V_n,V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_diff__nat__number__of,axiom, % 165.14/164.99 ! [V_v_2,V_v_H_2] : % 165.14/164.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 165.14/164.99 => 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)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__Suc__number__of,axiom, % 165.14/164.99 ! [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)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_min__number__of__Suc,axiom, % 165.14/164.99 ! [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)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I19_J,axiom, % 165.14/164.99 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__Pls__right,axiom, % 165.14/164.99 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__Pls,axiom, % 165.14/164.99 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 165.14/164.99 % 165.14/164.99 fof(fact_succ__pred,axiom, % 165.14/164.99 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 165.14/164.99 % 165.14/164.99 fof(fact_Pls__def,axiom, % 165.14/164.99 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I2_J,axiom, % 165.14/164.99 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_minus__Pls,axiom, % 165.14/164.99 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 165.14/164.99 % 165.14/164.99 fof(fact_mult__Pls,axiom, % 165.14/164.99 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 165.14/164.99 % 165.14/164.99 fof(fact_diff__bin__simps_I1_J,axiom, % 165.14/164.99 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 165.14/164.99 % 165.14/164.99 fof(fact_semiring__norm_I112_J,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of__Pls,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__numeral__0,axiom, % 165.14/164.99 ! [V_a,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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 ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__numeral__0__right,axiom, % 165.14/164.99 ! [V_a,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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 ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_bin__less__0__simps_I1_J,axiom, % 165.14/164.99 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__number__of__Pls,axiom, % 165.14/164.99 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 165.14/164.99 % 165.14/164.99 fof(fact_semiring__norm_I113_J,axiom, % 165.14/164.99 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 165.14/164.99 % 165.14/164.99 fof(fact_zero__is__num__zero,axiom, % 165.14/164.99 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Suc__diff__number__of,axiom, % 165.14/164.99 ! [V_m,V_v] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 165.14/164.99 => 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))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_not__neg__number__of__Pls,axiom, % 165.14/164.99 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__number__of__add__1,axiom, % 165.14/164.99 ! [V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 165.14/164.99 => 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)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__1__add__number__of,axiom, % 165.14/164.99 ! [V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 165.14/164.99 => 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)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_le__iff__pred__less,axiom, % 165.14/164.99 ! [V_l_2,V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_pred__def,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__number__of__diff__1,axiom, % 165.14/164.99 ! [V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 165.14/164.99 => 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)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_divide__Numeral0,axiom, % 165.14/164.99 ! [V_x,T_a] : % 165.14/164.99 ( ( class_Fields_Ofield__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber__ring(T_a) ) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_eq__number__of__0,axiom, % 165.14/164.99 ! [V_v_2] : % 165.14/164.99 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_eq__0__number__of,axiom, % 165.14/164.99 ! [V_v_2] : % 165.14/164.99 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of2,axiom, % 165.14/164.99 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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__nat__number__of,axiom, % 165.14/164.99 ! [V_v_H_2,V_v_2] : % 165.14/164.99 ( 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))) % 165.14/164.99 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 165.14/164.99 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_le__nat__number__of,axiom, % 165.14/164.99 ! [V_v_H_2,V_v_2] : % 165.14/164.99 ( 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))) % 165.14/164.99 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_succ__def,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_le__special_I3_J,axiom, % 165.14/164.99 ! [V_x_2,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Rings_Olinordered__idom(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_le__special_I1_J,axiom, % 165.14/164.99 ! [V_y_2,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Rings_Olinordered__idom(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__special_I1_J,axiom, % 165.14/164.99 ! [V_y_2,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Rings_Olinordered__idom(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__special_I3_J,axiom, % 165.14/164.99 ! [V_x_2,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Rings_Olinordered__idom(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__0__number__of,axiom, % 165.14/164.99 ! [V_v_2] : % 165.14/164.99 ( 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))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__nat__number__of,axiom, % 165.14/164.99 ! [V_v_H,V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 165.14/164.99 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 165.14/164.99 => 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)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of__succ,axiom, % 165.14/164.99 ! [V_k,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of__pred,axiom, % 165.14/164.99 ! [V_w,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_mult__nat__number__of,axiom, % 165.14/164.99 ! [V_v_H,V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 165.14/164.99 => 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)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__number__of__mult__left,axiom, % 165.14/164.99 ! [V_k,V_v_H,V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 165.14/164.99 => 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) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 165.14/164.99 => 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) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_neg__number__of__pred__iff__0,axiom, % 165.14/164.99 ! [V_v_2] : % 165.14/164.99 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 165.14/164.99 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Suc__eq__number__of,axiom, % 165.14/164.99 ! [V_v_2,V_n_2] : % 165.14/164.99 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 165.14/164.99 <=> 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))))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_eq__number__of__Suc,axiom, % 165.14/164.99 ! [V_n_2,V_v_2] : % 165.14/164.99 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 165.14/164.99 <=> 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))))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__case__number__of,axiom, % 165.14/164.99 ! [V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),c_Int_Onat))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__number__of__Suc,axiom, % 165.14/164.99 ! [V_n_2,V_v_2] : % 165.14/164.99 ( 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))) % 165.14/164.99 <=> 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)))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__Suc__number__of,axiom, % 165.14/164.99 ! [V_v_2,V_n_2] : % 165.14/164.99 ( 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))) % 165.14/164.99 <=> 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))))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_le__Suc__number__of,axiom, % 165.14/164.99 ! [V_v_2,V_n_2] : % 165.14/164.99 ( 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))) % 165.14/164.99 <=> 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))))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_le__number__of__Suc,axiom, % 165.14/164.99 ! [V_n_2,V_v_2] : % 165.14/164.99 ( 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))) % 165.14/164.99 <=> 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)))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Suc__nat__number__of,axiom, % 165.14/164.99 ! [V_v] : % 165.14/164.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 165.14/164.99 => 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)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_max__Suc__number__of,axiom, % 165.14/164.99 ! [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)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_max__number__of__Suc,axiom, % 165.14/164.99 ! [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)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__case__add__eq__if,axiom, % 165.14/164.99 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_a,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__rec__add__eq__if,axiom, % 165.14/164.99 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__rec__number__of,axiom, % 165.14/164.99 ! [V_v_2,V_f_2,V_a_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_a,T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,T_a),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_a,V_a_2,V_f_2)),c_Int_Onat)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__equiv__class__type2,axiom, % 165.14/164.99 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 165.14/164.99 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 165.14/164.99 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 165.14/164.99 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A1_2),V_r1_2))) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A2_2),V_r2_2))) % 165.14/164.99 => ( ! [B_x1] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2)) % 165.14/164.99 => ! [B_x2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_c,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_UN__equiv__class__type,axiom, % 165.14/164.99 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 165.14/164.99 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/164.99 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 165.14/164.99 => ( ! [B_x] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__rec__0,axiom, % 165.14/164.99 ! [V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__rec__Suc,axiom, % 165.14/164.99 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_a,V_f1_2,V_f2_2),V_nat_2)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_eq__special_I3_J,axiom, % 165.14/164.99 ! [V_x_2,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a) % 165.14/164.99 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_eq__special_I1_J,axiom, % 165.14/164.99 ! [V_y_2,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 165.14/164.99 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power__number__of__odd__number__of,axiom, % 165.14/164.99 ! [V_v_2,V_w_2,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => ( ( 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))) % 165.14/164.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)))),c_COMBI(T_a))) ) % 165.14/164.99 & ( ~ 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))) % 165.14/164.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_zpower__number__of__odd,axiom, % 165.14/164.99 ! [V_z_2,V_w_2] : % 165.14/164.99 ( ( 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))) % 165.14/164.99 => 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))) ) % 165.14/164.99 & ( ~ 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))) % 165.14/164.99 => 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) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_iszero__number__of__Bit1,axiom, % 165.14/164.99 ! [V_w,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Int_Oring__char__0(T_a) ) % 165.14/164.99 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I34_J,axiom, % 165.14/164.99 ! [V_l_2,V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__eq__int__code_I16_J,axiom, % 165.14/164.99 ! [V_k2_2,V_k1_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I17_J,axiom, % 165.14/164.99 ! [V_l_2,V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__int__code_I16_J,axiom, % 165.14/164.99 ! [V_k2_2,V_k1_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I51_J,axiom, % 165.14/164.99 ! [V_l_2,V_k_2] : % 165.14/164.99 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 165.14/164.99 <=> V_k_2 = V_l_2 ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I46_J,axiom, % 165.14/164.99 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I39_J,axiom, % 165.14/164.99 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 165.14/164.99 % 165.14/164.99 fof(fact_not__iszero__Numeral1,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_iszero__def,axiom, % 165.14/164.99 ! [V_z_2,T_a] : % 165.14/164.99 ( class_Rings_Osemiring__1(T_a) % 165.14/164.99 => ( c_Int_Oiszero(T_a,V_z_2) % 165.14/164.99 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_iszero__0,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Rings_Osemiring__1(T_a) % 165.14/164.99 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_not__iszero__1,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Rings_Osemiring__1(T_a) % 165.14/164.99 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_bin__less__0__simps_I4_J,axiom, % 165.14/164.99 ! [V_w_2] : % 165.14/164.99 ( 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))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I22_J,axiom, % 165.14/164.99 ! [V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I12_J,axiom, % 165.14/164.99 ! [V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Bit1__def,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_neg__number__of__Bit1,axiom, % 165.14/164.99 ! [V_w_2] : % 165.14/164.99 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 165.14/164.99 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_minus__Bit1,axiom, % 165.14/164.99 ! [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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_succ__Pls,axiom, % 165.14/164.99 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of__Bit1,axiom, % 165.14/164.99 ! [V_w,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_mult__numeral__1,axiom, % 165.14/164.99 ! [V_a,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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 ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_mult__numeral__1__right,axiom, % 165.14/164.99 ! [V_a,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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 ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_semiring__norm_I110_J,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_numeral__1__eq__1,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I5_J,axiom, % 165.14/164.99 ! [V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I29_J,axiom, % 165.14/164.99 ! [V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_divide__Numeral1,axiom, % 165.14/164.99 ! [V_x,T_a] : % 165.14/164.99 ( ( class_Fields_Ofield(T_a) % 165.14/164.99 & class_Int_Onumber__ring(T_a) ) % 165.14/164.99 => 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 ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_divide__numeral__1,axiom, % 165.14/164.99 ! [V_a,T_a] : % 165.14/164.99 ( ( class_Fields_Ofield(T_a) % 165.14/164.99 & class_Int_Onumber__ring(T_a) ) % 165.14/164.99 => 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 ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_eq__special_I4_J,axiom, % 165.14/164.99 ! [V_x_2,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 165.14/164.99 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_eq__special_I2_J,axiom, % 165.14/164.99 ! [V_y_2,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 165.14/164.99 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_one__is__num__one,axiom, % 165.14/164.99 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__numeral__1__eq__1,axiom, % 165.14/164.99 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Numeral1__eq1__nat,axiom, % 165.14/164.99 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 165.14/164.99 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_iszero__Numeral0,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_numeral__1__eq__Suc__0,axiom, % 165.14/164.99 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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_numeral__3__eq__3,axiom, % 165.14/164.99 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)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power3__eq__cube,axiom, % 165.14/164.99 ! [V_a,T_a] : % 165.14/164.99 ( class_Groups_Omonoid__mult(T_a) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 165.14/164.99 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))))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Suc3__eq__add__3,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 165.14/164.99 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)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 165.14/164.99 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)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_le__special_I4_J,axiom, % 165.14/164.99 ! [V_x_2,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Rings_Olinordered__idom(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_le__special_I2_J,axiom, % 165.14/164.99 ! [V_y_2,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Rings_Olinordered__idom(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__special_I4_J,axiom, % 165.14/164.99 ! [V_x_2,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Rings_Olinordered__idom(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2)),c_Groups_Oone__class_Oone(T_a))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__special_I2_J,axiom, % 165.14/164.99 ! [V_y_2,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Rings_Olinordered__idom(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__special_I3_J,axiom, % 165.14/164.99 ! [V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__special_I2_J,axiom, % 165.14/164.99 ! [V_w,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Suc__diff__eq__diff__pred,axiom, % 165.14/164.99 ! [V_m,V_n] : % 165.14/164.99 ( 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)) % 165.14/164.99 => 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)))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_mod__Suc__eq__mod__add3,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Suc__mod__eq__add3__mod,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_div__Suc__eq__div__add3,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Suc__div__eq__add3__div,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_eq__number__of__eq,axiom, % 165.14/164.99 ! [V_y_2,V_x_2,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 165.14/164.99 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_diff__special_I1_J,axiom, % 165.14/164.99 ! [V_w,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_diff__special_I2_J,axiom, % 165.14/164.99 ! [V_v,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__number__of__Bit1,axiom, % 165.14/164.99 ! [V_w_2] : % 165.14/164.99 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 165.14/164.99 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 165.14/164.99 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 165.14/164.99 => 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)))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power__number__of__odd,axiom, % 165.14/164.99 ! [V_z_2,V_w_2,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => ( ( 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))) % 165.14/164.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2))),c_COMBI(T_a))) ) % 165.14/164.99 & ( ~ 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))) % 165.14/164.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_zmod__number__of__Bit1,axiom, % 165.14/164.99 ! [V_v,V_w] : % 165.14/164.99 ( ( 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))) % 165.14/164.99 => 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)) ) % 165.14/164.99 & ( ~ 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))) % 165.14/164.99 => 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)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_neg__zmod__mult__2,axiom, % 165.14/164.99 ! [V_b,V_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_arith__series__int,axiom, % 165.14/164.99 ! [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)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_pos__zdiv__mult__2,axiom, % 165.14/164.99 ! [V_b,V_a] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I49_J,axiom, % 165.14/164.99 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I50_J,axiom, % 165.14/164.99 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Bit0__Pls,axiom, % 165.14/164.99 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I38_J,axiom, % 165.14/164.99 ! [V_l_2] : % 165.14/164.99 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 165.14/164.99 <=> c_Int_OPls = V_l_2 ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I44_J,axiom, % 165.14/164.99 ! [V_k_2] : % 165.14/164.99 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 165.14/164.99 <=> V_k_2 = c_Int_OPls ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_diff__bin__simps_I7_J,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_minus__Bit0,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__int__code_I13_J,axiom, % 165.14/164.99 ! [V_k2_2,V_k1_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I14_J,axiom, % 165.14/164.99 ! [V_l_2,V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I48_J,axiom, % 165.14/164.99 ! [V_l_2,V_k_2] : % 165.14/164.99 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 165.14/164.99 <=> V_k_2 = V_l_2 ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_mult__Bit0,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Bit0__def,axiom, % 165.14/164.99 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__Bit0__Bit0,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__eq__int__code_I13_J,axiom, % 165.14/164.99 ! [V_k2_2,V_k1_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I31_J,axiom, % 165.14/164.99 ! [V_l_2,V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_bin__less__0__simps_I3_J,axiom, % 165.14/164.99 ! [V_w_2] : % 165.14/164.99 ( 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))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I21_J,axiom, % 165.14/164.99 ! [V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I27_J,axiom, % 165.14/164.99 ! [V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I32_J,axiom, % 165.14/164.99 ! [V_l_2,V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__eq__int__code_I14_J,axiom, % 165.14/164.99 ! [V_k2_2,V_k1_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I4_J,axiom, % 165.14/164.99 ! [V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I10_J,axiom, % 165.14/164.99 ! [V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I16_J,axiom, % 165.14/164.99 ! [V_l_2,V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__int__code_I15_J,axiom, % 165.14/164.99 ! [V_k2_2,V_k1_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__Bit0__Bit1,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__Bit1__Bit0,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_diff__bin__simps_I3_J,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_diff__bin__simps_I10_J,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_diff__bin__simps_I9_J,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_zdiv__number__of__Bit0,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_neg__number__of__Bit0,axiom, % 165.14/164.99 ! [V_w_2] : % 165.14/164.99 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 165.14/164.99 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_pred__Bit1,axiom, % 165.14/164.99 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 165.14/164.99 % 165.14/164.99 fof(fact_pred__Bit0,axiom, % 165.14/164.99 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_iszero__number__of__Bit0,axiom, % 165.14/164.99 ! [V_w_2,T_a] : % 165.14/164.99 ( ( class_Int_Onumber__ring(T_a) % 165.14/164.99 & class_Int_Oring__char__0(T_a) ) % 165.14/164.99 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2))) % 165.14/164.99 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_succ__Bit0,axiom, % 165.14/164.99 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 165.14/164.99 % 165.14/164.99 fof(fact_succ__Bit1,axiom, % 165.14/164.99 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__number__of__Bit0,axiom, % 165.14/164.99 ! [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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of__Bit0,axiom, % 165.14/164.99 ! [V_w,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I15_J,axiom, % 165.14/164.99 ! [V_l_2,V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__int__code_I14_J,axiom, % 165.14/164.99 ! [V_k2_2,V_k1_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_rel__simps_I33_J,axiom, % 165.14/164.99 ! [V_l_2,V_k_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_less__eq__int__code_I15_J,axiom, % 165.14/164.99 ! [V_k2_2,V_k1_2] : % 165.14/164.99 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_card__UNIV__bool,axiom, % 165.14/164.99 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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_mult__Bit1,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_diff__bin__simps_I8_J,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__Bit1__Bit1,axiom, % 165.14/164.99 ! [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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power__number__of__even,axiom, % 165.14/164.99 ! [V_w_2,V_z_2,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_zpower__number__of__even,axiom, % 165.14/164.99 ! [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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_double__number__of__Bit0,axiom, % 165.14/164.99 ! [V_w,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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)) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_number__of1,axiom, % 165.14/164.99 ! [V_n] : % 165.14/164.99 ( 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))) % 165.14/164.99 => ( 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)))) % 165.14/164.99 & 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)))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 165.14/164.99 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power__number__of__even__number__of,axiom, % 165.14/164.99 ! [V_w_2,V_v_2,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_a,T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Otimes__class_Otimes(T_a)),c_COMBI(T_a))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_mult__2__right,axiom, % 165.14/164.99 ! [V_z,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_mult__2,axiom, % 165.14/164.99 ! [V_z,T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_one__add__one__is__two,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Int_Onumber__ring(T_a) % 165.14/164.99 => 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))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_zero__power2,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Rings_Osemiring__1(T_a) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_zero__eq__power2,axiom, % 165.14/164.99 ! [V_a_2,T_a] : % 165.14/164.99 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 165.14/164.99 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) % 165.14/164.99 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_numeral__2__eq__2,axiom, % 165.14/164.99 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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_semiring__norm_I115_J,axiom, % 165.14/164.99 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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 165.14/164.99 ! [V_x,T_a] : % 165.14/164.99 ( class_Rings_Ocomm__semiring__1(T_a) % 165.14/164.99 => 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)))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power2__eq__square,axiom, % 165.14/164.99 ! [V_a,T_a] : % 165.14/164.99 ( class_Groups_Omonoid__mult(T_a) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 165.14/164.99 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))))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__2__eq__Suc,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__2__eq__Suc_H,axiom, % 165.14/164.99 ! [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)) ). % 165.14/164.99 % 165.14/164.99 fof(fact_one__power2,axiom, % 165.14/164.99 ! [T_a] : % 165.14/164.99 ( class_Rings_Osemiring__1(T_a) % 165.14/164.99 => 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) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power2__minus,axiom, % 165.14/164.99 ! [V_a,T_a] : % 165.14/164.99 ( class_Rings_Oring__1(T_a) % 165.14/164.99 => 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)))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__mult__2,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__mult__2__right,axiom, % 165.14/164.99 ! [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) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power__even__eq,axiom, % 165.14/164.99 ! [V_n,V_a,T_a] : % 165.14/164.99 ( class_Groups_Omonoid__mult(T_a) % 165.14/164.99 => 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)))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 165.14/164.99 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)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 165.14/164.99 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)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power2__abs,axiom, % 165.14/164.99 ! [V_a,T_a] : % 165.14/164.99 ( class_Rings_Olinordered__idom(T_a) % 165.14/164.99 => 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)))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_abs__power2,axiom, % 165.14/164.99 ! [V_a,T_a] : % 165.14/164.99 ( class_Rings_Olinordered__idom(T_a) % 165.14/164.99 => 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)))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_nat__1__add__1,axiom, % 165.14/164.99 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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_mod2__Suc__Suc,axiom, % 165.14/164.99 ! [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)))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_div2__Suc__Suc,axiom, % 165.14/164.99 ! [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))))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_zmod__number__of__Bit0,axiom, % 165.14/164.99 ! [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))) ). % 165.14/164.99 % 165.14/164.99 fof(fact_add__self__div__2,axiom, % 165.14/164.99 ! [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 ). % 165.14/164.99 % 165.14/164.99 fof(fact_half__gt__zero__iff,axiom, % 165.14/164.99 ! [V_r_2,T_a] : % 165.14/164.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber__ring(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 165.14/164.99 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_half__gt__zero,axiom, % 165.14/164.99 ! [V_r,T_a] : % 165.14/164.99 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 165.14/164.99 & class_Int_Onumber__ring(T_a) ) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 165.14/164.99 => 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)))))) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power2__eq__imp__eq,axiom, % 165.14/164.99 ! [V_y,V_x,T_a] : % 165.14/164.99 ( class_Rings_Olinordered__semidom(T_a) % 165.14/164.99 => ( 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)))) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 165.14/164.99 => V_x = V_y ) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power2__le__imp__le,axiom, % 165.14/164.99 ! [V_y,V_x,T_a] : % 165.14/164.99 ( class_Rings_Olinordered__semidom(T_a) % 165.14/164.99 => ( 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)))))) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 165.14/164.99 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_zero__le__power2,axiom, % 165.14/164.99 ! [V_a,T_a] : % 165.14/164.99 ( class_Rings_Olinordered__idom(T_a) % 165.14/164.99 => 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)))))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_power2__less__0,axiom, % 165.14/164.99 ! [V_a,T_a] : % 165.14/164.99 ( class_Rings_Olinordered__idom(T_a) % 165.14/164.99 => ~ 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))) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_zero__less__power2,axiom, % 165.14/164.99 ! [V_a_2,T_a] : % 165.14/164.99 ( class_Rings_Olinordered__idom(T_a) % 165.14/164.99 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) % 165.14/164.99 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 165.14/164.99 % 165.14/164.99 fof(fact_sum__power2__eq__zero__iff,axiom, % 165.14/164.99 ! [V_y_2,V_x_2,T_a] : % 165.14/164.99 ( class_Rings_Olinordered__idom(T_a) % 165.14/165.00 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_a) % 165.14/165.00 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 165.14/165.00 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_power2__eq__square__number__of,axiom, % 165.14/165.00 ! [V_w,T_b] : % 165.14/165.00 ( ( class_Groups_Omonoid__mult(T_b) % 165.14/165.00 & class_Int_Onumber(T_b) ) % 165.14/165.00 => 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_less__2__cases,axiom, % 165.14/165.00 ! [V_n] : % 165.14/165.00 ( 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))))) % 165.14/165.00 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.00 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_nat__2,axiom, % 165.14/165.00 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))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_power2__eq__1__iff,axiom, % 165.14/165.00 ! [V_a_2,T_a] : % 165.14/165.00 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 165.14/165.00 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) % 165.14/165.00 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a) % 165.14/165.00 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 165.14/165.00 ! [V_n,V_x,T_a] : % 165.14/165.00 ( class_Rings_Ocomm__semiring__1(T_a) % 165.14/165.00 => 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_power__minus__even,axiom, % 165.14/165.00 ! [V_n,V_a,T_a] : % 165.14/165.00 ( class_Rings_Oring__1(T_a) % 165.14/165.00 => 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_power2__less__imp__less,axiom, % 165.14/165.00 ! [V_y,V_x,T_a] : % 165.14/165.00 ( class_Rings_Olinordered__semidom(T_a) % 165.14/165.00 => ( 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)))))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_sum__power2__ge__zero,axiom, % 165.14/165.00 ! [V_y,V_x,T_a] : % 165.14/165.00 ( class_Rings_Olinordered__idom(T_a) % 165.14/165.00 => 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))))))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_sum__power2__le__zero__iff,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,T_a] : % 165.14/165.00 ( class_Rings_Olinordered__idom(T_a) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/165.00 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 165.14/165.00 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_sum__power2__gt__zero__iff,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,T_a] : % 165.14/165.00 ( class_Rings_Olinordered__idom(T_a) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) % 165.14/165.00 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 165.14/165.00 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_not__sum__power2__lt__zero,axiom, % 165.14/165.00 ! [V_y,V_x,T_a] : % 165.14/165.00 ( class_Rings_Olinordered__idom(T_a) % 165.14/165.00 => ~ 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))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_power2__sum,axiom, % 165.14/165.00 ! [V_y,V_x,T_a] : % 165.14/165.00 ( class_Int_Onumber__ring(T_a) % 165.14/165.00 => 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zero__le__even__power_H,axiom, % 165.14/165.00 ! [V_n,V_a,T_a] : % 165.14/165.00 ( class_Rings_Olinordered__idom(T_a) % 165.14/165.00 => 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)))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_power__odd__eq,axiom, % 165.14/165.00 ! [V_n,V_a,T_a] : % 165.14/165.00 ( class_Groups_Omonoid__mult(T_a) % 165.14/165.00 => 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))))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 165.14/165.00 ! [V_n,V_x,T_a] : % 165.14/165.00 ( class_Rings_Ocomm__semiring__1(T_a) % 165.14/165.00 => 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))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_power__minus1__even,axiom, % 165.14/165.00 ! [V_n,T_a] : % 165.14/165.00 ( class_Rings_Oring__1(T_a) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zdiv__number__of__Bit1,axiom, % 165.14/165.00 ! [V_v,V_w] : % 165.14/165.00 ( ( 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))) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( ~ 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))) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mod2__gr__0,axiom, % 165.14/165.00 ! [V_m_2] : % 165.14/165.00 ( 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)))))) % 165.14/165.00 <=> 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_div__2__gt__zero,axiom, % 165.14/165.00 ! [V_n] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 165.14/165.00 => 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)))))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_power2__diff,axiom, % 165.14/165.00 ! [V_y,V_x,T_a] : % 165.14/165.00 ( class_Int_Onumber__ring(T_a) % 165.14/165.00 => 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_odd__0__le__power__imp__0__le,axiom, % 165.14/165.00 ! [V_n,V_a,T_a] : % 165.14/165.00 ( class_Rings_Olinordered__idom(T_a) % 165.14/165.00 => ( 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))))) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_odd__power__less__zero,axiom, % 165.14/165.00 ! [V_n,V_a,T_a] : % 165.14/165.00 ( class_Rings_Olinordered__idom(T_a) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 165.14/165.00 => 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))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_power__minus1__odd,axiom, % 165.14/165.00 ! [V_n,T_a] : % 165.14/165.00 ( class_Rings_Oring__1(T_a) % 165.14/165.00 => 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Suc__n__div__2__gt__zero,axiom, % 165.14/165.00 ! [V_n] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 165.14/165.00 => 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)))))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_of__nat__double,axiom, % 165.14/165.00 ! [V_x,T_a] : % 165.14/165.00 ( class_Rings_Osemiring__1(T_a) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 165.14/165.00 => 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))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pos__zmod__mult__2,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 165.14/165.00 => 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))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_neg__zdiv__mult__2,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_int__of__code,axiom, % 165.14/165.00 ! [V_k] : % 165.14/165.00 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 165.14/165.00 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 165.14/165.00 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 165.14/165.00 => ( ( 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) % 165.14/165.00 => 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)))))) ) % 165.14/165.00 & ( 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) % 165.14/165.00 => 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)) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_of__int__num,axiom, % 165.14/165.00 ! [V_k_2,T_a] : % 165.14/165.00 ( class_Rings_Oring__1(T_a) % 165.14/165.00 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) ) % 165.14/165.00 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) ) % 165.14/165.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,T_a),T_a),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_a,T_a)),tc_fun(tc_Int_Oint,T_a)),tc_Int_Oint),c_COMBB(tc_fun(T_a,T_a),T_a,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_fun(T_a,T_a),T_a),tc_Int_Oint),c_HOL_OLet(T_a,T_a)),c_Int_Oring__1__class_Oof__int(T_a)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,T_a)),tc_Int_Oint),c_COMBS(T_a,T_a,T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_a,T_a)),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_fun(T_a,T_a))),tc_Int_Oint),c_COMBB(T_a,tc_fun(T_a,T_a),T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),tc_Int_Oint),c_If(T_a)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a))))),hAPP(hAPP(c_COMBC(T_a,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_a),c_Groups_Oplus__class_Oplus(T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,T_a),c_Groups_Oplus__class_Oplus(T_a)),c_COMBI(T_a)))),c_Groups_Oone__class_Oone(T_a))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_power__m1__odd,axiom, % 165.14/165.00 ! [V_n,T_a] : % 165.14/165.00 ( class_Int_Onumber__ring(T_a) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I45_J,axiom, % 165.14/165.00 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I42_J,axiom, % 165.14/165.00 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I24_J,axiom, % 165.14/165.00 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I7_J,axiom, % 165.14/165.00 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_code__numeral__zero__minus__one,axiom, % 165.14/165.00 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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I37_J,axiom, % 165.14/165.00 c_Int_OPls != c_Int_OMin ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I40_J,axiom, % 165.14/165.00 c_Int_OMin != c_Int_OPls ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I47_J,axiom, % 165.14/165.00 ! [V_k_2] : % 165.14/165.00 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 165.14/165.00 <=> V_k_2 = c_Int_OMin ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I43_J,axiom, % 165.14/165.00 ! [V_l_2] : % 165.14/165.00 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 165.14/165.00 <=> c_Int_OMin = V_l_2 ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Bit1__Min,axiom, % 165.14/165.00 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 165.14/165.00 % 165.14/165.00 fof(fact_bin__less__0__simps_I2_J,axiom, % 165.14/165.00 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I20_J,axiom, % 165.14/165.00 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I23_J,axiom, % 165.14/165.00 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I30_J,axiom, % 165.14/165.00 ! [V_k_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I26_J,axiom, % 165.14/165.00 ! [V_k_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I3_J,axiom, % 165.14/165.00 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I6_J,axiom, % 165.14/165.00 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I13_J,axiom, % 165.14/165.00 ! [V_k_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I9_J,axiom, % 165.14/165.00 ! [V_k_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I28_J,axiom, % 165.14/165.00 ! [V_k_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I8_J,axiom, % 165.14/165.00 ! [V_k_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_eq__number__of__Pls__Min,axiom, % 165.14/165.00 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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Int_OMin__def,axiom, % 165.14/165.00 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mult__Min,axiom, % 165.14/165.00 ! [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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_neg__number__of__Min,axiom, % 165.14/165.00 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pred__Pls,axiom, % 165.14/165.00 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 165.14/165.00 % 165.14/165.00 fof(fact_add__Min__right,axiom, % 165.14/165.00 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 165.14/165.00 % 165.14/165.00 fof(fact_add__Min,axiom, % 165.14/165.00 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pred__Min,axiom, % 165.14/165.00 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 165.14/165.00 % 165.14/165.00 fof(fact_nonzero__number__of__Min,axiom, % 165.14/165.00 ! [T_a] : % 165.14/165.00 ( class_Int_Onumber__ring(T_a) % 165.14/165.00 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_succ__Min,axiom, % 165.14/165.00 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 165.14/165.00 % 165.14/165.00 fof(fact_diff__bin__simps_I2_J,axiom, % 165.14/165.00 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mult__minus1__right,axiom, % 165.14/165.00 ! [V_z,T_a] : % 165.14/165.00 ( class_Int_Onumber__ring(T_a) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mult__minus1,axiom, % 165.14/165.00 ! [V_z,T_a] : % 165.14/165.00 ( class_Int_Onumber__ring(T_a) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_number__of__Min,axiom, % 165.14/165.00 ! [T_a] : % 165.14/165.00 ( class_Int_Onumber__ring(T_a) % 165.14/165.00 => 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_arith__simps_I31_J,axiom, % 165.14/165.00 ! [T_a] : % 165.14/165.00 ( class_Int_Onumber__ring(T_a) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_abs__minus__one,axiom, % 165.14/165.00 ! [T_a] : % 165.14/165.00 ( ( class_Int_Onumber__ring(T_a) % 165.14/165.00 & class_Rings_Olinordered__idom(T_a) ) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divide__minus1,axiom, % 165.14/165.00 ! [V_x,T_a] : % 165.14/165.00 ( ( class_Fields_Ofield__inverse__zero(T_a) % 165.14/165.00 & class_Int_Onumber__ring(T_a) ) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I11_J,axiom, % 165.14/165.00 ! [V_k_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rel__simps_I25_J,axiom, % 165.14/165.00 ! [V_k_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zmod__minus1__right,axiom, % 165.14/165.00 ! [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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_diff__bin__simps_I4_J,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_minus__Min,axiom, % 165.14/165.00 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 165.14/165.00 ! [V_n,V_m] : % 165.14/165.00 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 165.14/165.00 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 165.14/165.00 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zmult__eq__1__iff,axiom, % 165.14/165.00 ! [V_n_2,V_m_2] : % 165.14/165.00 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 165.14/165.00 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 165.14/165.00 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 165.14/165.00 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 165.14/165.00 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_diff__bin__simps_I6_J,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_diff__bin__simps_I5_J,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_of__int__m1,axiom, % 165.14/165.00 ! [T_a] : % 165.14/165.00 ( class_Int_Onumber__ring(T_a) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zdiv__minus1__right,axiom, % 165.14/165.00 ! [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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zero__code__numeral__code,axiom, % 165.14/165.00 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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_minus1__divide,axiom, % 165.14/165.00 ! [V_x,T_a] : % 165.14/165.00 ( ( class_Fields_Ofield__inverse__zero(T_a) % 165.14/165.00 & class_Int_Onumber__ring(T_a) ) % 165.14/165.00 => 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_abs__power__minus__one,axiom, % 165.14/165.00 ! [V_n,T_a] : % 165.14/165.00 ( ( class_Int_Onumber__ring(T_a) % 165.14/165.00 & class_Rings_Olinordered__idom(T_a) ) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_div__eq__minus1,axiom, % 165.14/165.00 ! [V_b] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_div__pos__neg__trivial,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 165.14/165.00 => ( 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))) % 165.14/165.00 => 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) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zmod__minus1,axiom, % 165.14/165.00 ! [V_b] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_one__code__numeral__code,axiom, % 165.14/165.00 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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_power__m1__even,axiom, % 165.14/165.00 ! [V_n,T_a] : % 165.14/165.00 ( class_Int_Onumber__ring(T_a) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Nitpick_OFrac__def,axiom, % 165.14/165.00 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)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_small__int__def,axiom, % 165.14/165.00 ! [V_d_2,V_f_2] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),V_f_2),V_d_2) = c_Smallcheck_Osmall_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_int__ge__less__than__def,axiom, % 165.14/165.00 ! [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)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inj__graph,axiom, % 165.14/165.00 ! [T_b,T_a] : c_Fun_Oinj__on(tc_fun(T_a,T_b),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Set_OCollect(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,T_b)),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool)),hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_int__ge__less__than2__def,axiom, % 165.14/165.00 ! [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)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Nitpick_Oprod__def,axiom, % 165.14/165.00 ! [V_B_2,V_A_2,T_b,T_a] : c_Nitpick_Oprod(T_a,T_b,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_nat__of__aux__code,axiom, % 165.14/165.00 ! [V_n,V_i] : % 165.14/165.00 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 165.14/165.00 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 165.14/165.00 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__int__rel__def,axiom, % 165.14/165.00 ! [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))))))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_finite__psubset__def,axiom, % 165.14/165.00 ! [T_a] : c_Wellfounded_Ofinite__psubset(T_a) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_a)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_full__small__int__def,axiom, % 165.14/165.00 ! [V_d_2,V_f_2] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,V_f_2,V_d_2) = c_Smallcheck_Ofull__small_H(V_f_2,hAPP(c_Code__Numeral_Oint__of,V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,V_d_2))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__int__correct,axiom, % 165.14/165.00 ! [V_a,V_b] : % 165.14/165.00 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zmult2__lemma,axiom, % 165.14/165.00 ! [V_c,V_r,V_q,V_b,V_a] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 165.14/165.00 => 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)))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_code__numeral_Osize_I1_J,axiom, % 165.14/165.00 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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Nats__number__of,axiom, % 165.14/165.00 ! [V_w_2,T_a] : % 165.14/165.00 ( class_Int_Onumber__ring(T_a) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_sup__Un__eq2,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2)) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pred__subset__eq2,axiom, % 165.14/165.00 ! [V_S_2,V_R_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2))) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pred__equals__eq2,axiom, % 165.14/165.00 ! [V_S_2,V_R_2,T_b,T_a] : % 165.14/165.00 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2) % 165.14/165.00 <=> V_R_2 = V_S_2 ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inf__Int__eq2,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)),V_x_2),V_y_2)) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_R_2),V_S_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_congruent2D,axiom, % 165.14/165.00 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_c,T_b,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y1_2),V_z1_2)),V_r1_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y2_2),V_z2_2)),V_r2_2)) % 165.14/165.00 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_congruentD,axiom, % 165.14/165.00 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_r_2)) % 165.14/165.00 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_bot__empty__eq2,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2)) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_small__prod__def,axiom, % 165.14/165.00 ! [V_d_2,V_f_2,T_a,T_b] : % 165.14/165.00 ( ( class_Smallcheck_Osmall(T_b) % 165.14/165.00 & class_Smallcheck_Osmall(T_a) ) % 165.14/165.00 => hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(T_a,T_b)),V_f_2),V_d_2) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(T_a),hAPP(hAPP(c_COMBC(T_a,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),c_Smallcheck_Osmall__class_Osmall(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b)))),V_d_2)),V_d_2) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Image__iff,axiom, % 165.14/165.00 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 165.14/165.00 <=> ? [B_x] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 165.14/165.00 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rev__ImageI,axiom, % 165.14/165.00 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__int__rel__0,axiom, % 165.14/165.00 ! [V_b] : % 165.14/165.00 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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)))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_self__remainder,axiom, % 165.14/165.00 ! [V_r,V_q,V_a] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_unique__quotient,axiom, % 165.14/165.00 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( 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))) % 165.14/165.00 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => V_q = V_q_H ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_unique__remainder,axiom, % 165.14/165.00 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( 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))) % 165.14/165.00 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => V_r = V_r_H ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_SUP__UN__eq2,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c))))),V_r_2)),V_x_2),V_y_2)) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_self__quotient,axiom, % 165.14/165.00 ! [V_r,V_q,V_a] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__int__rel__mod,axiom, % 165.14/165.00 ! [V_r,V_q,V_b,V_a] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__int__rel__div,axiom, % 165.14/165.00 ! [V_r,V_q,V_b,V_a] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Nats__0,axiom, % 165.14/165.00 ! [T_a] : % 165.14/165.00 ( class_Rings_Osemiring__1(T_a) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__int__mod__div,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Nats__add,axiom, % 165.14/165.00 ! [V_b_2,V_a_2,T_a] : % 165.14/165.00 ( class_Rings_Osemiring__1(T_a) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Nats__mult,axiom, % 165.14/165.00 ! [V_b_2,V_a_2,T_a] : % 165.14/165.00 ( class_Rings_Osemiring__1(T_a) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Nats__1,axiom, % 165.14/165.00 ! [T_a] : % 165.14/165.00 ( class_Rings_Osemiring__1(T_a) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_of__nat__in__Nats,axiom, % 165.14/165.00 ! [V_n_2,T_a] : % 165.14/165.00 ( class_Rings_Osemiring__1(T_a) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Image__singleton__iff,axiom, % 165.14/165.00 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_equiv__class__eq,axiom, % 165.14/165.00 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 165.14/165.00 => hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_quotient__eqI,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 165.14/165.00 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_quotient__eq__iff,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 165.14/165.00 => ( V_X_2 = V_Y_2 % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__int__rel__div__mod,axiom, % 165.14/165.00 ! [V_a,V_b] : % 165.14/165.00 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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)))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Image__singleton,axiom, % 165.14/165.00 ! [V_a_2,V_r_2,T_a,T_b] : hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_b,T_a))),hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2))),V_r_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_equiv__class__eq__iff,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 165.14/165.00 <=> ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 165.14/165.00 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.00 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_eq__equiv__class__iff,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 165.14/165.00 => ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_eq__equiv__class,axiom, % 165.14/165.00 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] : % 165.14/165.00 ( hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 165.14/165.00 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_equiv__class__subset,axiom, % 165.14/165.00 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_eq__equiv__class__iff2,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 165.14/165.00 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_r_2) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zadd1__lemma,axiom, % 165.14/165.00 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( 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))) % 165.14/165.00 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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)))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zminus1__lemma,axiom, % 165.14/165.00 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 165.14/165.00 ( 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))) % 165.14/165.00 => 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))))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_subset__equiv__class,axiom, % 165.14/165.00 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_equiv__class__nondisjoint,axiom, % 165.14/165.00 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))))) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__int__relI,axiom, % 165.14/165.00 ! [V_r,V_q,V_b,V_a] : % 165.14/165.00 ( 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) % 165.14/165.00 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 165.14/165.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 165.14/165.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 165.14/165.00 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 165.14/165.00 => 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))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zmult1__lemma,axiom, % 165.14/165.00 ! [V_a,V_r,V_q,V_c,V_b] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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)))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pair__imageI,axiom, % 165.14/165.00 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_A_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),V_A_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_norm__frac_Osimps,axiom, % 165.14/165.00 ! [V_a_2,V_b_2] : % 165.14/165.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 165.14/165.00 => 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))) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_adjust__def,axiom, % 165.14/165.00 ! [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))))))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_sup2CI,axiom, % 165.14/165.00 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] : % 165.14/165.00 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 165.14/165.00 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_sup2E,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 165.14/165.00 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inf2I,axiom, % 165.14/165.00 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inf2E,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 165.14/165.00 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 165.14/165.00 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mem__splitI,axiom, % 165.14/165.00 ! [T_c,T_b,V_b_2,V_a_2,V_ca_2,V_z_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2))) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_splitI,axiom, % 165.14/165.00 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_prod__caseI,axiom, % 165.14/165.00 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_bot2E,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,T_b,T_a] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_x_2),V_y_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_swap__inj__on,axiom, % 165.14/165.00 ! [V_A_2,T_b,T_a] : c_Fun_Oinj__on(tc_prod(T_a,T_b),tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_b,T_a)),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))),V_A_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_splitD_H,axiom, % 165.14/165.00 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_ca_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inf2D1,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inf2D2,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_predicate2D,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rev__predicate2D,axiom, % 165.14/165.00 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_P_2),V_Q_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_sup2I2,axiom, % 165.14/165.00 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_sup2I1,axiom, % 165.14/165.00 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_split__paired__All,axiom, % 165.14/165.00 ! [T_b,T_a,V_P_2] : % 165.14/165.00 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 165.14/165.00 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Pair__eq,axiom, % 165.14/165.00 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.00 ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2) % 165.14/165.00 <=> ( V_a_2 = V_a_H_2 % 165.14/165.00 & V_b_2 = V_b_H_2 ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Pair__inject,axiom, % 165.14/165.00 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 165.14/165.00 ( 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) % 165.14/165.00 => ~ ( V_a = V_a_H % 165.14/165.00 => V_b != V_b_H ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_split__weak__cong,axiom, % 165.14/165.00 ! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] : % 165.14/165.00 ( V_p_2 = V_q_2 % 165.14/165.00 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_ca_2),V_q_2) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_in__finite__psubset,axiom, % 165.14/165.00 ! [V_B_2,V_A_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a))) % 165.14/165.00 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 165.14/165.00 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_split__twice,axiom, % 165.14/165.00 ! [V_p_2,V_g_2,T_e,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_b,T_c)),tc_fun(T_e,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_e),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2))),V_g_2)),V_p_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_split__conv,axiom, % 165.14/165.00 ! [V_b_2,V_a_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_prod_Osimps_I2_J,axiom, % 165.14/165.00 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_splitD,axiom, % 165.14/165.00 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2))) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_split__eta,axiom, % 165.14/165.00 ! [V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,T_c),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),T_c,T_b),V_f_2)),c_Product__Type_OPair(T_a,T_b))) = V_f_2 ). % 165.14/165.00 % 165.14/165.00 fof(fact_split__paired__The,axiom, % 165.14/165.00 ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),V_P_2) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_The__split__eq,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_adjust__eq,axiom, % 165.14/165.00 ! [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))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_in__rel__def,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_div__mod__code__numeral__def,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 165.14/165.00 ! [V_w] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ( 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)))) % 165.14/165.00 => 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))) ) % 165.14/165.00 & ( ~ 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)))) % 165.14/165.00 => 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)))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_negDivAlg__correct,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_negDivAlg__div__mod,axiom, % 165.14/165.00 ! [V_l,V_k] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_negDivAlg__minus1,axiom, % 165.14/165.00 ! [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))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_negDivAlg_Osimps,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( ( ( 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))) % 165.14/165.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( ~ ( 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))) % 165.14/165.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 165.14/165.00 => 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))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_negDivAlg__eqn__number__of,axiom, % 165.14/165.00 ! [V_w,V_v] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ( 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)))) % 165.14/165.00 => 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))) ) % 165.14/165.00 & ( ~ 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)))) % 165.14/165.00 => 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)))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_negDivAlg__eqn,axiom, % 165.14/165.00 ! [V_a,V_b] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => ( ( 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))) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( ~ 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))) % 165.14/165.00 => 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))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Nitpick_Orefl_H__def,axiom, % 165.14/165.00 ! [V_r_2,T_a] : % 165.14/165.00 ( c_Nitpick_Orefl_H(T_a,V_r_2) % 165.14/165.00 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 165.14/165.00 ! [V_w] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ( 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))) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( ~ 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))) % 165.14/165.00 => 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)))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_posDivAlg_Osimps,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 165.14/165.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 165.14/165.00 => 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) ) % 165.14/165.00 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 165.14/165.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 165.14/165.00 => 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))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_posDivAlg__0,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_posDivAlg__correct,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_posDivAlg__div__mod,axiom, % 165.14/165.00 ! [V_l,V_k] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_posDivAlg__eqn,axiom, % 165.14/165.00 ! [V_a,V_b] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 165.14/165.00 => 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) ) % 165.14/165.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 165.14/165.00 => 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))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_posDivAlg__eqn__number__of,axiom, % 165.14/165.00 ! [V_w,V_v] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ( 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))) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( ~ 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))) % 165.14/165.00 => 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)))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__int__def,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 165.14/165.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 165.14/165.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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))) ) ) ) ) ) % 165.14/165.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 165.14/165.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 165.14/165.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => 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))) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__step,axiom, % 165.14/165.00 ! [V_m,V_n] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__int__pdivmod,axiom, % 165.14/165.00 ! [V_l_2,V_k_2] : % 165.14/165.00 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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) ) % 165.14/165.00 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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)))) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_negateSnd__def,axiom, % 165.14/165.00 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_apsnd__conv,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),hAPP(V_f_2,V_y_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__zero,axiom, % 165.14/165.00 ! [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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__base,axiom, % 165.14/165.00 ! [V_n,V_m] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_negateSnd__eq,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__div__mod,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__int__rel__neg,axiom, % 165.14/165.00 ! [V_qr,V_b,V_a] : % 165.14/165.00 ( 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)) % 165.14/165.00 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__if,axiom, % 165.14/165.00 ! [V_m_2,V_n_2] : % 165.14/165.00 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 165.14/165.00 => 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) ) % 165.14/165.00 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pdivmod__def,axiom, % 165.14/165.00 ! [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))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pdivmod__posDivAlg,axiom, % 165.14/165.00 ! [V_k,V_l] : % 165.14/165.00 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__int__code,axiom, % 165.14/165.00 ! [V_l_2,V_k_2] : % 165.14/165.00 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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) ) % 165.14/165.00 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 => 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)))) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_UN__equiv__class__inject,axiom, % 165.14/165.00 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.00 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 165.14/165.00 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Y_2),V_f_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 165.14/165.00 => ( ! [B_x] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.00 => ! [B_y] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 165.14/165.00 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) ) ) ) % 165.14/165.00 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 165.14/165.00 ! [V_a,V_r,V_q,V_c,V_b] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 165.14/165.00 => 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)))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 165.14/165.00 ! [V_c,V_r,V_q,V_b,V_a] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 165.14/165.00 => 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)))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__rel__unique,axiom, % 165.14/165.00 ! [V_qr_H,V_qr,V_n,V_m] : % 165.14/165.00 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 165.14/165.00 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 165.14/165.00 => V_qr = V_qr_H ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__eq,axiom, % 165.14/165.00 ! [V_qr,V_n,V_m] : % 165.14/165.00 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 165.14/165.00 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 165.14/165.00 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__def,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mod__eq,axiom, % 165.14/165.00 ! [V_r,V_q,V_n,V_m] : % 165.14/165.00 ( 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))) % 165.14/165.00 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_div__eq,axiom, % 165.14/165.00 ! [V_r,V_q,V_n,V_m] : % 165.14/165.00 ( 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))) % 165.14/165.00 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__rel,axiom, % 165.14/165.00 ! [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)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__rel__add1__eq,axiom, % 165.14/165.00 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( 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))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 165.14/165.00 => 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)))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_negDivAlg_Opsimps,axiom, % 165.14/165.00 ! [V_b_2,V_a_2] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ( ( 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))) % 165.14/165.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( ~ ( 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))) % 165.14/165.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 165.14/165.00 => 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))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_small_H_Opsimps,axiom, % 165.14/165.00 ! [V_i_2,V_d_2,V_f_2] : % 165.14/165.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_f_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))) % 165.14/165.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 165.14/165.00 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 165.14/165.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 165.14/165.00 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),tc_List_Olist(tc_Code__Evaluation_Oterm),c_Smallcheck_Osmall_H(V_f_2,V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(V_f_2,V_i_2)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_posDivAlg_Opsimps,axiom, % 165.14/165.00 ! [V_b_2,V_a_2] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 165.14/165.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 165.14/165.00 => 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) ) % 165.14/165.00 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 165.14/165.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 165.14/165.00 => 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))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_accp_Osimps,axiom, % 165.14/165.00 ! [V_a_2,V_r_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 165.14/165.00 <=> ! [B_x] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 165.14/165.00 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_accp_Oequations,axiom, % 165.14/165.00 ! [V_a_2,V_r_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 165.14/165.00 <=> ! [B_x] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 165.14/165.00 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_accp__downward,axiom, % 165.14/165.00 ! [V_a_2,V_b_2,V_r_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 165.14/165.00 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_accp__subset,axiom, % 165.14/165.00 ! [V_R2_2,V_R1_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_R1_2),V_R2_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_a,V_R2_2)),c_Wellfounded_Oaccp(T_a,V_R1_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_norm__frac_Opsimps,axiom, % 165.14/165.00 ! [V_b_2,V_a_2] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 165.14/165.00 => 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)) ) % 165.14/165.00 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 165.14/165.00 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 165.14/165.00 => 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))) ) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_negDivAlg_Opinduct,axiom, % 165.14/165.00 ! [V_P_2,V_a1_2,V_a0_2] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ! [B_a,B_b] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ( ~ ( 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))) % 165.14/165.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) ) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_posDivAlg_Opinduct,axiom, % 165.14/165.00 ! [V_P_2,V_a1_2,V_a0_2] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ! [B_a,B_b] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 165.14/165.00 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) ) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_nat__gcd_Opsimps,axiom, % 165.14/165.00 ! [V_y_2,V_x_2] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.00 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 165.14/165.00 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.00 => 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)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_small_H_Opinduct,axiom, % 165.14/165.00 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] : % 165.14/165.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),V_a0_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a1_2),V_a2_2)))) % 165.14/165.00 => ( ! [B_f,B_d,B_i] : % 165.14/165.00 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),c_Smallcheck_Osmall_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),tc_prod(tc_Int_Oint,tc_Int_Oint)),B_f),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))) % 165.14/165.00 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 165.14/165.00 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 165.14/165.00 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) % 165.14/165.00 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) ) % 165.14/165.00 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mod__pos__neg__1__number__of,axiom, % 165.14/165.00 ! [V_w] : % 165.14/165.00 ( 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))) % 165.14/165.00 => 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))))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_snd__apsnd,axiom, % 165.14/165.00 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapsnd(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_apsnd__eq__conv,axiom, % 165.14/165.00 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] : % 165.14/165.00 ( hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_g_2),V_x_2) % 165.14/165.00 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_c),V_x_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_snd__def,axiom, % 165.14/165.00 ! [V_p_2,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,T_a),hAPP(c_COMBK(tc_fun(T_a,T_a),T_b),c_COMBI(T_a))),V_p_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_snd__conv,axiom, % 165.14/165.00 ! [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 ). % 165.14/165.00 % 165.14/165.00 fof(fact_snd__eqD,axiom, % 165.14/165.00 ! [V_a,V_y,V_x,T_a,T_b] : % 165.14/165.00 ( 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 % 165.14/165.00 => V_y = V_a ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mod__int__def,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mod__neg__pos,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mod__pos__pos,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mod__pos__pos__1__number__of,axiom, % 165.14/165.00 ! [V_w] : % 165.14/165.00 ( 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))) % 165.14/165.00 => 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))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mod__pos__neg,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => 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)))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mod__neg__neg,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => 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)))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_in__measure,axiom, % 165.14/165.00 ! [V_f_2,V_y_2,V_x_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_a),V_f_2))) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_irrefl__def,axiom, % 165.14/165.00 ! [V_r_2,T_a] : % 165.14/165.00 ( c_Relation_Oirrefl(T_a,V_r_2) % 165.14/165.00 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_norm__frac_Opinduct,axiom, % 165.14/165.00 ! [V_P_2,V_a1_2,V_a0_2] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ! [B_a,B_b] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) ) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mod__nat__def,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_div__pos__neg__1__number__of,axiom, % 165.14/165.00 ! [V_w] : % 165.14/165.00 ( 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))) % 165.14/165.00 => 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))))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_nat__def,axiom, % 165.14/165.00 ! [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)))))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_nat__gcd_Opinduct,axiom, % 165.14/165.00 ! [V_P_2,V_a1_2,V_a0_2] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ! [B_x,B_y] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) ) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Pair__fst__snd__eq,axiom, % 165.14/165.00 ! [T_b,T_a,V_t_2,V_s_2] : % 165.14/165.00 ( V_s_2 = V_t_2 % 165.14/165.00 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2) % 165.14/165.00 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_prod__eqI,axiom, % 165.14/165.00 ! [V_q,V_p,T_b,T_a] : % 165.14/165.00 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 165.14/165.00 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 165.14/165.00 => V_p = V_q ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_fst__apsnd,axiom, % 165.14/165.00 ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_a,T_c),V_x_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_fst__def,axiom, % 165.14/165.00 ! [V_p_2,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_a),c_COMBK(T_a,T_b)),V_p_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Rep__Integ__inject,axiom, % 165.14/165.00 ! [V_y_2,V_x_2] : % 165.14/165.00 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 165.14/165.00 <=> V_x_2 = V_y_2 ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_fst__conv,axiom, % 165.14/165.00 ! [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 ). % 165.14/165.00 % 165.14/165.00 fof(fact_fst__eqD,axiom, % 165.14/165.00 ! [V_a,V_y,V_x,T_b,T_a] : % 165.14/165.00 ( 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 % 165.14/165.00 => V_x = V_a ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_surjective__pairing,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pair__collapse,axiom, % 165.14/165.00 ! [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 ). % 165.14/165.00 % 165.14/165.00 fof(fact_prod__case__beta,axiom, % 165.14/165.00 ! [V_p_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_div__int__def,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_split__beta,axiom, % 165.14/165.00 ! [V_z_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_z_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_z_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_split__comp__eq,axiom, % 165.14/165.00 ! [V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),tc_prod(T_a,T_b)),V_f_2),hAPP(hAPP(c_COMBB(T_a,T_d,tc_prod(T_a,T_b)),V_g_2),c_Product__Type_Ofst(T_a,T_b)))),c_Product__Type_Osnd(T_a,T_b)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,T_c),T_a),V_f_2),V_g_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_split__def,axiom, % 165.14/165.00 ! [V_p_2,V_ca_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_The__split,axiom, % 165.14/165.00 ! [V_P_2,T_b,T_a] : c_HOL_OThe(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_div__neg__pos,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_div__pos__pos,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_div__pos__pos__1__number__of,axiom, % 165.14/165.00 ! [V_w] : % 165.14/165.00 ( 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))) % 165.14/165.00 => 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))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_div__pos__neg,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => 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)))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_div__neg__neg,axiom, % 165.14/165.00 ! [V_b,V_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 165.14/165.00 => 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)))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_prod__size__simp,axiom, % 165.14/165.00 ! [V_p_2,V_g_2,V_f_2,T_b,T_a] : c_Product__Type_Oprod_Oprod__size(T_a,T_b,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_conjI__realizer,axiom, % 165.14/165.00 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] : % 165.14/165.00 ( hBOOL(hAPP(V_P_2,V_p_2)) % 165.14/165.00 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 165.14/165.00 => ( hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2)))) % 165.14/165.00 & hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_p_2),V_q_2)))) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_exI__realizer,axiom, % 165.14/165.00 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_div__nat__def,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_divmod__nat__rel__def,axiom, % 165.14/165.00 ! [V_qr_2,V_n_2,V_m_2] : % 165.14/165.00 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 165.14/165.00 <=> ( 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)) % 165.14/165.00 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.00 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 165.14/165.00 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.00 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 165.14/165.00 => ( 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))) % 165.14/165.00 & 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)) ) ) % 165.14/165.00 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 165.14/165.00 => ( 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))) % 165.14/165.00 & 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))) ) ) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inv__image__def,axiom, % 165.14/165.00 ! [V_f_2,V_r_2,T_a,T_b] : hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_b,T_b)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_b,T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_prod(T_b,T_b))),T_a),c_COMBB(T_b,tc_prod(T_b,T_b),T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_prod(T_b,T_b)),T_a),c_Product__Type_OPair(T_b,T_b)),V_f_2))),V_f_2)))),V_r_2))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mlex__leq,axiom, % 165.14/165.00 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_code__numeral_Osize_I2_J,axiom, % 165.14/165.00 ! [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))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_code__numeral_Oinject,axiom, % 165.14/165.00 ! [V_code__numeral_H_2,V_code__numeral_2] : % 165.14/165.00 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 165.14/165.00 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_code__numeral_Osimps_I2_J,axiom, % 165.14/165.00 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 165.14/165.00 % 165.14/165.00 fof(fact_code__numeral_Osimps_I3_J,axiom, % 165.14/165.00 ! [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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_in__inv__image,axiom, % 165.14/165.00 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_r_2),V_f_2))) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Suc__code__numeral__minus__one,axiom, % 165.14/165.00 ! [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 ). % 165.14/165.00 % 165.14/165.00 fof(fact_mlex__less,axiom, % 165.14/165.00 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_code__numeral_Osize_I4_J,axiom, % 165.14/165.00 ! [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))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rp__inv__image__def,axiom, % 165.14/165.00 ! [T_b,T_a] : c_FunDef_Orp__inv__image(T_a,T_b) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_COMBS(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_a),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),tc_fun(T_b,T_a)),c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),c_Relation_Oinv__image(T_a,T_b))))),c_Relation_Oinv__image(T_a,T_b))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_prod_Orecs,axiom, % 165.14/165.00 ! [V_b_2,V_a_2,V_f1_2,T_a,T_c,T_b] : c_Product__Type_Oprod_Oprod__rec(T_b,T_c,T_a,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_code__numeral_Osize_I3_J,axiom, % 165.14/165.00 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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__add__map__of__foldr,axiom, % 165.14/165.00 ! [V_ps_2,V_m_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)) = c_List_Ofoldr(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b))),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)))))),c_Option_Ooption_OSome(T_b))),V_ps_2,V_m_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_in__lex__prod,axiom, % 165.14/165.00 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2))) % 165.14/165.00 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_H_2)),V_r_2)) % 165.14/165.00 | ( V_a_2 = V_a_H_2 % 165.14/165.00 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_equivp__equiv,axiom, % 165.14/165.00 ! [V_A_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2) % 165.14/165.00 <=> c_Equiv__Relations_Oequivp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_A_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_identity__equivp,axiom, % 165.14/165.00 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ). % 165.14/165.00 % 165.14/165.00 fof(fact_equivp__def,axiom, % 165.14/165.00 ! [V_R_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 165.14/165.00 <=> ! [B_x,B_y] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 165.14/165.00 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_equivp__reflp,axiom, % 165.14/165.00 ! [V_x_2,V_R_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_equivp__symp,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_R_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_equivp__transp,axiom, % 165.14/165.00 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] : % 165.14/165.00 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_same__fstI,axiom, % 165.14/165.00 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] : % 165.14/165.00 ( hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2))) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_apsnd__apfst,axiom, % 165.14/165.00 ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_d,T_c),V_x_2))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_apfst__apsnd,axiom, % 165.14/165.00 ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_apfst__conv,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_x_2)),V_y_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_fst__apfst,axiom, % 165.14/165.00 ! [V_x_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_apfst__eq__conv,axiom, % 165.14/165.00 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] : % 165.14/165.00 ( hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_g_2),V_x_2) % 165.14/165.00 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_b),V_x_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_snd__apfst,axiom, % 165.14/165.00 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Oapfst(T_c,T_b,T_a,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_c,T_a),V_x_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_apsnd__apfst__commute,axiom, % 165.14/165.00 ! [V_p_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_a,T_c,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,V_g_2),hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_d,V_f_2),V_p_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pair__lessI2,axiom, % 165.14/165.00 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_ImageE,axiom, % 165.14/165.00 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 165.14/165.00 => ~ ! [B_x] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) % 165.14/165.00 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mlex__prod__def,axiom, % 165.14/165.00 ! [V_R_2,V_f_2,T_a] : c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_a),T_a),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_a,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(tc_Nat_Onat,T_a)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_a,tc_prod(tc_Nat_Onat,T_a)),T_a),c_Product__Type_OPair(tc_Nat_Onat,T_a)),V_f_2)),c_COMBI(T_a))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pair__less__def,axiom, % 165.14/165.00 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 165.14/165.00 % 165.14/165.00 fof(fact_measure__def,axiom, % 165.14/165.00 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ). % 165.14/165.00 % 165.14/165.00 fof(fact_less__than__iff,axiom, % 165.14/165.00 ! [V_y_2,V_x_2] : % 165.14/165.00 ( 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)) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pair__lessI1,axiom, % 165.14/165.00 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 165.14/165.00 => 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pair__leqI2,axiom, % 165.14/165.00 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_smax__insertI,axiom, % 165.14/165.00 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 165.14/165.00 => ( 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)) % 165.14/165.00 => ( 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)) % 165.14/165.00 => 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)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_smin__insertI,axiom, % 165.14/165.00 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 165.14/165.00 => ( 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)) % 165.14/165.00 => ( 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)) % 165.14/165.00 => 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)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_smin__emptyI,axiom, % 165.14/165.00 ! [V_X_2] : % 165.14/165.00 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 165.14/165.00 => 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_smax__emptyI,axiom, % 165.14/165.00 ! [V_Y_2] : % 165.14/165.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 165.14/165.00 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_pair__leqI1,axiom, % 165.14/165.00 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 165.14/165.00 => 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_wmin__insertI,axiom, % 165.14/165.00 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 165.14/165.00 => ( 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)) % 165.14/165.00 => ( 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)) % 165.14/165.00 => 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)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_wmax__insertI,axiom, % 165.14/165.00 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 165.14/165.00 => ( 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)) % 165.14/165.00 => ( 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)) % 165.14/165.00 => 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)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Field__insert,axiom, % 165.14/165.00 ! [V_r_2,V_b_2,V_a_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_a),V_r_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Field__empty,axiom, % 165.14/165.00 ! [T_a] : hAPP(c_Relation_OField(T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mono__Field,axiom, % 165.14/165.00 ! [V_s_2,V_r_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Field__Un,axiom, % 165.14/165.00 ! [V_s_2,V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_Relation_OField(T_a),V_s_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_finite__Field,axiom, % 165.14/165.00 ! [V_r_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 165.14/165.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_wmax__emptyI,axiom, % 165.14/165.00 ! [V_X_2] : % 165.14/165.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 165.14/165.00 => 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_wmin__emptyI,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_min__weak__def,axiom, % 165.14/165.00 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)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_max__weak__def,axiom, % 165.14/165.00 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)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Id__on__def,axiom, % 165.14/165.00 ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),T_a),c_Set_Oinsert(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Id__on__def_H,axiom, % 165.14/165.00 ! [V_A_2,T_a] : c_Relation_OId__on(T_a,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj)),c_fequal))),V_A_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Id__on__empty,axiom, % 165.14/165.00 ! [T_a] : c_Relation_OId__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Image__Id__on,axiom, % 165.14/165.00 ! [V_B_2,V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Id__on__eqI,axiom, % 165.14/165.00 ! [V_A_2,T_a,V_b_2,V_a_2] : % 165.14/165.00 ( V_a_2 = V_b_2 % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId__on(T_a,V_A_2))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Id__on__iff,axiom, % 165.14/165.00 ! [V_A_2,V_y_2,V_x_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Relation_OId__on(T_a,V_A_2))) % 165.14/165.00 <=> ( V_x_2 = V_y_2 % 165.14/165.00 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_max__strict__def,axiom, % 165.14/165.00 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 165.14/165.00 % 165.14/165.00 fof(fact_max__ext__additive,axiom, % 165.14/165.00 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_min__strict__def,axiom, % 165.14/165.00 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 165.14/165.00 % 165.14/165.00 fof(fact_max__extp__max__ext__eq,axiom, % 165.14/165.00 ! [V_xa_2,V_x_2,V_R_2,T_a] : % 165.14/165.00 ( c_Wellfounded_Omax__extp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_R_2),V_x_2,V_xa_2) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_min__rpair__set,axiom, % 165.14/165.00 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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_max__rpair__set,axiom, % 165.14/165.00 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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_rp__inv__image__rp,axiom, % 165.14/165.00 ! [V_f_2,T_b,V_P_2,T_a] : % 165.14/165.00 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 165.14/165.00 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_equiv__intrel__iff,axiom, % 165.14/165.00 ! [V_y_2,V_x_2] : % 165.14/165.00 ( 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)))) % 165.14/165.00 <=> 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)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_intrel__iff,axiom, % 165.14/165.00 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 165.14/165.00 ( 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)) % 165.14/165.00 <=> 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Id__onE,axiom, % 165.14/165.00 ! [V_A_2,V_ca_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2))) % 165.14/165.00 => ~ ! [B_x] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.00 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_equiv__intrel,axiom, % 165.14/165.00 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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_of__int,axiom, % 165.14/165.00 ! [V_j_2,V_i_2,T_a] : % 165.14/165.00 ( class_Rings_Oring__1(T_a) % 165.14/165.00 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_j_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_One__int__def,axiom, % 165.14/165.00 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))))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_mult,axiom, % 165.14/165.00 ! [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))))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Rep__Integ__inverse,axiom, % 165.14/165.00 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 165.14/165.00 % 165.14/165.00 fof(fact_minus,axiom, % 165.14/165.00 ! [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))))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Zero__int__def,axiom, % 165.14/165.00 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))))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_int__def,axiom, % 165.14/165.00 ! [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))))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_add,axiom, % 165.14/165.00 ! [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))))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_nat,axiom, % 165.14/165.00 ! [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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_minus__int__def,axiom, % 165.14/165.00 ! [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))))))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_less,axiom, % 165.14/165.00 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 165.14/165.00 ( 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))))))) % 165.14/165.00 <=> 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))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_le,axiom, % 165.14/165.00 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 165.14/165.00 ( 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))))))) % 165.14/165.00 <=> 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))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_eq__Abs__Integ,axiom, % 165.14/165.00 ! [V_z_2] : % 165.14/165.00 ~ ! [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))))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Integ__def,axiom, % 165.14/165.00 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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__mapk__SomeI,axiom, % 165.14/165.00 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 165.14/165.00 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_c),V_t_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2) % 165.14/165.00 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_a),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_t_2)),hAPP(V_f_2,V_k_2)) = hAPP(c_Option_Ooption_OSome(T_c),V_x_2) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inj__mapI,axiom, % 165.14/165.00 ! [V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 165.14/165.00 => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inj__map,axiom, % 165.14/165.00 ! [V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) % 165.14/165.00 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inj__map__eq__map,axiom, % 165.14/165.00 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 165.14/165.00 => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2) % 165.14/165.00 <=> V_xs_2 = V_ys_2 ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inj__mapD,axiom, % 165.14/165.00 ! [V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) % 165.14/165.00 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__injective,axiom, % 165.14/165.00 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 165.14/165.00 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2) % 165.14/165.00 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 165.14/165.00 => V_xs_2 = V_ys_2 ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__ident,axiom, % 165.14/165.00 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ). % 165.14/165.00 % 165.14/165.00 fof(fact_Rep__Integ,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_type__definition__Integ,axiom, % 165.14/165.00 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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__map__keys,axiom, % 165.14/165.00 ! [V_m_2,T_b,V_xs_2,T_a] : % 165.14/165.00 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2) % 165.14/165.00 => hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),T_b,T_a),c_Option_Othe(T_b)),V_m_2))),V_xs_2)) = V_m_2 ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__map,axiom, % 165.14/165.00 ! [V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),V_xs_2)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Map_Omap__of(T_a,T_c),V_xs_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_finite__set,axiom, % 165.14/165.00 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__eq__conv,axiom, % 165.14/165.00 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] : % 165.14/165.00 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2) % 165.14/165.00 <=> ! [B_x] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 165.14/165.00 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_List_Omap_Ocomp,axiom, % 165.14/165.00 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__comp__map,axiom, % 165.14/165.00 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_b),tc_List_Olist(T_a),hAPP(c_List_Omap(T_c,T_b),V_f_2)),hAPP(c_List_Omap(T_a,T_c),V_g_2)) = hAPP(c_List_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_List_Omap_Ocompositionality,axiom, % 165.14/165.00 ! [V_list_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_list_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__map,axiom, % 165.14/165.00 ! [V_xs_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_xs_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inj__on__imageI,axiom, % 165.14/165.00 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2),V_A_2) % 165.14/165.00 => c_Fun_Oinj__on(T_c,T_b,V_g_2,hAPP(c_Set_Oimage(T_a,T_c,V_f_2),V_A_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_comp__inj__on,axiom, % 165.14/165.00 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 165.14/165.00 => ( c_Fun_Oinj__on(T_b,T_c,V_g_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) % 165.14/165.00 => c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_f_2),V_A_2) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_comp__inj__on__iff,axiom, % 165.14/165.00 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 165.14/165.00 => ( c_Fun_Oinj__on(T_b,T_c,V_f_H_2,hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2)) % 165.14/165.00 <=> c_Fun_Oinj__on(T_a,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_f_H_2),V_f_2),V_A_2) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_apfst__compose,axiom, % 165.14/165.00 ! [V_x_2,V_g_2,T_d,V_f_2,T_b,T_a,T_c] : hAPP(c_Product__Type_Oapfst(T_c,T_a,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_d,T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_d,V_f_2),V_g_2)),V_x_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_apsnd__compose,axiom, % 165.14/165.00 ! [V_x_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Product__Type_Oapsnd(T_c,T_b,T_a,V_f_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_a,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_x_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_image__compose,axiom, % 165.14/165.00 ! [V_r_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_a,T_b,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_c,T_a,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_r_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_fun__upd__comp,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_c),V_g_2),V_x_2),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)),V_x_2),hAPP(V_f_2,V_y_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_vimage__compose,axiom, % 165.14/165.00 ! [V_x_2,V_f_2,V_g_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_a,T_c,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_g_2),V_x_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_comp__cong,axiom, % 165.14/165.00 ! [T_e,T_d,T_c,T_a,T_b,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] : % 165.14/165.00 ( 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)) % 165.14/165.00 => hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2),V_g_H_2),V_x_H_2) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_o__assoc,axiom, % 165.14/165.00 ! [V_h_2,V_g_2,T_d,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),hAPP(c_Fun_Ocomp(T_d,T_c,T_a,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_h_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_o__apply,axiom, % 165.14/165.00 ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_o__eq__dest,axiom, % 165.14/165.00 ! [V_v_2,V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 165.14/165.00 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_ca_2),V_d_2) % 165.14/165.00 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_o__eq__elim,axiom, % 165.14/165.00 ! [V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 165.14/165.00 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_ca_2),V_d_2) % 165.14/165.00 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Option_Omap_Ocomp,axiom, % 165.14/165.00 ! [V_g_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(c_Option_Omap(T_a,T_c),V_g_2)) = hAPP(c_Option_Omap(T_a,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_2),V_g_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_o__def,axiom, % 165.14/165.00 ! [V_x_2,V_g_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_K__record__comp,axiom, % 165.14/165.00 ! [V_x_2,V_f_2,V_ca_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_f_2),V_x_2) = V_ca_2 ). % 165.14/165.00 % 165.14/165.00 fof(fact_o__eq__dest__lhs,axiom, % 165.14/165.00 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 165.14/165.00 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_ca_2 % 165.14/165.00 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Option_Omap_Ocompositionality,axiom, % 165.14/165.00 ! [V_option_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_option_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_option_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_option__map__comp,axiom, % 165.14/165.00 ! [V_opt_2,V_g_2,T_c,V_f_2,T_a,T_b] : hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_Option_Omap(T_c,T_b),V_g_2),V_opt_2)) = hAPP(hAPP(c_Option_Omap(T_c,T_a),hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2)),V_opt_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 165.14/165.00 ! [V_x_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 165.14/165.00 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inj__on__imageI2,axiom, % 165.14/165.00 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(T_a,T_b,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_f_H_2),V_f_2),V_A_2) % 165.14/165.00 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_infinite__UNIV__listI,axiom, % 165.14/165.00 ! [T_a] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_comp__surj,axiom, % 165.14/165.00 ! [V_g_2,T_c,V_f_2,T_a,T_b] : % 165.14/165.00 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.00 => ( hAPP(c_Set_Oimage(T_a,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 165.14/165.00 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_a,T_c,T_b,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inj__comp,axiom, % 165.14/165.00 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 165.14/165.00 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 165.14/165.00 => c_Fun_Oinj__on(T_c,T_b,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_set__map,axiom, % 165.14/165.00 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_option__map__o__empty,axiom, % 165.14/165.00 ! [V_x_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_b),tc_Option_Ooption(T_a),T_c,hAPP(c_Option_Omap(T_b,T_a),V_f_2)),hAPP(c_COMBK(tc_Option_Ooption(T_b),T_c),c_Option_Ooption_ONone(T_b))),V_x_2) = c_Option_Ooption_ONone(T_a) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__map__restrict,axiom, % 165.14/165.00 ! [V_ks_2,V_f_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBS(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_ks_2)) = c_Map_Orestrict__map(T_a,T_b,hAPP(c_Fun_Ocomp(T_b,tc_Option_Ooption(T_b),T_a,c_Option_Ooption_OSome(T_b)),V_f_2),hAPP(c_List_Oset(T_a),V_ks_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_setsum__reindex,axiom, % 165.14/165.00 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 165.14/165.00 ( class_Groups_Ocomm__monoid__add(T_c) % 165.14/165.00 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 165.14/165.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_setprod__reindex,axiom, % 165.14/165.00 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 165.14/165.00 ( class_Groups_Ocomm__monoid__mult(T_c) % 165.14/165.00 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 165.14/165.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_B_2) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_setprod__reindex__cong,axiom, % 165.14/165.00 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 165.14/165.00 ( class_Groups_Ocomm__monoid__mult(T_c) % 165.14/165.00 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 165.14/165.00 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 165.14/165.00 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2) % 165.14/165.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_inj__on__map__eq__map,axiom, % 165.14/165.00 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2))) % 165.14/165.00 => ( hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2) % 165.14/165.00 <=> V_xs_2 = V_ys_2 ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__inj__on,axiom, % 165.14/165.00 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 165.14/165.00 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2) % 165.14/165.00 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2))) % 165.14/165.00 => V_xs_2 = V_ys_2 ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__fun__upd,axiom, % 165.14/165.00 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] : % 165.14/165.00 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 => hAPP(hAPP(c_List_Omap(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_y_2),V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_option__map__o__map__upd,axiom, % 165.14/165.00 ! [V_b_2,V_a_2,V_m_2,V_f_2,T_a,T_b,T_c] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_c),tc_Option_Ooption(T_b),T_a,hAPP(c_Option_Omap(T_c,T_b),V_f_2)),V_m_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_b_2))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__eq__dom,axiom, % 165.14/165.00 ! [V_ys_2,V_xs_2,T_b,T_a] : % 165.14/165.00 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 165.14/165.00 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_setsum_Oreindex,axiom, % 165.14/165.00 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 165.14/165.00 ( class_Groups_Ocomm__monoid__add(T_b) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 165.14/165.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_setprod_Oreindex,axiom, % 165.14/165.00 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 165.14/165.00 ( class_Groups_Ocomm__monoid__mult(T_b) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 165.14/165.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_g_2),hAPP(c_Set_Oimage(T_a,T_a,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_the__inv__into__comp,axiom, % 165.14/165.00 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2)) % 165.14/165.00 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2)))) % 165.14/165.00 => hAPP(c_Fun_Othe__inv__into(T_c,T_b,V_A_2,hAPP(c_Fun_Ocomp(T_a,T_b,T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_a,T_c,T_b,c_Fun_Othe__inv__into(T_c,T_a,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_a,T_b,hAPP(c_Set_Oimage(T_c,T_a,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__SomeD,axiom, % 165.14/165.00 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] : % 165.14/165.00 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_k_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xs_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__is__SomeD,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] : % 165.14/165.00 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_dom__map__of__conv__image__fst,axiom, % 165.14/165.00 ! [V_xys_2,T_b,T_a] : c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_fold__image__reindex,axiom, % 165.14/165.00 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] : % 165.14/165.00 ( class_Groups_Oab__semigroup__mult(T_c) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2) % 165.14/165.00 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__eq__None__iff,axiom, % 165.14/165.00 ! [V_x_2,V_xys_2,T_a,T_b] : % 165.14/165.00 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a) % 165.14/165.00 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(c_List_Oset(tc_prod(T_b,T_a)),V_xys_2)))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_type__definition_ORep__range,axiom, % 165.14/165.00 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 165.14/165.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 165.14/165.00 => hAPP(c_Set_Oimage(T_a,T_b,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = V_A_2 ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_type__definition_OAbs__image,axiom, % 165.14/165.00 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 165.14/165.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 165.14/165.00 => hAPP(c_Set_Oimage(T_b,T_a,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding_Oremove,axiom, % 165.14/165.00 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.00 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_UN__o,axiom, % 165.14/165.00 ! [V_f_2,V_g_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_c,tc_fun(T_a,tc_HOL_Obool),T_b,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_g_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 165.14/165.00 ! [V_h_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e,V_F_2,V_fa_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2) % 165.14/165.00 => 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) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding_Ocommute__comp,axiom, % 165.14/165.00 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding_Ocommute__left__comp,axiom, % 165.14/165.00 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_y_2)),V_g_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_foldr__map,axiom, % 165.14/165.00 ! [V_a_2,V_xs_2,V_f_2,T_c,V_g_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_g_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_c,T_a,hAPP(c_Fun_Ocomp(T_b,tc_fun(T_a,T_a),T_c,V_g_2),V_f_2),V_xs_2,V_a_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_split__comp,axiom, % 165.14/165.00 ! [V_x_2,V_g_2,V_f_2,T_d,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_c,T_a),T_b,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_x_2))),hAPP(c_Product__Type_Osnd(T_b,T_c),V_x_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 165.14/165.00 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/165.00 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding_Ocommute__comp_H_H,axiom, % 165.14/165.00 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/165.00 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding_Ocommute__left__comp_H,axiom, % 165.14/165.00 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding_Ocommute__comp_H,axiom, % 165.14/165.00 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_type__definition_ORep__inverse,axiom, % 165.14/165.00 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 165.14/165.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 165.14/165.00 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_type__definition_ORep__inject,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 165.14/165.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 165.14/165.00 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 165.14/165.00 <=> V_x_2 = V_y_2 ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding_Oinsert,axiom, % 165.14/165.00 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.00 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding_Ounion__inter,axiom, % 165.14/165.00 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/165.00 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_type__definition_ORep,axiom, % 165.14/165.00 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 165.14/165.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_type__definition_OAbs__inverse,axiom, % 165.14/165.00 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 165.14/165.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 165.14/165.00 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_type__definition_OAbs__inject,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 165.14/165.00 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 165.14/165.00 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 165.14/165.00 <=> V_x_2 = V_y_2 ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding_Oinsert__remove,axiom, % 165.14/165.00 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding_Ounion,axiom, % 165.14/165.00 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/165.00 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.00 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Loop__sound__lemma,axiom, % 165.14/165.00 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 165.14/165.00 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 165.14/165.00 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_hoare__derivs_OIf,axiom, % 165.14/165.00 ! [V_d_2,V_Q_2,V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 165.14/165.00 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 165.14/165.00 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 165.14/165.00 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OCond(V_b_2,V_ca_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Loop,axiom, % 165.14/165.00 ! [V_ca_2,V_b_2,V_P_2,V_G_2,T_a] : % 165.14/165.00 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 165.14/165.00 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_peek__and__def,axiom, % 165.14/165.00 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2)) % 165.14/165.00 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) % 165.14/165.00 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_ran__distinct,axiom, % 165.14/165.00 ! [V_al_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_al_2))) % 165.14/165.00 => c_Map_Oran(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_al_2)) = hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_al_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_set__map__of__compr,axiom, % 165.14/165.00 ! [V_xs_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))) % 165.14/165.00 => hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool),T_a),c_fequal),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)))),c_Option_Ooption_OSome(T_b)))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding__image_Oreindex,axiom, % 165.14/165.00 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 165.14/165.00 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 165.14/165.00 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_b,T_a,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding__image_Odistrib,axiom, % 165.14/165.00 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 165.14/165.00 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_distinct__map,axiom, % 165.14/165.00 ! [V_xs_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 165.14/165.00 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 165.14/165.00 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding__image_Oeq__fold,axiom, % 165.14/165.00 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 165.14/165.00 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__inject__set,axiom, % 165.14/165.00 ! [V_ys_2,V_xs_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2))) % 165.14/165.00 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2))) % 165.14/165.00 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 165.14/165.00 <=> hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xs_2) = hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_ys_2) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__is__SomeI,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) % 165.14/165.00 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__eq__Some__iff,axiom, % 165.14/165.00 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 165.14/165.00 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_Some__eq__map__of__iff,axiom, % 165.14/165.00 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xys_2))) % 165.14/165.00 => ( hAPP(c_Option_Ooption_OSome(T_b),V_y_2) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xys_2),V_x_2) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_xys_2))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_setsum__reindex__nonzero,axiom, % 165.14/165.00 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] : % 165.14/165.00 ( class_Groups_Ocomm__monoid__add(T_c) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 165.14/165.00 => ( ! [B_x] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 165.14/165.00 => ! [B_y] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2)) % 165.14/165.00 => ( B_x != B_y % 165.14/165.00 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 165.14/165.00 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) % 165.14/165.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2)),V_S_2) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_greaterThanLessThan__upto,axiom, % 165.14/165.00 ! [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)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_weak__map__of__SomeI,axiom, % 165.14/165.00 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_k_2),V_x_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),V_l_2))) % 165.14/165.00 => ? [B_x] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_l_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_x) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_distinct__upto,axiom, % 165.14/165.00 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_atLeastAtMost__upto,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_set__upto,axiom, % 165.14/165.00 ! [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) ). % 165.14/165.00 % 165.14/165.00 fof(fact_atLeastLessThan__upto,axiom, % 165.14/165.00 ! [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)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_greaterThanAtMost__upto,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_nat__list__def,axiom, % 165.14/165.00 ! [V_l_2] : % 165.14/165.00 ( c_List_Onat__list(V_l_2) % 165.14/165.00 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding__idem_Ounion__idem,axiom, % 165.14/165.00 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 165.14/165.00 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 165.14/165.00 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 165.14/165.00 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding__idem_Oidem__left__comp,axiom, % 165.14/165.00 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_c,hAPP(V_f_2,V_x_2)),V_g_2) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding__idem_Oidem__comp,axiom, % 165.14/165.00 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding__idem_Oin__comp__idem,axiom, % 165.14/165.00 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.00 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_folding__idem_Oinsert__idem,axiom, % 165.14/165.00 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_set__remove1__eq,axiom, % 165.14/165.00 ! [V_x_2,V_xs_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.00 => hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__zip__map,axiom, % 165.14/165.00 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 165.14/165.00 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),hAPP(V_f_2,V_x_2)) ) % 165.14/165.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_strong__setprod__reindex__cong,axiom, % 165.14/165.00 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 165.14/165.00 ( class_Groups_Ocomm__monoid__mult(T_c) % 165.14/165.00 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 165.14/165.00 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 165.14/165.00 => ( ! [B_x] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.00 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2),B_x) ) % 165.14/165.00 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_distinct__zipI1,axiom, % 165.14/165.00 ! [V_ys,T_b,V_xs,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 165.14/165.00 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_distinct__remove1,axiom, % 165.14/165.00 ! [V_x,V_xs,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 165.14/165.00 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_distinct__zipI2,axiom, % 165.14/165.00 ! [V_xs,T_b,V_ys,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 165.14/165.00 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_remove1__commute,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_remove1__idem,axiom, % 165.14/165.00 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.00 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_notin__set__remove1,axiom, % 165.14/165.00 ! [V_y_2,V_xs_2,V_x_2,T_a] : % 165.14/165.00 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_y_2,V_xs_2)))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_in__set__remove1,axiom, % 165.14/165.00 ! [V_xs_2,T_a,V_b_2,V_a_2] : % 165.14/165.00 ( V_a_2 != V_b_2 % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_b_2,V_xs_2)))) % 165.14/165.00 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zip__same__conv__map,axiom, % 165.14/165.00 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_a,tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))),V_xs_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_set__remove1__subset,axiom, % 165.14/165.00 ! [V_xs_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zip__map__fst__snd,axiom, % 165.14/165.00 ! [V_zs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2)) = V_zs_2 ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__zip__map,axiom, % 165.14/165.00 ! [V_ys_2,V_xs_2,V_g_2,T_d,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_a),T_d),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_c),V_f_2)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__zip__map2,axiom, % 165.14/165.00 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_a,T_c,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_a),V_f_2),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,T_a),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_c)),tc_fun(T_d,T_a),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_a,T_d),V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zip__same,axiom, % 165.14/165.00 ! [V_xs_2,V_b_2,V_a_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_xs_2)))) % 165.14/165.00 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 & V_a_2 = V_b_2 ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_set__zip__leftD,axiom, % 165.14/165.00 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_set__zip__rightD,axiom, % 165.14/165.00 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_in__set__zipE,axiom, % 165.14/165.00 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 165.14/165.00 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zip__map__map,axiom, % 165.14/165.00 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,tc_prod(T_a,T_b))),T_c),c_COMBB(T_b,tc_prod(T_a,T_b),T_d)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zip__map1,axiom, % 165.14/165.00 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_b),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zip__map2,axiom, % 165.14/165.00 ! [V_ys_2,V_f_2,T_c,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_c),tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_c,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_prod(T_a,T_b))),T_a),c_COMBB(T_b,tc_prod(T_a,T_b),T_c)),c_Product__Type_OPair(T_a,T_b))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_a,T_c),V_xs_2),V_ys_2)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_sorted__list__of__set__remove,axiom, % 165.14/165.00 ! [V_x_2,V_A_2,T_a] : % 165.14/165.00 ( class_Orderings_Olinorder(T_a) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = c_List_Oremove1(T_a,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__zip__upd,axiom, % 165.14/165.00 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 165.14/165.00 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 165.14/165.00 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 165.14/165.00 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 165.14/165.00 => ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_y_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2))),V_x_2),hAPP(c_Option_Ooption_OSome(T_a),V_z_2)) % 165.14/165.00 => hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2)) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__removeAll__inj__on,axiom, % 165.14/165.00 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_length__zip,axiom, % 165.14/165.00 ! [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)) ). % 165.14/165.00 % 165.14/165.00 fof(fact_neq__if__length__neq,axiom, % 165.14/165.00 ! [V_ys,V_xs,T_a] : % 165.14/165.00 ( 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) % 165.14/165.00 => V_xs != V_ys ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_length__map,axiom, % 165.14/165.00 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__eq__imp__length__eq,axiom, % 165.14/165.00 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] : % 165.14/165.00 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_a),V_g_2),V_ys_2) % 165.14/165.00 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_distinct__removeAll,axiom, % 165.14/165.00 ! [V_x,V_xs,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 165.14/165.00 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_card__length,axiom, % 165.14/165.00 ! [V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_removeAll__id,axiom, % 165.14/165.00 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.00 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_card__distinct,axiom, % 165.14/165.00 ! [V_xs_2,T_a] : % 165.14/165.00 ( hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) % 165.14/165.00 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_distinct__card,axiom, % 165.14/165.00 ! [V_xs_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.00 => hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__zip__inject,axiom, % 165.14/165.00 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 165.14/165.00 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 165.14/165.00 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) % 165.14/165.00 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 165.14/165.00 => ( hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_ys_2)) = hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs_2),V_zs_2)) % 165.14/165.00 => V_ys_2 = V_zs_2 ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__fst__zip,axiom, % 165.14/165.00 ! [V_ys_2,T_b,V_xs_2,T_a] : % 165.14/165.00 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 165.14/165.00 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_xs_2 ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__snd__zip,axiom, % 165.14/165.00 ! [V_ys_2,T_b,V_xs_2,T_a] : % 165.14/165.00 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 165.14/165.00 => hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = V_ys_2 ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_distinct__remove1__removeAll,axiom, % 165.14/165.00 ! [V_x,V_xs,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 165.14/165.00 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_length__pos__if__in__set,axiom, % 165.14/165.00 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_zip__eq__conv,axiom, % 165.14/165.00 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] : % 165.14/165.00 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 165.14/165.00 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2 % 165.14/165.00 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_zs_2) = V_xs_2 % 165.14/165.00 & hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_b),c_Product__Type_Osnd(T_a,T_b)),V_zs_2) = V_ys_2 ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__removeAll__inj,axiom, % 165.14/165.00 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 165.14/165.00 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 165.14/165.00 => hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_b,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_finite__lists__length__eq,axiom, % 165.14/165.00 ! [V_n_2,V_A_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__zip__is__None,axiom, % 165.14/165.00 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 165.14/165.00 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 165.14/165.00 => ( hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_b) % 165.14/165.00 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_map__of__zip__is__Some,axiom, % 165.14/165.00 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 165.14/165.00 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 <=> ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_length__remove1,axiom, % 165.14/165.00 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.00 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) % 165.14/165.00 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_dom__map__of__zip,axiom, % 165.14/165.00 ! [V_ys_2,T_b,V_xs_2,T_a] : % 165.14/165.00 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 165.14/165.00 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.00 => c_Map_Odom(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_a),V_xs_2) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_finite__lists__length__le,axiom, % 165.14/165.00 ! [V_n_2,V_A_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_a)),hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_set__removeAll,axiom, % 165.14/165.00 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_length__sublist,axiom, % 165.14/165.00 ! [V_I_2,V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_set__zip,axiom, % 165.14/165.00 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_b)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_a,T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_b),tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_a,T_b)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_a,T_b)),c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),tc_Nat_Onat),c_Product__Type_OPair(T_a,T_b)),hAPP(c_List_Onth(T_a),V_xs_2))),hAPP(c_List_Onth(T_b),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)))))) ). % 165.14/165.00 % 165.14/165.00 fof(fact_sorted__list__of__set__insert,axiom, % 165.14/165.00 ! [V_x_2,V_A_2,T_a] : % 165.14/165.00 ( class_Orderings_Olinorder(T_a) % 165.14/165.00 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.00 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_nth__zip,axiom, % 165.14/165.00 ! [V_ys,T_b,V_xs,T_a,V_i] : % 165.14/165.00 ( 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))) % 165.14/165.00 => ( 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))) % 165.14/165.00 => 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)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_list__eq__iff__nth__eq,axiom, % 165.14/165.00 ! [T_a,V_ys_2,V_xs_2] : % 165.14/165.00 ( V_xs_2 = V_ys_2 % 165.14/165.00 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 165.14/165.00 & ! [B_i] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.00 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_distinct__sublistI,axiom, % 165.14/165.00 ! [V_I_2,V_xs_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.00 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_insort__left__comm,axiom, % 165.14/165.00 ! [V_xs_2,V_y_2,V_x_2,T_a] : % 165.14/165.00 ( class_Orderings_Olinorder(T_a) % 165.14/165.00 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_insort__key__left__comm,axiom, % 165.14/165.00 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 165.14/165.00 ( class_Orderings_Olinorder(T_a) % 165.14/165.00 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 165.14/165.00 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),V_xs_2)) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_remove1__insort,axiom, % 165.14/165.00 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.00 ( class_Orderings_Olinorder(T_a) % 165.14/165.00 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) = V_xs_2 ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_set__insort,axiom, % 165.14/165.00 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 165.14/165.00 ( class_Orderings_Olinorder(T_b) % 165.14/165.00 => hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_length__insort,axiom, % 165.14/165.00 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 165.14/165.00 ( class_Orderings_Olinorder(T_b) % 165.14/165.00 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_all__set__conv__all__nth,axiom, % 165.14/165.00 ! [V_P_2,V_xs_2,T_a] : % 165.14/165.00 ( ! [B_x] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.00 => hBOOL(hAPP(V_P_2,B_x)) ) % 165.14/165.00 <=> ! [B_i] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.00 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_nth__map,axiom, % 165.14/165.00 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.00 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_distinct__conv__nth,axiom, % 165.14/165.00 ! [V_xs_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.00 <=> ! [B_i] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.00 => ! [B_j] : % 165.14/165.00 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.00 => ( B_i != B_j % 165.14/165.00 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_nth__eq__iff__index__eq,axiom, % 165.14/165.00 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 165.14/165.00 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.00 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.00 => ( hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2) % 165.14/165.00 <=> V_i_2 = V_j_2 ) ) ) ) ). % 165.14/165.00 % 165.14/165.00 fof(fact_set__sublist,axiom, % 165.14/165.00 ! [V_I_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_in__set__sublistD,axiom, % 165.14/165.01 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_notin__set__sublistI,axiom, % 165.14/165.01 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2)))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__sublist__subset,axiom, % 165.14/165.01 ! [V_I_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__mem,axiom, % 165.14/165.01 ! [V_xs_2,T_a,V_n_2] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_in__set__conv__nth,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 <=> ? [B_i] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.01 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_distinct__insort,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 165.14/165.01 ( class_Orderings_Olinorder(T_b) % 165.14/165.01 => ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2))) % 165.14/165.01 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__conv__nth,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_a),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_insort__insert__insort__key,axiom, % 165.14/165.01 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 165.14/165.01 ( class_Orderings_Olinorder(T_a) % 165.14/165.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)))) % 165.14/165.01 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_distinct__list__update,axiom, % 165.14/165.01 ! [V_i_2,V_a_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) % 165.14/165.01 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_insort__insert__insort,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( class_Orderings_Olinorder(T_a) % 165.14/165.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_length__list__update,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update__id,axiom, % 165.14/165.01 ! [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 ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__list__update__neq,axiom, % 165.14/165.01 ! [V_x,V_xs,T_a,V_j,V_i] : % 165.14/165.01 ( V_i != V_j % 165.14/165.01 => 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) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_update__zip,axiom, % 165.14/165.01 ! [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))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_zip__update,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update__swap,axiom, % 165.14/165.01 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 165.14/165.01 ( V_i != V_i_H % 165.14/165.01 => 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) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update__overwrite,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__update,axiom, % 165.14/165.01 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update__beyond,axiom, % 165.14/165.01 ! [V_x,V_i,V_xs,T_a] : % 165.14/165.01 ( 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)) % 165.14/165.01 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_distinct__insort__insert,axiom, % 165.14/165.01 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] : % 165.14/165.01 ( class_Orderings_Olinorder(T_b) % 165.14/165.01 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.01 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__update__subsetI,axiom, % 165.14/165.01 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_A_2)) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__update__subset__insert,axiom, % 165.14/165.01 ! [V_x_2,V_i_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__list__update__eq,axiom, % 165.14/165.01 ! [V_x,V_xs,T_a,V_i] : % 165.14/165.01 ( 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))) % 165.14/165.01 => 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 ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update__same__conv,axiom, % 165.14/165.01 ! [V_x_2,V_xs_2,T_a,V_i_2] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.01 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 165.14/165.01 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__list__update,axiom, % 165.14/165.01 ! [V_x,V_j,V_xs,T_a,V_i] : % 165.14/165.01 ( 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))) % 165.14/165.01 => ( ( V_i = V_j % 165.14/165.01 => 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 ) % 165.14/165.01 & ( V_i != V_j % 165.14/165.01 => 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) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__update__memI,axiom, % 165.14/165.01 ! [V_x_2,V_xs_2,T_a,V_n_2] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_n_2),V_x_2)))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_insort__insert__triv,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( class_Orderings_Olinorder(T_a) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__insort__insert,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( class_Orderings_Olinorder(T_a) % 165.14/165.01 => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_insort__insert__key__triv,axiom, % 165.14/165.01 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 165.14/165.01 ( class_Orderings_Olinorder(T_a) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)))) % 165.14/165.01 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__setsum__nth,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__add(T_a) % 165.14/165.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_restrict__map__upds,axiom, % 165.14/165.01 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] : % 165.14/165.01 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),V_D_2)) % 165.14/165.01 => c_Map_Orestrict__map(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_a,T_b,c_Map_Orestrict__map(T_a,T_b,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_a),V_xs_2))),V_xs_2,V_ys_2) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Nitpick_Ocard_H__def,axiom, % 165.14/165.01 ! [V_A_2,T_a] : % 165.14/165.01 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.01 => c_Nitpick_Ocard_H(T_a,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a)))) ) % 165.14/165.01 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.01 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__add__upds,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_b,T_a] : c_Map_Omap__add(T_a,T_b,V_m1_2,c_Map_Omap__upds(T_a,T_b,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_a,T_b,c_Map_Omap__add(T_a,T_b,V_m1_2,V_m2_2),V_xs_2,V_ys_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_tfl__some,axiom, % 165.14/165.01 ! [T_a,B_P] : % 165.14/165.01 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 165.14/165.01 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_someI,axiom, % 165.14/165.01 ! [T_a,V_x_2,V_P_2] : % 165.14/165.01 ( hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.01 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_some__sym__eq__trivial,axiom, % 165.14/165.01 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 165.14/165.01 % 165.14/165.01 fof(fact_some__eq__trivial,axiom, % 165.14/165.01 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ). % 165.14/165.01 % 165.14/165.01 fof(fact_some__eq__ex,axiom, % 165.14/165.01 ! [T_a,V_P_2] : % 165.14/165.01 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) % 165.14/165.01 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_someI__ex,axiom, % 165.14/165.01 ! [T_a,V_P_2] : % 165.14/165.01 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 165.14/165.01 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 165.14/165.01 ! [V_ns_2] : % 165.14/165.01 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 165.14/165.01 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_exE__some,axiom, % 165.14/165.01 ! [T_a,V_ca_2,V_P_2] : % 165.14/165.01 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 165.14/165.01 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_a,V_P_2) % 165.14/165.01 => hBOOL(hAPP(V_P_2,V_ca_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_elem__le__listsum__nat,axiom, % 165.14/165.01 ! [V_ns,V_k] : % 165.14/165.01 ( 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))) % 165.14/165.01 => 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))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__upds__apply__nontin,axiom, % 165.14/165.01 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => hAPP(c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__0,axiom, % 165.14/165.01 ! [V_xs_2,T_b,T_a] : % 165.14/165.01 ( class_Groups_Omonoid__add(T_a) % 165.14/165.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),c_Groups_Ozero__class_Ozero(T_a))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__addf,axiom, % 165.14/165.01 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__add(T_a) % 165.14/165.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Oplus__class_Oplus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__const__mult,axiom, % 165.14/165.01 ! [V_xs_2,V_f_2,V_ca_2,T_b,T_a] : % 165.14/165.01 ( class_Rings_Osemiring__0(T_a) % 165.14/165.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__mult__const,axiom, % 165.14/165.01 ! [V_xs_2,V_ca_2,V_f_2,T_b,T_a] : % 165.14/165.01 ( class_Rings_Osemiring__0(T_a) % 165.14/165.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_ca_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),V_ca_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__subtractf,axiom, % 165.14/165.01 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 165.14/165.01 ( class_Groups_Oab__group__add(T_a) % 165.14/165.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBS(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Ominus__class_Ominus(T_a)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__update__nat,axiom, % 165.14/165.01 ! [V_n,V_ns,V_k] : % 165.14/165.01 ( 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))) % 165.14/165.01 => 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)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__abs,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : % 165.14/165.01 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_a,T_a),c_Groups_Oabs__class_Oabs(T_a)),V_xs_2)))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_uminus__listsum__map,axiom, % 165.14/165.01 ! [V_xs_2,V_f_2,T_b,T_a] : % 165.14/165.01 ( class_Groups_Oab__group__add(T_a) % 165.14/165.01 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(T_a,T_a,T_b,c_Groups_Ouminus__class_Ouminus(T_a)),V_f_2)),V_xs_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_distinct__listsum__conv__Setsum,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__add(T_a) % 165.14/165.01 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_a),c_COMBI(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 165.14/165.01 ! [V_f_2,V_xs_2,T_a,T_b] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__add(T_b) % 165.14/165.01 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_List_Oset(T_a),V_xs_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 165.14/165.01 ! [V_j_2,V_i_2,V_f_2,T_a] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__add(T_a) % 165.14/165.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 165.14/165.01 ! [V_l_2,V_k_2,V_f_2,T_a] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__add(T_a) % 165.14/165.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_a),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_a),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__upds__list__update2__drop,axiom, % 165.14/165.01 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_i_2)) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 165.14/165.01 => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__triv,axiom, % 165.14/165.01 ! [V_xs_2,V_r_2,T_b,T_a] : % 165.14/165.01 ( class_Rings_Osemiring__1(T_a) % 165.14/165.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),V_r_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__upds__twist,axiom, % 165.14/165.01 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] : % 165.14/165.01 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2))) % 165.14/165.01 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__map__remove1,axiom, % 165.14/165.01 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__add(T_b) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Nitpick_Osetsum_H__def,axiom, % 165.14/165.01 ! [V_f_2,V_A_2,T_a,T_b] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__add(T_b) % 165.14/165.01 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.01 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_a),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_List_Oset(T_a))),V_A_2))),c_List_Odistinct(T_a))))) ) % 165.14/165.01 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.01 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__mono,axiom, % 165.14/165.01 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] : % 165.14/165.01 ( ( class_Groups_Omonoid__add(T_b) % 165.14/165.01 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 165.14/165.01 => ( ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_g_2),V_xs_2)))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_all__nth__imp__all__set,axiom, % 165.14/165.01 ! [V_x_2,V_P_2,V_xs_2,T_a] : % 165.14/165.01 ( ! [B_i] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.01 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_split__paired__Eps,axiom, % 165.14/165.01 ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b)))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Eps__split__eq,axiom, % 165.14/165.01 ! [V_y_2,V_x_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Eps__split,axiom, % 165.14/165.01 ! [V_P_2,T_b,T_a] : c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(tc_prod(T_a,T_b),T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),tc_prod(T_a,T_b)),V_P_2),c_Product__Type_Ofst(T_a,T_b))),c_Product__Type_Osnd(T_a,T_b))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__size__conv__listsum,axiom, % 165.14/165.01 ! [V_xs_2,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_a,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__upd__upds__conv__if,axiom, % 165.14/165.01 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] : % 165.14/165.01 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2)))) % 165.14/165.01 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2) ) % 165.14/165.01 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2)))) % 165.14/165.01 => c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),V_y_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel__iff__nth,axiom, % 165.14/165.01 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 165.14/165.01 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 165.14/165.01 & ! [B_n] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_n))),V_r_2)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel__eq__len,axiom, % 165.14/165.01 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 165.14/165.01 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__all,axiom, % 165.14/165.01 ! [V_n,V_xs,T_a] : % 165.14/165.01 ( 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)) % 165.14/165.01 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_in__set__takeD,axiom, % 165.14/165.01 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__take__subset,axiom, % 165.14/165.01 ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__map,axiom, % 165.14/165.01 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__size__map,axiom, % 165.14/165.01 ! [V_xs_2,V_g_2,T_b,V_f_2,T_a] : c_List_Olist_Olist__size(T_a,V_f_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_b,hAPP(c_Fun_Ocomp(T_a,tc_Nat_Onat,T_b,V_f_2),V_g_2),V_xs_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__take,axiom, % 165.14/165.01 ! [V_xs,T_a,V_n,V_i] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 165.14/165.01 => 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) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_distinct__take,axiom, % 165.14/165.01 ! [V_i,V_xs,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 165.14/165.01 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel__mono,axiom, % 165.14/165.01 ! [V_s_2,V_r_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_List_Olistrel(T_a,V_s_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__take,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__zip,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_length__take,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_sublist__upt__eq__take,axiom, % 165.14/165.01 ! [V_n_2,V_l_2,T_a] : c_List_Osublist(T_a,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_l_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__take__subset__set__take,axiom, % 165.14/165.01 ! [V_xs_2,T_a,V_n_2,V_m_2] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_dom__map__upds,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Odom(T_a,T_b,c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)),V_xs_2))),c_Map_Odom(T_a,T_b,V_m_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__size__estimation,axiom, % 165.14/165.01 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__size__estimation_H,axiom, % 165.14/165.01 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexord__take__index__conv,axiom, % 165.14/165.01 ! [V_r_2,V_y_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 165.14/165.01 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2))) % 165.14/165.01 & hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),V_y_2) = V_x_2 ) % 165.14/165.01 | ? [B_i] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2)))) % 165.14/165.01 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2) % 165.14/165.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_y_2),B_i))),V_r_2)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrelp__listrel__eq,axiom, % 165.14/165.01 ! [V_xa_2,V_x_2,V_r_2,T_a] : % 165.14/165.01 ( c_List_Olistrelp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2),V_x_2,V_xa_2) % 165.14/165.01 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_xa_2)),c_List_Olistrel(T_a,V_r_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel__iff__zip,axiom, % 165.14/165.01 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 165.14/165.01 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 165.14/165.01 & ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2)))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),B_x)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Powp__def,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2)) % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 165.14/165.01 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_ball__empty,axiom, % 165.14/165.01 ! [V_P_2,T_a,B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 165.14/165.01 => hBOOL(hAPP(V_P_2,B_x)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_congruent__def,axiom, % 165.14/165.01 ! [V_f_2,V_r_2,T_b,T_a] : % 165.14/165.01 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_b),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__eq__iff__zip__eq,axiom, % 165.14/165.01 ! [T_a,V_ys_2,V_xs_2] : % 165.14/165.01 ( V_xs_2 = V_ys_2 % 165.14/165.01 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) % 165.14/165.01 & ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_a)),hAPP(hAPP(c_List_Ozip(T_a,T_a),V_xs_2),V_ys_2)))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_WT__bodies__def,axiom, % 165.14/165.01 ( c_Com_OWT__bodies % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexord__lex,axiom, % 165.14/165.01 ! [V_r_2,V_y_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olex(T_a,V_r_2))) % 165.14/165.01 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 165.14/165.01 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexn__length,axiom, % 165.14/165.01 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2))) % 165.14/165.01 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2 % 165.14/165.01 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_refl__on__def_H,axiom, % 165.14/165.01 ! [V_r_2,V_A_2,T_a] : % 165.14/165.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 165.14/165.01 <=> ( ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2))),B_x)) ) % 165.14/165.01 & ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_refl__on__Id__on,axiom, % 165.14/165.01 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lex__def,axiom, % 165.14/165.01 ! [V_r_2,T_a] : c_List_Olex(T_a,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_a,V_r_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_triples__valid__Suc,axiom, % 165.14/165.01 ! [V_n_2,V_ts_2,T_a] : % 165.14/165.01 ( ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 165.14/165.01 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 165.14/165.01 => ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 165.14/165.01 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexn_Osimps_I1_J,axiom, % 165.14/165.01 ! [V_r_2,T_a] : hAPP(c_List_Olexn(T_a,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_refl__on__empty,axiom, % 165.14/165.01 ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_hoare__valids__def,axiom, % 165.14/165.01 ! [V_ts_2,V_G_2,T_a] : % 165.14/165.01 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_G_2,V_ts_2) % 165.14/165.01 <=> ! [B_n] : % 165.14/165.01 ( ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_G_2)) % 165.14/165.01 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) % 165.14/165.01 => ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 165.14/165.01 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_refl__on__Un,axiom, % 165.14/165.01 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 165.14/165.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 165.14/165.01 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 165.14/165.01 => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_refl__on__Int,axiom, % 165.14/165.01 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 165.14/165.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 165.14/165.01 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 165.14/165.01 => c_Relation_Orefl__on(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_refl__onD,axiom, % 165.14/165.01 ! [V_a_2,V_r_2,V_A_2,T_a] : % 165.14/165.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_refl__onD1,axiom, % 165.14/165.01 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 165.14/165.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_refl__onD2,axiom, % 165.14/165.01 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 165.14/165.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lenlex__conv,axiom, % 165.14/165.01 ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBC(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))))),c_List_Olex(T_a,V_r_2)))))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lenlex__def,axiom, % 165.14/165.01 ! [V_r_2,T_a] : c_List_Olenlex(T_a,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_a),c_Wellfounded_Oless__than,c_List_Olex(T_a,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_a),tc_prod(tc_Nat_Onat,tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_a))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_COMBI(tc_List_Olist(T_a)))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_reflp__def,axiom, % 165.14/165.01 ! [V_r_2,T_a] : % 165.14/165.01 ( c_Predicate_Oreflp(T_a,V_r_2) % 165.14/165.01 <=> c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_reflpE,axiom, % 165.14/165.01 ! [V_x_2,V_r_2,T_a] : % 165.14/165.01 ( c_Predicate_Oreflp(T_a,V_r_2) % 165.14/165.01 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel1__subset__listrel,axiom, % 165.14/165.01 ! [V_r_H_2,V_r_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2)) % 165.14/165.01 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel(T_a,V_r_H_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexord__linear,axiom, % 165.14/165.01 ! [V_y_2,V_x_2,V_r_2,T_a] : % 165.14/165.01 ( ! [B_a,B_b] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_b)),V_r_2)) % 165.14/165.01 | B_a = B_b % 165.14/165.01 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_b),B_a)),V_r_2)) ) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 165.14/165.01 | V_x_2 = V_y_2 % 165.14/165.01 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_x_2)),c_List_Olexord(T_a,V_r_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexord__irreflexive,axiom, % 165.14/165.01 ! [V_y_2,V_r_2,T_a] : % 165.14/165.01 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) % 165.14/165.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_y_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel1__mono,axiom, % 165.14/165.01 ! [V_s_2,V_r_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,V_r_2)),c_List_Olistrel1(T_a,V_s_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel1__eq__len,axiom, % 165.14/165.01 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 165.14/165.01 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel1__iff__update,axiom, % 165.14/165.01 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 165.14/165.01 <=> ? [B_y,B_n] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n)),B_y)),V_r_2)) % 165.14/165.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.01 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__size__pointwise,axiom, % 165.14/165.01 ! [V_g_2,V_f_2,V_xs_2,T_a] : % 165.14/165.01 ( ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_a,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_a,V_g_2,V_xs_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_butlast__take,axiom, % 165.14/165.01 ! [V_xs,T_a,V_n] : % 165.14/165.01 ( 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))) % 165.14/165.01 => 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) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__butlast,axiom, % 165.14/165.01 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Obutlast(T_b,V_xs_2)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_in__set__butlastD,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__butlast,axiom, % 165.14/165.01 ! [V_xs,T_a,V_n] : % 165.14/165.01 ( 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))) % 165.14/165.01 => 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) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_length__butlast,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_butlast__conv__take,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_butlast__list__update,axiom, % 165.14/165.01 ! [V_x,V_xs,T_a,V_k] : % 165.14/165.01 ( ( 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)) % 165.14/165.01 => 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) ) % 165.14/165.01 & ( 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)) % 165.14/165.01 => 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) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__take__lemma,axiom, % 165.14/165.01 ! [V_ys,V_xs,T_a,V_k] : % 165.14/165.01 ( 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))) % 165.14/165.01 => ( 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))) % 165.14/165.01 => ( ! [B_i] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 165.14/165.01 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 165.14/165.01 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Cons__in__lex,axiom, % 165.14/165.01 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olex(T_a,V_r_2))) % 165.14/165.01 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 165.14/165.01 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) ) % 165.14/165.01 | ( V_x_2 = V_y_2 % 165.14/165.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olex(T_a,V_r_2))) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_partition__set,axiom, % 165.14/165.01 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 165.14/165.01 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2) % 165.14/165.01 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_yes_2)),hAPP(c_List_Oset(T_a),V_no_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_partition_Osimps_I2_J,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBS(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_List_Olist(T_a),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),hAPP(c_If(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_List_Olist_OCons(T_a),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)))),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_List_Olist(T_a))),c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)))),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_List_Opartition(T_a,V_P_2,V_xs_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_zip__Cons__Cons,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update__code_I3_J,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__Suc__Cons,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrelp_OCons,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 165.14/165.01 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2) % 165.14/165.01 => c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrelp_Oequations_I2_J,axiom, % 165.14/165.01 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] : % 165.14/165.01 ( c_List_Olistrelp(T_a,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a4_2)) % 165.14/165.01 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 165.14/165.01 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_impossible__Cons,axiom, % 165.14/165.01 ! [V_x,V_ys,V_xs,T_a] : % 165.14/165.01 ( 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))) % 165.14/165.01 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__simps_I2_J,axiom, % 165.14/165.01 ! [V_xs,V_x,T_a] : % 165.14/165.01 ( class_Groups_Omonoid__add(T_a) % 165.14/165.01 => 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)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update_Osimps_I2_J,axiom, % 165.14/165.01 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_a,tc_List_Olist(T_a)),c_List_Olist__update(T_a,V_xs_2)),V_v_2)),V_i_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__Cons__0,axiom, % 165.14/165.01 ! [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 ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__Cons__Suc,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_removeAll_Osimps_I2_J,axiom, % 165.14/165.01 ! [V_xs,T_a,V_y,V_x] : % 165.14/165.01 ( ( V_x = V_y % 165.14/165.01 => 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) ) % 165.14/165.01 & ( V_x != V_y % 165.14/165.01 => 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)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_not__Cons__self,axiom, % 165.14/165.01 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 165.14/165.01 % 165.14/165.01 fof(fact_not__Cons__self2,axiom, % 165.14/165.01 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 165.14/165.01 % 165.14/165.01 fof(fact_list_Oinject,axiom, % 165.14/165.01 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H_2),V_list_H_2) % 165.14/165.01 <=> ( V_a_2 = V_a_H_2 % 165.14/165.01 & V_list_2 = V_list_H_2 ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_foldr_Osimps_I2_J,axiom, % 165.14/165.01 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_remove1_Osimps_I2_J,axiom, % 165.14/165.01 ! [V_xs,T_a,V_y,V_x] : % 165.14/165.01 ( ( V_x = V_y % 165.14/165.01 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 165.14/165.01 & ( V_x != V_y % 165.14/165.01 => 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)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map_Osimps_I2_J,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update__code_I2_J,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__ConsD,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,V_y_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) % 165.14/165.01 => ( V_y_2 = V_x_2 % 165.14/165.01 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_List_Oset_Osimps_I2_J,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__subset__Cons,axiom, % 165.14/165.01 ! [V_x_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_insort__key_Osimps_I2_J,axiom, % 165.14/165.01 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 165.14/165.01 ( class_Orderings_Olinorder(T_a) % 165.14/165.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 165.14/165.01 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) % 165.14/165.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) % 165.14/165.01 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_ys_2)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth_Osimps,axiom, % 165.14/165.01 ! [V_n_2,V_xs_2,V_x_2,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_a,V_x_2,hAPP(c_List_Onth(T_a),V_xs_2),V_n_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_distinct_Osimps_I2_J,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) % 165.14/165.01 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__of__Cons__code_I2_J,axiom, % 165.14/165.01 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 165.14/165.01 ( ( V_l = V_k % 165.14/165.01 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Option_Ooption_OSome(T_c),V_v) ) % 165.14/165.01 & ( V_l != V_k % 165.14/165.01 => hAPP(hAPP(c_Map_Omap__of(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(hAPP(c_Map_Omap__of(T_b,T_c),V_ps),V_k) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel1I2,axiom, % 165.14/165.01 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__upds__Cons,axiom, % 165.14/165.01 ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_a,T_b,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_as_2,V_bs_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list_Osize_I4_J,axiom, % 165.14/165.01 ! [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))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__Cons_H,axiom, % 165.14/165.01 ! [V_xs,V_x,T_a,V_n] : % 165.14/165.01 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 165.14/165.01 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 => 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))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list_Osize_I2_J,axiom, % 165.14/165.01 ! [V_list_2,V_a_2,V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_a,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_partition__P,axiom, % 165.14/165.01 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 165.14/165.01 ( c_List_Opartition(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_yes_2),V_no_2) % 165.14/165.01 => ( ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2))) % 165.14/165.01 => hBOOL(hAPP(V_P_2,B_x)) ) % 165.14/165.01 & ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2))) % 165.14/165.01 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__Cons__number__of,axiom, % 165.14/165.01 ! [V_xs,V_x,T_a,V_v] : % 165.14/165.01 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 => 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 ) % 165.14/165.01 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 => 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))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel1I1,axiom, % 165.14/165.01 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_xs_2))),c_List_Olistrel1(T_a,V_r_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Cons__listrel1__Cons,axiom, % 165.14/165.01 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel1(T_a,V_r_2))) % 165.14/165.01 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 165.14/165.01 & V_xs_2 = V_ys_2 ) % 165.14/165.01 | ( V_x_2 = V_y_2 % 165.14/165.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel_OCons,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexord__cons__cons,axiom, % 165.14/165.01 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2))),c_List_Olexord(T_a,V_r_2))) % 165.14/165.01 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 165.14/165.01 | ( V_a_2 = V_b_2 % 165.14/165.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olexord(T_a,V_r_2))) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__of_Osimps_I2_J,axiom, % 165.14/165.01 ! [V_ps_2,V_p_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),hAPP(c_Map_Omap__of(T_a,T_b),V_ps_2)),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p_2)),hAPP(c_Option_Ooption_OSome(T_b),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel__Cons,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = c_List_Oset__Cons(T_a,hAPP(c_Relation_OImage(T_a,T_a,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__Cons__def,axiom, % 165.14/165.01 ! [V_XS_2,V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(tc_List_Olist(T_a)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBS(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_a)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a))),tc_fun(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))),tc_List_Olist(T_a)),c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_List_Olist(T_a),tc_HOL_Obool,tc_List_Olist(T_a))),c_fequal))),c_List_Olist_OCons(T_a)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),V_XS_2)))))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexn_Osimps_I2_J,axiom, % 165.14/165.01 ! [V_n_2,V_r_2,T_a] : hAPP(c_List_Olexn(T_a,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_a,tc_List_Olist(T_a)),tc_prod(T_a,tc_List_Olist(T_a))),tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_Product__Type_Omap__pair(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),c_Wellfounded_Olex__prod(T_a,tc_List_Olist(T_a),V_r_2,hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),hAPP(c_Nat_OSuc,V_n_2)))))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__pair__imageI,axiom, % 165.14/165.01 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_R_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_a,T_b),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)),V_R_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_fst__map__pair,axiom, % 165.14/165.01 ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_snd__prod__fun,axiom, % 165.14/165.01 ! [V_x_2,V_g_2,V_f_2,T_d,T_c,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(c_Product__Type_Omap__pair(T_c,T_b,T_d,T_a,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__pair__ident,axiom, % 165.14/165.01 ! [V_z_2,T_b,T_a] : hAPP(c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)),V_z_2) = V_z_2 ). % 165.14/165.01 % 165.14/165.01 fof(fact_fst__comp__map__pair,axiom, % 165.14/165.01 ! [V_g_2,V_f_2,T_b,T_a,T_d,T_c] : hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,tc_prod(T_a,T_b),c_Product__Type_Ofst(T_c,T_d)),c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_a,T_c,tc_prod(T_a,T_b),V_f_2),c_Product__Type_Ofst(T_a,T_b)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_snd__comp__map__pair,axiom, % 165.14/165.01 ! [V_g_2,V_f_2,T_b,T_a,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_c),T_c,tc_prod(T_a,T_b),c_Product__Type_Osnd(T_d,T_c)),c_Product__Type_Omap__pair(T_a,T_d,T_b,T_c,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_c,tc_prod(T_a,T_b),V_g_2),c_Product__Type_Osnd(T_a,T_b)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__pair_Ocompositionality,axiom, % 165.14/165.01 ! [V_prod_2,V_i_2,V_h_2,T_f,T_e,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_e,T_a,T_f,T_b,hAPP(c_Fun_Ocomp(T_c,T_a,T_e,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_g_2),V_i_2)),V_prod_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__pair__compose,axiom, % 165.14/165.01 ! [V_g2_2,V_g1_2,T_f,V_f2_2,V_f1_2,T_e,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_f2_2,V_g2_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__pair_Ocomp,axiom, % 165.14/165.01 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_b,T_a,T_d,T_c,T_f,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_a,T_e,T_b,T_f,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_a,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_g_2),V_i_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__pair__simp,axiom, % 165.14/165.01 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_b,T_d,T_a,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__pair__def,axiom, % 165.14/165.01 ! [V_g_2,V_f_2,T_d,T_b,T_c,T_a] : c_Product__Type_Omap__pair(T_a,T_c,T_b,T_d,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_d),tc_fun(T_b,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_b,T_d),tc_fun(T_b,tc_prod(T_c,T_d))),T_a),c_COMBB(T_d,tc_prod(T_c,T_d),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_a),c_Product__Type_OPair(T_c,T_d)),V_f_2))),V_g_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__pair__surj,axiom, % 165.14/165.01 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] : % 165.14/165.01 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) % 165.14/165.01 => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel__Cons2,axiom, % 165.14/165.01 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_List_Olistrel(T_a,V_r_2))) % 165.14/165.01 => ~ ! [B_x,B_xs] : % 165.14/165.01 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_y_2)),V_r_2)) % 165.14/165.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),B_xs),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel__Cons1,axiom, % 165.14/165.01 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_a,V_r_2))) % 165.14/165.01 => ~ ! [B_y,B_ys] : % 165.14/165.01 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),B_y)),V_r_2)) % 165.14/165.01 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),B_ys)),c_List_Olistrel(T_a,V_r_2))) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_prod__fun__imageE,axiom, % 165.14/165.01 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_ca_2,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_ca_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2)),V_R_2))) % 165.14/165.01 => ~ ! [B_x,B_y] : % 165.14/165.01 ( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 165.14/165.01 => ~ 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)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_image__split__eq__Sigma,axiom, % 165.14/165.01 ! [V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : hAPP(c_Set_Oimage(T_c,tc_prod(T_a,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_prod(T_a,T_b)),T_c),c_Product__Type_OPair(T_a,T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_Oimage(T_c,T_a,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_Oimage(T_c,T_b,V_g_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_a),c_Set_Ovimage(T_c,T_a,V_f_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))),V_A_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_SigmaI,axiom, % 165.14/165.01 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Sigma__Diff__distrib2,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Times__Diff__distrib1,axiom, % 165.14/165.01 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Sigma__Diff__distrib1,axiom, % 165.14/165.01 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Times__empty,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) % 165.14/165.01 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Sigma__empty2,axiom, % 165.14/165.01 ! [V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_setsum__cartesian__product,axiom, % 165.14/165.01 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__add(T_a) % 165.14/165.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_card__cartesian__product,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Sigma__empty1,axiom, % 165.14/165.01 ! [V_B_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Times__eq__cancel2,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 165.14/165.01 => ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)) % 165.14/165.01 <=> V_A_2 = V_B_2 ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Compl__Times__UNIV1,axiom, % 165.14/165.01 ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Compl__Times__UNIV2,axiom, % 165.14/165.01 ! [V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_setprod__cartesian__product,axiom, % 165.14/165.01 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__mult(T_a) % 165.14/165.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_a),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_a)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Sigma__Un__distrib2,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Times__Un__distrib1,axiom, % 165.14/165.01 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Sigma__Un__distrib1,axiom, % 165.14/165.01 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_finite__cartesian__product,axiom, % 165.14/165.01 ! [V_B_2,T_b,V_A_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 165.14/165.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_equiv__type,axiom, % 165.14/165.01 ! [V_r_2,V_A_2,T_a] : % 165.14/165.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Sigma__Int__distrib2,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Times__Int__distrib1,axiom, % 165.14/165.01 ! [V_C_2,V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_C_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Sigma__Int__distrib1,axiom, % 165.14/165.01 ! [V_C_2,V_J_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_J_2),V_C_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Id__on__subset__Times,axiom, % 165.14/165.01 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId__on(T_a,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_UNIV__Times__UNIV,axiom, % 165.14/165.01 ! [T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_SigmaE2,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 165.14/165.01 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.01 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_SigmaD2,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_SigmaD1,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_mem__Sigma__iff,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 165.14/165.01 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.01 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_card__cartesian__product__singleton,axiom, % 165.14/165.01 ! [V_A_2,V_x_2,T_b,T_a] : hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Times__subset__cancel2,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_B_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_C_2)))) % 165.14/165.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Image__subset,axiom, % 165.14/165.01 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_C_2)),V_B_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_finite__cartesian__productD1,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 165.14/165.01 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 165.14/165.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_finite__cartesian__productD2,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 165.14/165.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_SetCompr__Sigma__eq,axiom, % 165.14/165.01 ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),c_Set_OCollect(T_b)),V_Q_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Collect__split,axiom, % 165.14/165.01 ! [V_Q_2,V_P_2,T_b,T_a] : hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_Set_OCollect(T_a),V_P_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_OCollect(T_b),V_Q_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_fst__image__times,axiom, % 165.14/165.01 ! [V_A_2,T_b,T_a,V_B_2] : % 165.14/165.01 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 165.14/165.01 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_b,c_Product__Type_Ofst(T_b,T_a)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = V_A_2 ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_snd__image__times,axiom, % 165.14/165.01 ! [V_B_2,T_b,T_a,V_A_2] : % 165.14/165.01 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 165.14/165.01 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_b,c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) = V_B_2 ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__pair__surj__on,axiom, % 165.14/165.01 ! [V_B_H_2,V_B_2,V_g_2,T_c,T_d,V_A_H_2,V_A_2,V_f_2,T_a,T_b] : % 165.14/165.01 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2 % 165.14/165.01 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2 % 165.14/165.01 => hAPP(c_Set_Oimage(tc_prod(T_b,T_d),tc_prod(T_a,T_c),c_Product__Type_Omap__pair(T_b,T_a,T_d,T_c,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_H_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_H_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_swap__product,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),tc_prod(T_a,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_prod(T_a,T_b)),hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_A_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_refl__on__def,axiom, % 165.14/165.01 ! [V_r_2,V_A_2,T_a] : % 165.14/165.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 165.14/165.01 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 165.14/165.01 & ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_insert__times__insert,axiom, % 165.14/165.01 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_finite__equiv__class,axiom, % 165.14/165.01 ! [V_X_2,V_r_2,V_A_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) % 165.14/165.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__pair__inj__on,axiom, % 165.14/165.01 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] : % 165.14/165.01 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 165.14/165.01 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2) % 165.14/165.01 => c_Fun_Oinj__on(tc_prod(T_a,T_c),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_a,T_b,T_c,T_d,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_B_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_UN__Times__distrib,axiom, % 165.14/165.01 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_b,T_a,T_d,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_c,T_d),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),tc_fun(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_c),c_Product__Type_OSigma(T_a,T_b)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),T_d),c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_F_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Sigma__def,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_finite__quotient,axiom, % 165.14/165.01 ! [V_r_2,V_A_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 165.14/165.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_vimage__Times,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_f_2,T_c,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,tc_prod(T_b,T_c),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_a,T_b,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_b,T_a,c_Product__Type_Ofst(T_b,T_c)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_a,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_b,T_c),T_c,T_a,c_Product__Type_Osnd(T_b,T_c)),V_f_2)),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_setsum__mult__setsum__if__inj,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : % 165.14/165.01 ( class_Rings_Osemiring__0(T_c) % 165.14/165.01 => ( c_Fun_Oinj__on(tc_prod(T_a,T_b),T_c,hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))) % 165.14/165.01 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_a,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_a,tc_fun(T_b,T_c)),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool),T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,T_c),tc_fun(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),T_a),c_COMBB(T_c,T_c,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_a),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 165.14/165.01 ! [V_A_2,V_I_2,T_b,T_a] : % 165.14/165.01 ? [B_f] : % 165.14/165.01 ( c_Fun_Oinj__on(T_a,tc_prod(T_b,T_a),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) % 165.14/165.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_a,tc_prod(T_b,T_a),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_a),V_I_2),V_A_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_image__id,axiom, % 165.14/165.01 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ). % 165.14/165.01 % 165.14/165.01 fof(fact_apfst__id,axiom, % 165.14/165.01 ! [T_b,T_a] : c_Product__Type_Oapfst(T_a,T_a,T_b,c_Fun_Oid(T_a)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_apsnd__id,axiom, % 165.14/165.01 ! [T_a,T_b] : c_Product__Type_Oapsnd(T_b,T_b,T_a,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Option_Omap_Oidentity,axiom, % 165.14/165.01 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_vimage__id,axiom, % 165.14/165.01 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ). % 165.14/165.01 % 165.14/165.01 fof(fact_id__apply,axiom, % 165.14/165.01 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 165.14/165.01 % 165.14/165.01 fof(fact_Option_Omap_Oid,axiom, % 165.14/165.01 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_id__def,axiom, % 165.14/165.01 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 165.14/165.01 % 165.14/165.01 fof(fact_inj__on__id,axiom, % 165.14/165.01 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_of__int__eq__id,axiom, % 165.14/165.01 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 165.14/165.01 % 165.14/165.01 fof(fact_List_Omap_Oid,axiom, % 165.14/165.01 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_List_Omap_Oidentity,axiom, % 165.14/165.01 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_o__eq__id__dest,axiom, % 165.14/165.01 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 165.14/165.01 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_ca_2) % 165.14/165.01 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_o__id,axiom, % 165.14/165.01 ! [V_f_2,T_b,T_a] : hAPP(c_Fun_Ocomp(T_a,T_b,T_a,V_f_2),c_Fun_Oid(T_a)) = V_f_2 ). % 165.14/165.01 % 165.14/165.01 fof(fact_id__o,axiom, % 165.14/165.01 ! [V_g_2,T_a,T_b] : hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_g_2) = V_g_2 ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__pair_Oidentity,axiom, % 165.14/165.01 ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_COMBI(T_a),c_COMBI(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__pair_Oid,axiom, % 165.14/165.01 ! [T_b,T_a] : c_Product__Type_Omap__pair(T_a,T_a,T_b,T_b,c_Fun_Oid(T_a),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_surj__id,axiom, % 165.14/165.01 ! [T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_folding_Oempty,axiom, % 165.14/165.01 ! [V_F_2,V_f_2,T_b,T_a] : % 165.14/165.01 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 165.14/165.01 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_apfst__def,axiom, % 165.14/165.01 ! [V_f_2,T_b,T_c,T_a] : c_Product__Type_Oapfst(T_a,T_c,T_b,V_f_2) = c_Product__Type_Omap__pair(T_a,T_c,T_b,T_b,V_f_2,c_Fun_Oid(T_b)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_apsnd__def,axiom, % 165.14/165.01 ! [V_f_2,T_a,T_c,T_b] : c_Product__Type_Oapsnd(T_b,T_c,T_a,V_f_2) = c_Product__Type_Omap__pair(T_a,T_a,T_b,T_c,c_Fun_Oid(T_a),V_f_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_split__Pair,axiom, % 165.14/165.01 ! [T_b,T_a] : hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)) = c_Fun_Oid(tc_prod(T_a,T_b)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_setsum__reindex__id,axiom, % 165.14/165.01 ! [V_B_2,V_f_2,T_a,T_b] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__add(T_b) % 165.14/165.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 165.14/165.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_setprod__reindex__id,axiom, % 165.14/165.01 ! [V_B_2,V_f_2,T_a,T_b] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__mult(T_b) % 165.14/165.01 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 165.14/165.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_b),c_Fun_Oid(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_B_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_setprod__Sigma,axiom, % 165.14/165.01 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__mult(T_c) % 165.14/165.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.01 => ( ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 165.14/165.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_refl__onI,axiom, % 165.14/165.01 ! [V_A_2,V_r_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 165.14/165.01 => ( ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) % 165.14/165.01 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_setsum__Sigma,axiom, % 165.14/165.01 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__add(T_c) % 165.14/165.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.01 => ( ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 165.14/165.01 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c),T_a),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_a,T_b),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_fold__image__Sigma,axiom, % 165.14/165.01 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 165.14/165.01 ( class_Groups_Ocomm__monoid__mult(T_c) % 165.14/165.01 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.01 => ( ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 165.14/165.01 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_a,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBC(T_a,T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_c),tc_fun(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),T_c)),T_a),c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c))),V_g_2)),c_Groups_Oone__class_Oone(T_c))),V_B_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,tc_prod(T_a,T_b),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_g_2)),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_card__SigmaI,axiom, % 165.14/165.01 ! [V_B_2,T_b,V_A_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.01 => ( ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 165.14/165.01 => hAPP(c_Finite__Set_Ocard(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat,T_a),c_Finite__Set_Ocard(T_b)),V_B_2)),V_A_2) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_finite__SigmaI,axiom, % 165.14/165.01 ! [V_B_2,T_b,V_A_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.01 => ( ! [B_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 165.14/165.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel__subset,axiom, % 165.14/165.01 ! [V_A_2,V_r_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_List_Olist(T_a)),c_List_Olists(T_a,V_A_2))))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__Cons__number__of,axiom, % 165.14/165.01 ! [V_xs,V_x,T_a,V_v] : % 165.14/165.01 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 => 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) ) % 165.14/165.01 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 => 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)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lists_ONil,axiom, % 165.14/165.01 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olists(T_a,V_A_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel__Nil2,axiom, % 165.14/165.01 ! [V_r_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))) % 165.14/165.01 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel__Nil1,axiom, % 165.14/165.01 ! [V_r_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel(T_a,V_r_2))) % 165.14/165.01 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__eq__Nil,axiom, % 165.14/165.01 ! [V_xs_2,V_n_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 165.14/165.01 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__0,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list_Osimps_I2_J,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list_Osimps_I3_J,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lists__empty,axiom, % 165.14/165.01 ! [T_a] : c_List_Olists(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_List_Oset_Osimps_I1_J,axiom, % 165.14/165.01 ! [T_a] : hAPP(c_List_Oset(T_a),c_List_Olist_ONil(T_a)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__empty2,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : % 165.14/165.01 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2) % 165.14/165.01 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__empty,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : % 165.14/165.01 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_butlast_Osimps_I1_J,axiom, % 165.14/165.01 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__Nil,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrelp_ONil,axiom, % 165.14/165.01 ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrelp_Oequations_I1_J,axiom, % 165.14/165.01 ! [V_r_2,T_a] : c_List_Olistrelp(T_a,V_r_2,c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lists__mono,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olists(T_a,V_A_2)),c_List_Olists(T_a,V_B_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_length__0__conv,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : % 165.14/165.01 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list_Osize_I3_J,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update__code_I1_J,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update_Osimps_I1_J,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update__nonempty,axiom, % 165.14/165.01 ! [V_x_2,V_k_2,V_xs_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a) % 165.14/165.01 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_removeAll_Osimps_I1_J,axiom, % 165.14/165.01 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 165.14/165.01 % 165.14/165.01 fof(fact_distinct_Osimps_I1_J,axiom, % 165.14/165.01 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_foldr_Osimps_I1_J,axiom, % 165.14/165.01 ! [V_a_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b),V_a_2) = V_a_2 ). % 165.14/165.01 % 165.14/165.01 fof(fact_remove1_Osimps_I1_J,axiom, % 165.14/165.01 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 165.14/165.01 % 165.14/165.01 fof(fact_zip_Osimps_I1_J,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_zip__Nil,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_sublist__nil,axiom, % 165.14/165.01 ! [V_A_2,T_a] : c_List_Osublist(T_a,c_List_Olist_ONil(T_a),V_A_2) = c_List_Olist_ONil(T_a) ). % 165.14/165.01 % 165.14/165.01 fof(fact_insort__not__Nil,axiom, % 165.14/165.01 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] : % 165.14/165.01 ( class_Orderings_Olinorder(T_b) % 165.14/165.01 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__upds__Nil2,axiom, % 165.14/165.01 ! [V_as_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_as_2,c_List_Olist_ONil(T_b)) = V_m_2 ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__upds__Nil1,axiom, % 165.14/165.01 ! [V_bs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,c_List_Olist_ONil(T_a),V_bs_2) = V_m_2 ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__is__Nil__conv,axiom, % 165.14/165.01 ! [V_xs_2,V_f_2,T_a,T_b] : % 165.14/165.01 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a) % 165.14/165.01 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map_Osimps_I1_J,axiom, % 165.14/165.01 ! [V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Nil__is__map__conv,axiom, % 165.14/165.01 ! [V_xs_2,V_f_2,T_b,T_a] : % 165.14/165.01 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) % 165.14/165.01 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__simps_I1_J,axiom, % 165.14/165.01 ! [T_a] : % 165.14/165.01 ( class_Groups_Omonoid__add(T_a) % 165.14/165.01 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_insort__key_Osimps_I1_J,axiom, % 165.14/165.01 ! [V_x_2,V_f_2,T_a,T_b] : % 165.14/165.01 ( class_Orderings_Olinorder(T_b) % 165.14/165.01 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__of__Cons__code_I1_J,axiom, % 165.14/165.01 ! [V_k,T_a,T_b] : hAPP(hAPP(c_Map_Omap__of(T_b,T_a),c_List_Olist_ONil(tc_prod(T_b,T_a))),V_k) = c_Option_Ooption_ONone(T_a) ). % 165.14/165.01 % 165.14/165.01 fof(fact_butlast_Osimps_I2_J,axiom, % 165.14/165.01 ! [V_x,T_a,V_xs] : % 165.14/165.01 ( ( V_xs = c_List_Olist_ONil(T_a) % 165.14/165.01 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 165.14/165.01 & ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => 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)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_upto__empty,axiom, % 165.14/165.01 ! [V_i,V_j] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 165.14/165.01 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_distinct__butlast,axiom, % 165.14/165.01 ! [T_a,V_xs] : % 165.14/165.01 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 165.14/165.01 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list_Osize_I1_J,axiom, % 165.14/165.01 ! [V_fa_2,T_a] : c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 165.14/165.01 % 165.14/165.01 fof(fact_sorted__list__of__set__empty,axiom, % 165.14/165.01 ! [T_a] : % 165.14/165.01 ( class_Orderings_Olinorder(T_a) % 165.14/165.01 => c_List_Olinorder__class_Osorted__list__of__set(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_sublist__empty,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_a) ). % 165.14/165.01 % 165.14/165.01 fof(fact_partition_Osimps_I1_J,axiom, % 165.14/165.01 ! [V_P_2,T_a] : c_List_Opartition(T_a,V_P_2,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__of_Osimps_I1_J,axiom, % 165.14/165.01 ! [V_x_1,T_b,T_a] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),c_List_Olist_ONil(tc_prod(T_a,T_b))),V_x_1) = c_Option_Ooption_ONone(T_b) ). % 165.14/165.01 % 165.14/165.01 fof(fact_length__greater__0__conv,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.01 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lists__UNIV,axiom, % 165.14/165.01 ! [T_a] : c_List_Olists(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_equiv__listrel,axiom, % 165.14/165.01 ! [V_r_2,V_A_2,T_a] : % 165.14/165.01 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.01 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel__refl__on,axiom, % 165.14/165.01 ! [V_r_2,V_A_2,T_a] : % 165.14/165.01 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 165.14/165.01 => c_Relation_Orefl__on(tc_List_Olist(T_a),c_List_Olists(T_a,V_A_2),c_List_Olistrel(T_a,V_r_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__1__Cons,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_not__listrel1__Nil,axiom, % 165.14/165.01 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olistrel1(T_a,V_r_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_not__Nil__listrel1,axiom, % 165.14/165.01 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)),c_List_Olistrel1(T_a,V_r_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel_ONil,axiom, % 165.14/165.01 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_a))),c_List_Olistrel(T_a,V_r_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexord__Nil__right,axiom, % 165.14/165.01 ! [V_r_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olexord(T_a,V_r_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Nil__notin__lex,axiom, % 165.14/165.01 ! [V_r_2,V_ys_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_ys_2)),c_List_Olex(T_a,V_r_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Nil2__notin__lex,axiom, % 165.14/165.01 ! [V_r_2,V_xs_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a))),c_List_Olex(T_a,V_r_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Cons__in__lists__iff,axiom, % 165.14/165.01 ! [V_A_2,V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_List_Olists(T_a,V_A_2))) % 165.14/165.01 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.01 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_in__lists__conv__set,axiom, % 165.14/165.01 ! [V_A_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__Cons,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_a),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otake(T_a)),V_xs_2)),V_n_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_upto_Osimps,axiom, % 165.14/165.01 ! [V_j,V_i] : % 165.14/165.01 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 165.14/165.01 => 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)) ) % 165.14/165.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 165.14/165.01 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_sublist__singleton,axiom, % 165.14/165.01 ! [V_x_2,T_a,V_A_2] : % 165.14/165.01 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 165.14/165.01 => c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) % 165.14/165.01 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 165.14/165.01 => c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)),V_A_2) = c_List_Olist_ONil(T_a) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lists__eq__set,axiom, % 165.14/165.01 ! [V_A_2,T_a] : c_List_Olists(T_a,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),V_A_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__Cons_H,axiom, % 165.14/165.01 ! [V_xs,V_x,T_a,V_n] : % 165.14/165.01 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 => 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) ) % 165.14/165.01 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 => 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)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_upto__rec__number__of,axiom, % 165.14/165.01 ! [V_n,V_m] : % 165.14/165.01 ( ( 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))) % 165.14/165.01 => 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))) ) % 165.14/165.01 & ( ~ 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))) % 165.14/165.01 => 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) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel__Nil,axiom, % 165.14/165.01 ! [V_r_2,T_a] : hAPP(c_Relation_OImage(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olistrel(T_a,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__Cons__sing__Nil,axiom, % 165.14/165.01 ! [V_A_2,T_a] : c_List_Oset__Cons(T_a,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_a,tc_List_Olist(T_a),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))),V_A_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_upto_Opsimps,axiom, % 165.14/165.01 ! [V_j_2,V_i_2] : % 165.14/165.01 ( 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))) % 165.14/165.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 165.14/165.01 => 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)) ) % 165.14/165.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 165.14/165.01 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_anamorph_Osimps,axiom, % 165.14/165.01 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 165.14/165.01 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 165.14/165.01 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2) ) % 165.14/165.01 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 165.14/165.01 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(tc_List_Olist(T_a),T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),c_COMBB(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),T_a),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),T_b))),c_List_Olist_OCons(T_a))))),hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listset_Osimps_I1_J,axiom, % 165.14/165.01 ! [T_a] : c_List_Olistset(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_zip__Cons,axiom, % 165.14/165.01 ! [V_ys_2,V_y_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_a,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_prod(T_a,T_b)))),T_a),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_a),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(hAPP(c_COMBC(T_a,T_b,tc_prod(T_a,T_b)),c_Product__Type_OPair(T_a,T_b)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),c_List_Ozip(T_a,T_b)),V_ys_2))),V_xs_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list_Osimps_I5_J,axiom, % 165.14/165.01 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list_Osimps_I4_J,axiom, % 165.14/165.01 ! [V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2),c_List_Olist_ONil(T_b)) = V_f1_2 ). % 165.14/165.01 % 165.14/165.01 fof(fact_listset_Osimps_I2_J,axiom, % 165.14/165.01 ! [V_As_2,V_A_2,T_a] : c_List_Olistset(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_a,V_A_2,c_List_Olistset(T_a,V_As_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_zip__Cons1,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_a,T_b)),T_b,c_List_Olist_ONil(tc_prod(T_a,T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_a,T_b)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_List_Olist(tc_prod(T_a,T_b)),tc_List_Olist(tc_prod(T_a,T_b))),T_b),c_List_Olist_OCons(tc_prod(T_a,T_b))),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)))),hAPP(c_List_Ozip(T_a,T_b),V_xs_2))),V_ys_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_upto_Opinduct,axiom, % 165.14/165.01 ! [V_P_2,V_a1_2,V_a0_2] : % 165.14/165.01 ( 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))) % 165.14/165.01 => ( ! [B_i,B_j] : % 165.14/165.01 ( 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))) % 165.14/165.01 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 165.14/165.01 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) ) % 165.14/165.01 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) % 165.14/165.01 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__upds__append1,axiom, % 165.14/165.01 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 165.14/165.01 => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b)),c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_b),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__eq__Cons__conv,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) % 165.14/165.01 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 165.14/165.01 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) % 165.14/165.01 | ? [B_ys_H] : % 165.14/165.01 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) % 165.14/165.01 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Cons__eq__append__conv,axiom, % 165.14/165.01 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2) % 165.14/165.01 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 165.14/165.01 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 ) % 165.14/165.01 | ? [B_ys_H] : % 165.14/165.01 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 % 165.14/165.01 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append1__eq__conv,axiom, % 165.14/165.01 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) % 165.14/165.01 <=> ( V_xs_2 = V_ys_2 % 165.14/165.01 & V_x_2 = V_y_2 ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_butlast__append,axiom, % 165.14/165.01 ! [V_xs,T_a,V_ys] : % 165.14/165.01 ( ( V_ys = c_List_Olist_ONil(T_a) % 165.14/165.01 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 165.14/165.01 & ( V_ys != c_List_Olist_ONil(T_a) % 165.14/165.01 => 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)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__Nil,axiom, % 165.14/165.01 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 165.14/165.01 % 165.14/165.01 fof(fact_Nil__is__append__conv,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 165.14/165.01 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 165.14/165.01 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__Nil2,axiom, % 165.14/165.01 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 165.14/165.01 % 165.14/165.01 fof(fact_self__append__conv,axiom, % 165.14/165.01 ! [V_ys_2,T_a,V_xs_2] : % 165.14/165.01 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 165.14/165.01 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_self__append__conv2,axiom, % 165.14/165.01 ! [V_xs_2,T_a,V_ys_2] : % 165.14/165.01 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 165.14/165.01 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__is__Nil__conv,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a) % 165.14/165.01 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 165.14/165.01 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__self__conv,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2 % 165.14/165.01 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__self__conv2,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2 % 165.14/165.01 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_eq__Nil__appendI,axiom, % 165.14/165.01 ! [T_a,V_ys,V_xs] : % 165.14/165.01 ( V_xs = V_ys % 165.14/165.01 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__of__append,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),V_xs_2),V_ys_2)) = c_Map_Omap__add(T_a,T_b,hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__append,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__append,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_ys_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_foldr__append,axiom, % 165.14/165.01 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,c_List_Ofoldr(T_b,T_a,V_f_2,V_ys_2,V_a_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__eq__appendI,axiom, % 165.14/165.01 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 165.14/165.01 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 165.14/165.01 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__same__eq,axiom, % 165.14/165.01 ! [V_zs_2,V_xs_2,V_ys_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_xs_2) % 165.14/165.01 <=> V_ys_2 = V_zs_2 ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_same__append__eq,axiom, % 165.14/165.01 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2) % 165.14/165.01 <=> V_ys_2 = V_zs_2 ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__eq__append__conv2,axiom, % 165.14/165.01 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2) % 165.14/165.01 <=> ? [B_us] : % 165.14/165.01 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) % 165.14/165.01 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 ) % 165.14/165.01 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2 % 165.14/165.01 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__assoc,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_removeAll__append,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_length__append,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_zip__append,axiom, % 165.14/165.01 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 165.14/165.01 ( 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) % 165.14/165.01 => ( 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) % 165.14/165.01 => 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)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__append,axiom, % 165.14/165.01 ! [V_ys,V_xs,T_a] : % 165.14/165.01 ( class_Groups_Omonoid__add(T_a) % 165.14/165.01 => 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)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_fun__upds__append2__drop,axiom, % 165.14/165.01 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 165.14/165.01 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 165.14/165.01 => c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_fun__upds__append__drop,axiom, % 165.14/165.01 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 165.14/165.01 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 165.14/165.01 => c_Map_Omap__upds(T_a,T_b,V_m_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__Cons,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Cons__eq__appendI,axiom, % 165.14/165.01 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 165.14/165.01 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 165.14/165.01 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__in__lists__conv,axiom, % 165.14/165.01 ! [V_A_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)),c_List_Olists(T_a,V_A_2))) % 165.14/165.01 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 165.14/165.01 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__append__length,axiom, % 165.14/165.01 ! [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 ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__append__length__plus,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__append,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update__append1,axiom, % 165.14/165.01 ! [V_x,V_ys,V_xs,T_a,V_i] : % 165.14/165.01 ( 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))) % 165.14/165.01 => 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) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update__length,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_remove1__append,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oremove1(T_a,V_x_2,V_xs_2)),V_ys_2) ) % 165.14/165.01 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => c_List_Oremove1(T_a,V_x_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oremove1(T_a,V_x_2,V_ys_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_in__set__butlast__appendI,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 165.14/165.01 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) ) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_butlast__snoc,axiom, % 165.14/165.01 ! [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 ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__listrel1I,axiom, % 165.14/165.01 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 165.14/165.01 & V_us_2 = V_vs_2 ) % 165.14/165.01 | ( V_xs_2 = V_ys_2 % 165.14/165.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_us_2),V_vs_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_vs_2))),c_List_Olistrel1(T_a,V_r_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexord__append__leftI,axiom, % 165.14/165.01 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_distinct__append,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 165.14/165.01 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.01 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 165.14/165.01 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__append,axiom, % 165.14/165.01 ! [V_ys,V_xs,T_a,V_n] : % 165.14/165.01 ( ( 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))) % 165.14/165.01 => 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) ) % 165.14/165.01 & ( ~ 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))) % 165.14/165.01 => 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))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_list__update__append,axiom, % 165.14/165.01 ! [V_x,V_ys,V_xs,T_a,V_n] : % 165.14/165.01 ( ( 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))) % 165.14/165.01 => 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) ) % 165.14/165.01 & ( ~ 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))) % 165.14/165.01 => 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)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_sublist__append,axiom, % 165.14/165.01 ! [V_A_2,V_l_H_2,V_l_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Osublist(T_a,V_l_2,V_A_2)),c_List_Osublist(T_a,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_l_2)))),V_A_2)))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel1I,axiom, % 165.14/165.01 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) % 165.14/165.01 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_vs_2)) % 165.14/165.01 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_vs_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexord__append__left__rightI,axiom, % 165.14/165.01 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_a),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_b_2),V_y_2)))),c_List_Olexord(T_a,V_r_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__Suc__conv__app__nth,axiom, % 165.14/165.01 ! [V_xs,T_a,V_i] : % 165.14/165.01 ( 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))) % 165.14/165.01 => 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))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_snoc__listrel1__snoc__iff,axiom, % 165.14/165.01 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))),hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))))),c_List_Olistrel1(T_a,V_r_2))) % 165.14/165.01 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 165.14/165.01 & V_x_2 = V_y_2 ) % 165.14/165.01 | ( V_xs_2 = V_ys_2 % 165.14/165.01 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_r_2)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_sublist__Cons,axiom, % 165.14/165.01 ! [V_A_2,V_l_2,V_x_2,T_a] : c_List_Osublist(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_a)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))),c_List_Olist_ONil(T_a))),c_List_Osublist(T_a,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listrel1E,axiom, % 165.14/165.01 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 165.14/165.01 => ~ ! [B_x,B_y] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_r_2)) % 165.14/165.01 => ! [B_us,B_vs] : % 165.14/165.01 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs)) % 165.14/165.01 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexord__append__leftD,axiom, % 165.14/165.01 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_v_2))),c_List_Olexord(T_a,V_r_2))) % 165.14/165.01 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_a),B_a)),V_r_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_u_2),V_v_2)),c_List_Olexord(T_a,V_r_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate1__def,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : hAPP(c_List_Orotate1(T_a),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)))),V_xs_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_upd__conv__take__nth__drop,axiom, % 165.14/165.01 ! [V_a,V_xs,T_a,V_i] : % 165.14/165.01 ( 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))) % 165.14/165.01 => 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))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__take__drop__id,axiom, % 165.14/165.01 ! [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 ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__Nil,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate1__is__Nil__conv,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : % 165.14/165.01 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 165.14/165.01 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__take,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_length__drop,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__rotate1,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__map,axiom, % 165.14/165.01 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_distinct1__rotate,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2))) % 165.14/165.01 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__zip,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__0,axiom, % 165.14/165.01 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__drop,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_distinct__drop,axiom, % 165.14/165.01 ! [V_i,V_xs,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 165.14/165.01 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_length__rotate1,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_butlast__drop,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__butlast,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__drop,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_in__set__dropD,axiom, % 165.14/165.01 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2)))) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__drop__subset,axiom, % 165.14/165.01 ! [V_xs_2,V_n_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__Suc__Cons,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__1__Cons,axiom, % 165.14/165.01 ! [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 ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__via__drop,axiom, % 165.14/165.01 ! [V_ys,V_y,V_xs,V_n,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 165.14/165.01 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__drop__subset__set__drop,axiom, % 165.14/165.01 ! [V_xs_2,T_a,V_m_2,V_n_2] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2)))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__all,axiom, % 165.14/165.01 ! [V_n,V_xs,T_a] : % 165.14/165.01 ( 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)) % 165.14/165.01 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__eq__Nil,axiom, % 165.14/165.01 ! [V_xs_2,V_n_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 165.14/165.01 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_n_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__append,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__eq__conv__conj,axiom, % 165.14/165.01 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2 % 165.14/165.01 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2) % 165.14/165.01 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__Cons,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,V_n_2,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Odrop(T_a)),V_xs_2),V_n_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__Cons_H,axiom, % 165.14/165.01 ! [V_xs,V_x,T_a,V_n] : % 165.14/165.01 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 => 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) ) % 165.14/165.01 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 => 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) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__drop,axiom, % 165.14/165.01 ! [V_xs,T_a,V_i,V_n] : % 165.14/165.01 ( 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))) % 165.14/165.01 => 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)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__eq__append__conv__if,axiom, % 165.14/165.01 ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_a),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2) % 165.14/165.01 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2))) % 165.14/165.01 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) % 165.14/165.01 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) ) % 165.14/165.01 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2))) % 165.14/165.01 => ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 % 165.14/165.01 & hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2 ) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_nth__drop_H,axiom, % 165.14/165.01 ! [V_xs,T_a,V_i] : % 165.14/165.01 ( 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))) % 165.14/165.01 => 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) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate__simps,axiom, % 165.14/165.01 ! [V_xs,V_x,T_b,T_a] : % 165.14/165.01 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 165.14/165.01 & 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))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__Cons__number__of,axiom, % 165.14/165.01 ! [V_xs,V_x,T_a,V_v] : % 165.14/165.01 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 => 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) ) % 165.14/165.01 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 => 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) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__add,axiom, % 165.14/165.01 ! [V_xs,T_a,V_j,V_i] : % 165.14/165.01 ( 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))) % 165.14/165.01 => 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))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate1__length01,axiom, % 165.14/165.01 ! [V_xs,T_a] : % 165.14/165.01 ( 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))) % 165.14/165.01 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_zip__append1,axiom, % 165.14/165.01 ! [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))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_zip__append2,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_id__take__nth__drop,axiom, % 165.14/165.01 ! [V_xs,T_a,V_i] : % 165.14/165.01 ( 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))) % 165.14/165.01 => 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))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__hd__drop,axiom, % 165.14/165.01 ! [V_xs,T_a,V_n] : % 165.14/165.01 ( 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))) % 165.14/165.01 => 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) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_hd__drop__conv__nth,axiom, % 165.14/165.01 ! [V_n,T_a,V_xs] : % 165.14/165.01 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => ( 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))) % 165.14/165.01 => 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) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_hd_Osimps,axiom, % 165.14/165.01 ! [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 ). % 165.14/165.01 % 165.14/165.01 fof(fact_hd__map,axiom, % 165.14/165.01 ! [V_f_2,T_b,T_a,V_xs_2] : % 165.14/165.01 ( V_xs_2 != c_List_Olist_ONil(T_a) % 165.14/165.01 => hAPP(c_List_Ohd(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_a),V_xs_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_hd__append2,axiom, % 165.14/165.01 ! [V_ys,T_a,V_xs] : % 165.14/165.01 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => 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) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_hd__append,axiom, % 165.14/165.01 ! [V_ys,T_a,V_xs] : % 165.14/165.01 ( ( V_xs = c_List_Olist_ONil(T_a) % 165.14/165.01 => 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) ) % 165.14/165.01 & ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => 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) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_hd__in__set,axiom, % 165.14/165.01 ! [T_a,V_xs_2] : % 165.14/165.01 ( V_xs_2 != c_List_Olist_ONil(T_a) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_hd__conv__nth,axiom, % 165.14/165.01 ! [T_a,V_xs] : % 165.14/165.01 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => 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)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate1__hd__tl,axiom, % 165.14/165.01 ! [T_a,V_xs] : % 165.14/165.01 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => 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))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_hd__rotate__conv__nth,axiom, % 165.14/165.01 ! [V_n,T_a,V_xs] : % 165.14/165.01 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => 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))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__tl,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_tl__drop,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_tl_Osimps_I1_J,axiom, % 165.14/165.01 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate__is__Nil__conv,axiom, % 165.14/165.01 ! [V_xs_2,V_n_2,T_a] : % 165.14/165.01 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 165.14/165.01 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_set__rotate,axiom, % 165.14/165.01 ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__tl,axiom, % 165.14/165.01 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Otl(T_b),V_xs_2)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate__map,axiom, % 165.14/165.01 ! [V_xs_2,V_f_2,T_b,V_n_2,T_a] : hAPP(c_List_Orotate(T_a,V_n_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate__rotate,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_distinct__rotate,axiom, % 165.14/165.01 ! [V_xs_2,V_n_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2))) % 165.14/165.01 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_distinct__tl,axiom, % 165.14/165.01 ! [V_xs,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 165.14/165.01 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_length__rotate,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_tl_Osimps_I2_J,axiom, % 165.14/165.01 ! [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 ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate1__rotate__swap,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_tl__append2,axiom, % 165.14/165.01 ! [V_ys,T_a,V_xs] : % 165.14/165.01 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => 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) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__tl,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate__conv__mod,axiom, % 165.14/165.01 ! [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) ). % 165.14/165.01 % 165.14/165.01 fof(fact_drop__Suc,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate__Suc,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_tl__append,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,hAPP(c_List_Otl(T_a),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Oappend(T_a)),V_ys_2))),V_xs_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate0,axiom, % 165.14/165.01 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate__add,axiom, % 165.14/165.01 ! [V_n_2,V_m_2,T_a] : c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orotate(T_a,V_m_2)),c_List_Orotate(T_a,V_n_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate__id,axiom, % 165.14/165.01 ! [V_xs,T_a,V_n] : % 165.14/165.01 ( 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) % 165.14/165.01 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate__length01,axiom, % 165.14/165.01 ! [V_n,V_xs,T_a] : % 165.14/165.01 ( 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))) % 165.14/165.01 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_length__tl,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_tl__take,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_take__Suc,axiom, % 165.14/165.01 ! [V_n,T_a,V_xs] : % 165.14/165.01 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => 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))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_rotate__drop__take,axiom, % 165.14/165.01 ! [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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_fold1__set,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : % 165.14/165.01 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 165.14/165.01 => ( V_xs_2 != c_List_Olist_ONil(T_a) % 165.14/165.01 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Ohd(T_a),V_xs_2)),hAPP(c_List_Otl(T_a),V_xs_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexord__append__rightI,axiom, % 165.14/165.01 ! [V_r_2,V_x_2,T_a,V_y_2] : % 165.14/165.01 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),hAPP(hAPP(c_List_Oappend(T_a),V_x_2),V_y_2))),c_List_Olexord(T_a,V_r_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_foldl__Cons,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_start__le__sum,axiom, % 165.14/165.01 ! [V_ns_2,V_n_2,V_m_2] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 165.14/165.01 => 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))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_foldl__absorb0,axiom, % 165.14/165.01 ! [V_zs_2,V_x_2,T_a] : % 165.14/165.01 ( class_Groups_Omonoid__add(T_a) % 165.14/165.01 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_zs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_zs_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_foldl__assoc,axiom, % 165.14/165.01 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 165.14/165.01 ( class_Groups_Osemigroup__add(T_a) % 165.14/165.01 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_y_2),V_zs_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_foldl__map,axiom, % 165.14/165.01 ! [V_xs_2,V_f_2,T_c,V_a_2,V_g_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,T_a)),T_a),c_COMBB(T_b,T_a,T_c)),V_g_2)),V_f_2),V_a_2),V_xs_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_foldl__Nil,axiom, % 165.14/165.01 ! [V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),c_List_Olist_ONil(T_b)) = V_a_2 ). % 165.14/165.01 % 165.14/165.01 fof(fact_foldl__append,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2)),V_ys_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_foldr__conv__foldl,axiom, % 165.14/165.01 ! [V_a_2,V_xs_2,T_a] : % 165.14/165.01 ( class_Groups_Oab__semigroup__add(T_a) % 165.14/165.01 => c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsum__foldl,axiom, % 165.14/165.01 ! [T_a] : % 165.14/165.01 ( class_Groups_Omonoid__add(T_a) % 165.14/165.01 => c_List_Omonoid__add__class_Olistsum(T_a) = c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_foldl__foldr1__lemma,axiom, % 165.14/165.01 ! [V_xs_2,V_a_2,T_a] : % 165.14/165.01 ( class_Groups_Omonoid__add(T_a) % 165.14/165.01 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_foldl__foldr1,axiom, % 165.14/165.01 ! [V_xs_2,T_a] : % 165.14/165.01 ( class_Groups_Omonoid__add(T_a) % 165.14/165.01 => hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_xs_2) = c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_sum__eq__0__conv,axiom, % 165.14/165.01 ! [V_ns_2,V_m_2] : % 165.14/165.01 ( 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) % 165.14/165.01 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.01 & ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 165.14/165.01 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Sup__fin__set__fold,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( class_Lattices_Olattice(T_a) % 165.14/165.01 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_xs_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Inf__fin__set__fold,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( class_Lattices_Olattice(T_a) % 165.14/165.01 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_xs_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Min__fin__set__fold,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( class_Orderings_Olinorder(T_a) % 165.14/165.01 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Max__fin__set__fold,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( class_Orderings_Olinorder(T_a) % 165.14/165.01 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_min__max_OInf__fin__set__fold,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( class_Orderings_Olinorder(T_a) % 165.14/165.01 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omin(T_a),V_x_2),V_xs_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_min__max_OSup__fin__set__fold,axiom, % 165.14/165.01 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.01 ( class_Orderings_Olinorder(T_a) % 165.14/165.01 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_x_2),V_xs_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_SUPR__set__fold,axiom, % 165.14/165.01 ! [V_f_2,V_xs_2,T_b,T_a] : % 165.14/165.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_f_2)),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_map__upds__fold__map__upd,axiom, % 165.14/165.01 ! [V_vs_2,V_ks_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_ks_2,V_vs_2) = hAPP(c_List_Ofoldl(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(tc_prod(T_a,T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_a,tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),c_COMBC(T_a,tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)))),tc_fun(T_a,tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b))))),tc_fun(T_a,tc_Option_Ooption(T_b))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b))),tc_fun(tc_fun(T_b,tc_Option_Ooption(T_b)),tc_fun(T_b,tc_fun(T_a,tc_Option_Ooption(T_b)))),T_a),c_COMBB(tc_Option_Ooption(T_b),tc_fun(T_a,tc_Option_Ooption(T_b)),T_b))),c_Fun_Ofun__upd(T_a,tc_Option_Ooption(T_b))))),c_Option_Ooption_OSome(T_b))),V_m_2),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ks_2),V_vs_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_elem__le__sum,axiom, % 165.14/165.01 ! [V_ns_2,V_n_2] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 165.14/165.01 => 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))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lexord__Nil__left,axiom, % 165.14/165.01 ! [V_r_2,V_y_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_y_2)),c_List_Olexord(T_a,V_r_2))) % 165.14/165.01 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_last__list__update,axiom, % 165.14/165.01 ! [V_x,V_k,T_a,V_xs] : % 165.14/165.01 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => ( ( 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)) % 165.14/165.01 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 165.14/165.01 & ( 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)) % 165.14/165.01 => 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) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_last__ConsL,axiom, % 165.14/165.01 ! [V_x,T_a,V_xs] : % 165.14/165.01 ( V_xs = c_List_Olist_ONil(T_a) % 165.14/165.01 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_last__ConsR,axiom, % 165.14/165.01 ! [V_x,T_a,V_xs] : % 165.14/165.01 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_last_Osimps,axiom, % 165.14/165.01 ! [V_x,T_a,V_xs] : % 165.14/165.01 ( ( V_xs = c_List_Olist_ONil(T_a) % 165.14/165.01 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 165.14/165.01 & ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_last__map,axiom, % 165.14/165.01 ! [V_f_2,T_b,T_a,V_xs_2] : % 165.14/165.01 ( V_xs_2 != c_List_Olist_ONil(T_a) % 165.14/165.01 => c_List_Olast(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_a,V_xs_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_last__append,axiom, % 165.14/165.01 ! [V_xs,T_a,V_ys] : % 165.14/165.01 ( ( V_ys = c_List_Olist_ONil(T_a) % 165.14/165.01 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 165.14/165.01 & ( V_ys != c_List_Olist_ONil(T_a) % 165.14/165.01 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_last__appendR,axiom, % 165.14/165.01 ! [V_xs,T_a,V_ys] : % 165.14/165.01 ( V_ys != c_List_Olist_ONil(T_a) % 165.14/165.01 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_last__appendL,axiom, % 165.14/165.01 ! [V_xs,T_a,V_ys] : % 165.14/165.01 ( V_ys = c_List_Olist_ONil(T_a) % 165.14/165.01 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_last__in__set,axiom, % 165.14/165.01 ! [T_a,V_as_2] : % 165.14/165.01 ( V_as_2 != c_List_Olist_ONil(T_a) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_last__snoc,axiom, % 165.14/165.01 ! [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 ). % 165.14/165.01 % 165.14/165.01 fof(fact_last__drop,axiom, % 165.14/165.01 ! [V_xs,T_a,V_n] : % 165.14/165.01 ( 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))) % 165.14/165.01 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__butlast__last__id,axiom, % 165.14/165.01 ! [T_a,V_xs] : % 165.14/165.01 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => 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 ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_snoc__eq__iff__butlast,axiom, % 165.14/165.01 ! [V_ys_2,V_x_2,V_xs_2,T_a] : % 165.14/165.01 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))) = V_ys_2 % 165.14/165.01 <=> ( V_ys_2 != c_List_Olist_ONil(T_a) % 165.14/165.01 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2 % 165.14/165.01 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_last__conv__nth,axiom, % 165.14/165.01 ! [T_a,V_xs] : % 165.14/165.01 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.01 => 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))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lists_Osimps,axiom, % 165.14/165.01 ! [V_A_2,V_a_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2))) % 165.14/165.01 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 165.14/165.01 | ? [B_a,B_l] : % 165.14/165.01 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) % 165.14/165.01 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 165.14/165.01 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INFI__set__fold,axiom, % 165.14/165.01 ! [V_f_2,V_xs_2,T_b,T_a] : % 165.14/165.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),hAPP(c_List_Oset(T_b),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_f_2)),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INF2__D,axiom, % 165.14/165.01 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INF2__E,axiom, % 165.14/165.01 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 165.14/165.01 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 165.14/165.01 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INF1__D,axiom, % 165.14/165.01 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INF1__E,axiom, % 165.14/165.01 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 165.14/165.01 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 165.14/165.01 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__E,axiom, % 165.14/165.01 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 165.14/165.01 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) % 165.14/165.01 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__D,axiom, % 165.14/165.01 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_finite__INT,axiom, % 165.14/165.01 ! [V_A_2,T_b,V_I_2,T_a] : % 165.14/165.01 ( ? [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2)) % 165.14/165.01 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) ) % 165.14/165.01 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Image__INT__subset,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_c,V_r_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__subset__iff,axiom, % 165.14/165.01 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2))) % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_le__INF__iff,axiom, % 165.14/165.01 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] : % 165.14/165.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_M_2))) % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INF__INT__eq2,axiom, % 165.14/165.01 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_a),hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c))))),V_r_2)),V_x_2),V_y_2)) % 165.14/165.01 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__lower,axiom, % 165.14/165.01 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__simps_I10_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_f_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_a,tc_HOL_Obool),T_c),V_B_2),V_f_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__extend__simps_I10_J,axiom, % 165.14/165.01 ! [V_f_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_a,tc_HOL_Obool),T_b),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Compl__INT,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Compl__UN,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__insert__distrib,axiom, % 165.14/165.01 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INF__INT__eq,axiom, % 165.14/165.01 ! [V_x_2,V_r_2,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b))),V_r_2)),V_x_2)) % 165.14/165.01 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__iff,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__absorb,axiom, % 165.14/165.01 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 165.14/165.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__Int__distrib,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_I_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__simps_I5_J,axiom, % 165.14/165.01 ! [V_B_2,V_a_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__extend__simps_I5_J,axiom, % 165.14/165.01 ! [V_B_2,V_C_2,T_b,V_a_2,T_a] : hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_a),V_a_2)),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__insert,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_a_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INF__const,axiom, % 165.14/165.01 ! [V_M_2,T_a,V_A_2,T_b] : % 165.14/165.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 165.14/165.01 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),hAPP(c_COMBK(T_b,T_a),V_M_2)) = V_M_2 ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__constant,axiom, % 165.14/165.01 ! [V_ca_2,T_b,T_a,V_A_2] : % 165.14/165.01 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 165.14/165.01 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = V_ca_2 ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__empty,axiom, % 165.14/165.01 ! [V_B_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__extend__simps_I1_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 165.14/165.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) % 165.14/165.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__extend__simps_I2_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 165.14/165.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 165.14/165.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__Un,axiom, % 165.14/165.01 ! [V_M_2,V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_M_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Collect__ball__eq,axiom, % 165.14/165.01 ! [V_P_2,V_A_2,T_b,T_a] : hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_OCollect(T_a)),hAPP(c_COMBC(T_a,T_b,tc_HOL_Obool),V_P_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INFI__bool__eq,axiom, % 165.14/165.01 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INF__less__iff,axiom, % 165.14/165.01 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] : % 165.14/165.01 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.01 & class_Orderings_Olinorder(T_a) ) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_f_2)),V_a_2)) % 165.14/165.01 <=> ? [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 165.14/165.01 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__simps_I7_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__simps_I6_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__extend__simps_I7_J,axiom, % 165.14/165.01 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Un__INT__distrib,axiom, % 165.14/165.01 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_B_2)),V_A_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__extend__simps_I6_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_C_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Un__INT__distrib2,axiom, % 165.14/165.01 ! [V_B_2,V_J_2,T_c,V_A_2,V_I_2,T_b,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2))),V_B_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INFI__apply,axiom, % 165.14/165.01 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 165.14/165.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.01 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,T_a)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_f_2),V_x_2)) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INF__commute,axiom, % 165.14/165.01 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 165.14/165.01 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_a),T_a,T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_a),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_a),T_a,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2)),hAPP(c_COMBC(T_b,T_c,T_a),V_f_2))) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_Pow__INT__eq,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Set_OPow(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_b),c_Set_OPow(T_a)),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_a,T_b] : % 165.14/165.01 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 165.14/165.01 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a] : % 165.14/165.01 ( c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 165.14/165.01 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_UN__extend__simps_I7_J,axiom, % 165.14/165.01 ! [V_B_2,V_C_2,T_b,V_A_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_UN__simps_I7_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_vimage__INT,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__simps_I9_J,axiom, % 165.14/165.01 ! [V_C_2,V_B_2,V_A_2,T_c,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__extend__simps_I9_J,axiom, % 165.14/165.01 ! [V_C_2,V_B_2,T_c,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INF__subset,axiom, % 165.14/165.01 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 165.14/165.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INTER__def,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_member(T_a))),V_B_2)))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__simps_I2_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 165.14/165.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 165.14/165.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__simps_I1_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 165.14/165.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 165.14/165.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__simps_I3_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 165.14/165.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 165.14/165.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__extend__simps_I3_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 165.14/165.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) ) % 165.14/165.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__extend__simps_I4_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 165.14/165.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) % 165.14/165.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INF__leI,axiom, % 165.14/165.01 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 165.14/165.01 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 165.14/165.01 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__greaterThan__UNIV,axiom, % 165.14/165.01 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)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INT__simps_I4_J,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 165.14/165.01 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 165.14/165.01 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.01 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_transpose__aux__max,axiom, % 165.14/165.01 ! [V_xss_2,T_b,V_xs_2,T_a] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_lists__Int__eq,axiom, % 165.14/165.01 ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_a))),c_List_Olists(T_a,V_B_2))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsp_ONil,axiom, % 165.14/165.01 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INF1__iff,axiom, % 165.14/165.01 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_INF2__iff,axiom, % 165.14/165.01 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.01 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_sum__length__filter__compl,axiom, % 165.14/165.01 ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_append__in__listsp__conv,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,V_A_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 165.14/165.01 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 165.14/165.01 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_filter__append,axiom, % 165.14/165.01 ! [V_ys_2,V_xs_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_filter__map,axiom, % 165.14/165.01 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)) ). % 165.14/165.01 % 165.14/165.01 fof(fact_filter_Osimps_I1_J,axiom, % 165.14/165.01 ! [V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 165.14/165.01 % 165.14/165.01 fof(fact_listsp_Oequations_I1_J,axiom, % 165.14/165.01 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 165.14/165.01 % 165.14/165.01 fof(fact_filter__empty__conv,axiom, % 165.14/165.01 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.01 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a) % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_partition__filter1,axiom, % 165.14/165.01 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ). % 165.14/165.01 % 165.14/165.01 fof(fact_in__listsp__conv__set,axiom, % 165.14/165.01 ! [V_xs_2,V_A_2,T_a] : % 165.14/165.01 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 165.14/165.01 <=> ! [B_x] : % 165.14/165.01 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.01 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 165.14/165.01 % 165.14/165.01 fof(fact_filter__id__conv,axiom, % 165.14/165.01 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.02 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2 % 165.14/165.02 <=> ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_filter__insort__triv,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] : % 165.14/165.02 ( class_Orderings_Olinorder(T_b) % 165.14/165.02 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_filter__remove1,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,V_Q_2,T_a] : hAPP(c_List_Ofilter(T_a,V_Q_2),c_List_Oremove1(T_a,V_x_2,V_xs_2)) = c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_remove1__filter__not,axiom, % 165.14/165.02 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 165.14/165.02 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => c_List_Oremove1(T_a,V_x_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_listsp__conj__eq,axiom, % 165.14/165.02 ! [V_x_2,V_B_2,V_A_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_A_2)),V_B_2)),V_x_2)) % 165.14/165.02 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) % 165.14/165.02 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_filter__filter,axiom, % 165.14/165.02 ! [V_xs_2,V_Q_2,V_P_2,T_a] : hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Ofilter(T_a,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_Q_2)),V_P_2)),V_xs_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_distinct__filter,axiom, % 165.14/165.02 ! [V_P_2,V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.02 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_removeAll__filter__not__eq,axiom, % 165.14/165.02 ! [V_x_2,T_a] : c_List_OremoveAll(T_a,V_x_2) = c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(c_fequal,V_x_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_removeAll__filter__not,axiom, % 165.14/165.02 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 165.14/165.02 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => hAPP(c_List_OremoveAll(T_a,V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_listsp__inf__eq,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a] : c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_listsp__infI,axiom, % 165.14/165.02 ! [V_B_2,V_l_2,V_A_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2)) % 165.14/165.02 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2)) % 165.14/165.02 => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__filter__le,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_filter__is__subset,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_filter_Osimps_I2_J,axiom, % 165.14/165.02 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 165.14/165.02 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) ) % 165.14/165.02 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_listsp_Oequations_I2_J,axiom, % 165.14/165.02 ! [V_a2_2,V_a1_2,V_A_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2))) % 165.14/165.02 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 165.14/165.02 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_partition__filter2,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Opartition(T_a,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_P_2)),V_xs_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_set__filter,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),V_xs_2)))),V_P_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__filter__map,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2)),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__filter__less,axiom, % 165.14/165.02 ! [V_P_2,V_xs_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_partition__filter__conv,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_a] : c_List_Opartition(T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_a,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot),V_f_2)),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_listsp__mono,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),c_List_Olistsp(T_a,V_A_2)),c_List_Olistsp(T_a,V_B_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_set__minus__filter__out,axiom, % 165.14/165.02 ! [V_y_2,V_xs_2,T_a] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_filter__in__sublist,axiom, % 165.14/165.02 ! [V_s_2,V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.02 => hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),hAPP(c_List_Oset(T_a),c_List_Osublist(T_a,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_a,V_xs_2,V_s_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_listsp__lists__eq,axiom, % 165.14/165.02 ! [V_x_2,V_A_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),V_x_2)) % 165.14/165.02 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__filter__conv__card,axiom, % 165.14/165.02 ! [V_xs_2,V_p_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_a),V_xs_2))))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_lists__IntI,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,V_l_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2))) % 165.14/165.02 => hBOOL(hAPP(c_List_Olistsp(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_B_2))),V_l_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_map__filter__def,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),V_f_2)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool),T_b),c_fequal),V_f_2)),c_Option_Ooption_ONone(T_a)))),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose__max__length,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose_Osimps_I2_J,axiom, % 165.14/165.02 ! [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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose__map__map,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),c_List_Otranspose(T_b,V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose__empty,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a)) % 165.14/165.02 <=> ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose_Osimps_I1_J,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_map__filter__simps_I2_J,axiom, % 165.14/165.02 ! [V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ). % 165.14/165.02 % 165.14/165.02 fof(fact_map__of__filter__in,axiom, % 165.14/165.02 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] : % 165.14/165.02 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xs_2),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2)) % 165.14/165.02 => hAPP(hAPP(c_Map_Omap__of(T_b,T_a),hAPP(c_List_Ofilter(tc_prod(T_b,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_z_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_map__filter__simps_I1_J,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omap__filter(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(T_a),T_a,c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2))),hAPP(V_f_2,V_x_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sublist__shift__lemma__Suc,axiom, % 165.14/165.02 ! [V_is_2,V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_a,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_a,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_a,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_nth__transpose,axiom, % 165.14/165.02 ! [V_xs_2,T_a,V_i_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) % 165.14/165.02 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__transpose,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_map__filter__map__filter,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = c_List_Omap__filter(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,tc_Option_Ooption(T_a),tc_Option_Ooption(T_a)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_a),tc_fun(tc_Option_Ooption(T_a),tc_Option_Ooption(T_a))),T_b),c_If(tc_Option_Ooption(T_a))),V_P_2)),hAPP(hAPP(c_COMBB(T_a,tc_Option_Ooption(T_a),T_b),c_Option_Ooption_OSome(T_a)),V_f_2))),c_Option_Ooption_ONone(T_a)),V_xs_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_insort__key__remove1,axiom, % 165.14/165.02 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] : % 165.14/165.02 ( class_Orderings_Olinorder(T_b) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 165.14/165.02 => ( hAPP(c_List_Ohd(T_a),hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_a),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2 % 165.14/165.02 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sublist__def,axiom, % 165.14/165.02 ! [V_A_2,V_xs_2,T_a] : c_List_Osublist(T_a,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted_ONil,axiom, % 165.14/165.02 ! [T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__single,axiom, % 165.14/165.02 ! [V_x,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__filter,axiom, % 165.14/165.02 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__same,axiom, % 165.14/165.02 ! [V_xs_2,V_g_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Ofilter(T_a,hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__butlast,axiom, % 165.14/165.02 ! [V_xs,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__insort__key,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2))) % 165.14/165.02 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__map__remove1,axiom, % 165.14/165.02 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__drop,axiom, % 165.14/165.02 ! [V_n,V_xs,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_drop__upt,axiom, % 165.14/165.02 ! [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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_hd__upt,axiom, % 165.14/165.02 ! [V_j,V_i] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 165.14/165.02 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_upt__Suc,axiom, % 165.14/165.02 ! [V_j,V_i] : % 165.14/165.02 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 165.14/165.02 => 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))) ) % 165.14/165.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 165.14/165.02 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_upt__Suc__append,axiom, % 165.14/165.02 ! [V_j,V_i] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 165.14/165.02 => 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))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_upt__add__eq__append,axiom, % 165.14/165.02 ! [V_k,V_j,V_i] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 165.14/165.02 => 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))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_upt__conv__Nil,axiom, % 165.14/165.02 ! [V_i,V_j] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 165.14/165.02 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_upt__eq__Nil__conv,axiom, % 165.14/165.02 ! [V_j_2,V_i_2] : % 165.14/165.02 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 165.14/165.02 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.02 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted_Oequations_I1_J,axiom, % 165.14/165.02 ! [T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_upt__0,axiom, % 165.14/165.02 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 165.14/165.02 % 165.14/165.02 fof(fact_map__Suc__upt,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__insort,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)) % 165.14/165.02 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__remove1,axiom, % 165.14/165.02 ! [V_a,V_xs,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__upto,axiom, % 165.14/165.02 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__upt,axiom, % 165.14/165.02 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_distinct__upt,axiom, % 165.14/165.02 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__list__of__set__range,axiom, % 165.14/165.02 ! [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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__insort__insert,axiom, % 165.14/165.02 ! [V_x_2,V_xs_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__take,axiom, % 165.14/165.02 ! [V_n,V_xs,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__distinct__set__unique,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 165.14/165.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 165.14/165.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 165.14/165.02 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 165.14/165.02 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_take__upt,axiom, % 165.14/165.02 ! [V_n,V_m,V_i] : % 165.14/165.02 ( 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)) % 165.14/165.02 => 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)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_upt__conv__Cons,axiom, % 165.14/165.02 ! [V_j,V_i] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 165.14/165.02 => 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)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__many,axiom, % 165.14/165.02 ! [V_zs,V_y,V_x,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 165.14/165.02 => 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))) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__many__eq,axiom, % 165.14/165.02 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2))) % 165.14/165.02 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 165.14/165.02 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_upt__rec,axiom, % 165.14/165.02 ! [V_j,V_i] : % 165.14/165.02 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 165.14/165.02 => 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)) ) % 165.14/165.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 165.14/165.02 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__tl,axiom, % 165.14/165.02 ! [V_xs,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__insort__insert__key,axiom, % 165.14/165.02 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_set__upt,axiom, % 165.14/165.02 ! [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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_atLeastLessThan__upt,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__map__same,axiom, % 165.14/165.02 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__upt,axiom, % 165.14/165.02 ! [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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__Cons,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 165.14/165.02 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 165.14/165.02 & ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__append,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 165.14/165.02 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 165.14/165.02 & c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 165.14/165.02 & ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => ! [B_xa] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_upt__rec__number__of,axiom, % 165.14/165.02 ! [V_n,V_m] : % 165.14/165.02 ( ( 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))) % 165.14/165.02 => 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))) ) % 165.14/165.02 & ( ~ 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))) % 165.14/165.02 => 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) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_upt__eq__Cons__conv,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 165.14/165.02 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 165.14/165.02 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 165.14/165.02 & V_i_2 = V_x_2 % 165.14/165.02 & 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 ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_last__upt,axiom, % 165.14/165.02 ! [V_j,V_i] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 165.14/165.02 => 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)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_filter__insort,axiom, % 165.14/165.02 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 165.14/165.02 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_map__nth,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),hAPP(c_List_Onth(T_a),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) = V_xs_2 ). % 165.14/165.02 % 165.14/165.02 fof(fact_atLeastAtMost__upt,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_atLeast__upt,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 165.14/165.02 ! [V_n_2,V_m_2,V_f_2,T_a] : % 165.14/165.02 ( class_Groups_Ocomm__monoid__add(T_a) % 165.14/165.02 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 165.14/165.02 ! [V_n_2,V_m_2,V_f_2,T_a] : % 165.14/165.02 ( class_Groups_Ocomm__monoid__add(T_a) % 165.14/165.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_nth__upt,axiom, % 165.14/165.02 ! [V_j,V_k,V_i] : % 165.14/165.02 ( 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)) % 165.14/165.02 => 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) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_greaterThanAtMost__upt,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted_Oequations_I2_J,axiom, % 165.14/165.02 ! [V_a1_2,V_a2_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2)) % 165.14/165.02 <=> ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) ) % 165.14/165.02 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_greaterThanLessThan__upt,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_nth__map__upt,axiom, % 165.14/165.02 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] : % 165.14/165.02 ( 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))) % 165.14/165.02 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__list__of__set,axiom, % 165.14/165.02 ! [V_A_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.02 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2 % 165.14/165.02 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) % 165.14/165.02 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_atMost__upto,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_insort__remove1,axiom, % 165.14/165.02 ! [V_xs_2,V_a_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 165.14/165.02 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_a_2),c_List_Oremove1(T_a,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__nth__mono,axiom, % 165.14/165.02 ! [V_j,V_i,V_xs,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 165.14/165.02 => ( 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))) % 165.14/165.02 => 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))) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__equals__nth__mono,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 165.14/165.02 <=> ! [B_j] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => ! [B_i] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j))) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_map__sorted__distinct__set__unique,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 165.14/165.02 ( class_Orderings_Olinorder(T_b) % 165.14/165.02 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_List_Oset(T_a),V_ys_2))) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 165.14/165.02 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)) % 165.14/165.02 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))) % 165.14/165.02 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 165.14/165.02 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sublist__shift__lemma,axiom, % 165.14/165.02 ! [V_i_2,V_xs_2,V_A_2,T_a] : hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_a,tc_Nat_Onat),T_a),c_Product__Type_Ofst(T_a,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_a,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_a,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_a,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_a,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_a,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_a,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose__rectangle,axiom, % 165.14/165.02 ! [V_n_2,T_a,V_xs_2] : % 165.14/165.02 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 165.14/165.02 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 165.14/165.02 => ( ! [B_i] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 165.14/165.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),B_i)) = V_n_2 ) % 165.14/165.02 => c_List_Otranspose(T_a,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_a),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_a)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_a)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_Nat_Onat,T_a),tc_Nat_Onat),c_List_Onth(T_a)),hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose_Opsimps_I2_J,axiom, % 165.14/165.02 ! [V_xss_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2))) % 165.14/165.02 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss_2)) = c_List_Otranspose(T_a,V_xss_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose_Opsimps_I1_J,axiom, % 165.14/165.02 ! [T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a)))) % 165.14/165.02 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose__column,axiom, % 165.14/165.02 ! [V_i_2,V_xs_2,T_a] : % 165.14/165.02 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 165.14/165.02 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,T_a),c_List_Onth(T_a)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose__aux__filter__head,axiom, % 165.14/165.02 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),T_a),c_List_Ohd(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_inj__on__rev,axiom, % 165.14/165.02 ! [V_A_2,T_a] : c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Orev(T_a),V_A_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev_Osimps_I1_J,axiom, % 165.14/165.02 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Nil__is__rev__conv,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2) % 165.14/165.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__is__Nil__conv,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 165.14/165.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__concat,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Orev(T_a)),hAPP(c_List_Orev(tc_List_Olist(T_a)),V_xs_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__map,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_b,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_singleton__rev__conv,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.02 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) = hAPP(c_List_Orev(T_a),V_xs_2) % 165.14/165.02 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__singleton__conv,axiom, % 165.14/165.02 ! [V_x_2,V_xs_2,T_a] : % 165.14/165.02 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) % 165.14/165.02 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__foldl__cons,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)),V_xs_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_foldl__conv__concat,axiom, % 165.14/165.02 ! [V_xss_2,V_xs_2,T_a] : hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_Oconcat(T_a,V_xss_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_distinct__rev,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2))) % 165.14/165.02 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__append,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_concat__append,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__rev,axiom, % 165.14/165.02 ! [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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__is__rev__conv,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,T_a] : % 165.14/165.02 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2) % 165.14/165.02 <=> V_xs_2 = V_ys_2 ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__swap,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,T_a] : % 165.14/165.02 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2 % 165.14/165.02 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__rev__ident,axiom, % 165.14/165.02 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 165.14/165.02 % 165.14/165.02 fof(fact_listsum__rev,axiom, % 165.14/165.02 ! [V_xs,T_a] : % 165.14/165.02 ( class_Groups_Ocomm__monoid__add(T_a) % 165.14/165.02 => 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) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_set__rev,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_zip__rev,axiom, % 165.14/165.02 ! [V_ys,T_b,V_xs,T_a] : % 165.14/165.02 ( 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) % 165.14/165.02 => 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)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__filter,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),hAPP(c_List_Orev(T_a),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_concat__conv__foldl,axiom, % 165.14/165.02 ! [V_xss_2,T_a] : c_List_Oconcat(T_a,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_xss_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_foldr__foldl,axiom, % 165.14/165.02 ! [V_a_2,V_xs_2,V_f_2,T_a,T_b] : c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_a,T_b,hAPP(c_COMBC(T_b,T_a,T_a),V_f_2),V_a_2),hAPP(c_List_Orev(T_b),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_foldl__foldr,axiom, % 165.14/165.02 ! [V_xs_2,V_a_2,V_f_2,T_b,T_a] : hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_a),V_f_2),hAPP(c_List_Orev(T_b),V_xs_2),V_a_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_concat_Osimps_I1_J,axiom, % 165.14/165.02 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 165.14/165.02 % 165.14/165.02 fof(fact_concat_Osimps_I2_J,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_concat__eq__Nil__conv,axiom, % 165.14/165.02 ! [V_xss_2,T_a] : % 165.14/165.02 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a) % 165.14/165.02 <=> ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 165.14/165.02 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Nil__eq__concat__conv,axiom, % 165.14/165.02 ! [V_xss_2,T_a] : % 165.14/165.02 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2) % 165.14/165.02 <=> ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 165.14/165.02 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_map__concat,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_a)),hAPP(c_List_Omap(T_b,T_a),V_f_2)),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_filter__concat,axiom, % 165.14/165.02 ! [V_xs_2,V_p_2,T_a] : hAPP(c_List_Ofilter(T_a,V_p_2),c_List_Oconcat(T_a,V_xs_2)) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Ofilter(T_a,V_p_2)),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev_Osimps_I2_J,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__eq__Cons__iff,axiom, % 165.14/165.02 ! [V_ys_2,V_y_2,V_xs_2,T_a] : % 165.14/165.02 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 165.14/165.02 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__concat,axiom, % 165.14/165.02 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oconcat(T_a,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xss_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_set__concat,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oconcat(T_a,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2)),c_List_Oset(T_a)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_last__rev,axiom, % 165.14/165.02 ! [T_a,V_xs] : % 165.14/165.02 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.02 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_hd__rev,axiom, % 165.14/165.02 ! [T_a,V_xs] : % 165.14/165.02 ( V_xs != c_List_Olist_ONil(T_a) % 165.14/165.02 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__transpose,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__take,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__drop,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rotate__rev,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose_Osimps_I3_J,axiom, % 165.14/165.02 ! [V_xss_2,V_xs_2,V_x_2,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__nth,axiom, % 165.14/165.02 ! [V_xs,T_a,V_n] : % 165.14/165.02 ( 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))) % 165.14/165.02 => 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))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_concat__eq__concat__iff,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,T_a] : % 165.14/165.02 ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) ) % 165.14/165.02 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2) % 165.14/165.02 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 165.14/165.02 <=> V_xs_2 = V_ys_2 ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_concat__injective,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,T_a] : % 165.14/165.02 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 165.14/165.02 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_ys_2) % 165.14/165.02 => ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_a),tc_Nat_Onat),tc_fun(tc_List_Olist(T_a),tc_HOL_Obool)),tc_List_Olist(T_a)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),B_x)) ) % 165.14/165.02 => V_xs_2 = V_ys_2 ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rev__update,axiom, % 165.14/165.02 ! [V_y,V_xs,T_a,V_k] : % 165.14/165.02 ( 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))) % 165.14/165.02 => 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) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_concat__map__singleton,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_b),c_List_Olist_OCons(T_a)),V_f_2)),c_List_Olist_ONil(T_a))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__rev__nth__mono,axiom, % 165.14/165.02 ! [V_j,V_i,V_xs,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 165.14/165.02 => ( 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))) % 165.14/165.02 => 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))) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_foldr__max__sorted,axiom, % 165.14/165.02 ! [V_y_2,V_xs_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2)) % 165.14/165.02 => ( ( V_xs_2 = c_List_Olist_ONil(T_a) % 165.14/165.02 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 ) % 165.14/165.02 & ( V_xs_2 != c_List_Olist_ONil(T_a) % 165.14/165.02 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose_Opsimps_I3_J,axiom, % 165.14/165.02 ! [V_xss_2,V_xs_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_a)),c_List_Otranspose__rel(T_a)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2))) % 165.14/165.02 => c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),hAPP(hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a),c_COMBK(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))))),V_xss_2)))),c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2))))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__transpose__sorted,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 165.14/165.02 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 165.14/165.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 165.14/165.02 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a)) % 165.14/165.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose__column__length,axiom, % 165.14/165.02 ! [V_i_2,V_xs_2,T_a] : % 165.14/165.02 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),V_xs_2))) % 165.14/165.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),c_List_Otranspose(T_a,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_i_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose__aux__filter__tail,axiom, % 165.14/165.02 ! [V_xss_2,T_a] : c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_a)),T_a,c_List_Olist_ONil(tc_List_Olist(T_a)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),T_a),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_List_Olist_OCons(tc_List_Olist(T_a))),c_List_Olist_ONil(tc_List_Olist(T_a)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Otl(T_a)),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a)))),V_xss_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_nth__nth__transpose__sorted,axiom, % 165.14/165.02 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 165.14/165.02 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2)))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),hAPP(c_List_Ofilter(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_xs_2)))) % 165.14/165.02 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),c_List_Otranspose(T_a,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_a)),V_xs_2),V_j_2)),V_i_2) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transpose__transpose,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))) % 165.14/165.02 => c_List_Otranspose(T_a,c_List_Otranspose(T_a,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_a))),V_xs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 165.14/165.02 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_zip__takeWhile__fst,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Ofst(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_zip__takeWhile__snd,axiom, % 165.14/165.02 ! [V_ys_2,V_P_2,V_xs_2,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_a,T_b),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_a,T_b),V_P_2),c_Product__Type_Osnd(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_set__takeWhileD,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile__eq__all__conv,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.02 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2 % 165.14/165.02 <=> ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__takeWhile__le,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile__eq__take,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_distinct__takeWhile,axiom, % 165.14/165.02 ! [V_P_2,V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.02 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile__tail,axiom, % 165.14/165.02 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] : % 165.14/165.02 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2))) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile_Osimps_I2_J,axiom, % 165.14/165.02 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 165.14/165.02 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) % 165.14/165.02 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_a) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__takeWhile,axiom, % 165.14/165.02 ! [V_P_2,V_xs_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile_Osimps_I1_J,axiom, % 165.14/165.02 ! [V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile__map,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OtakeWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_return__list__def,axiom, % 165.14/165.02 ! [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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile__append1,axiom, % 165.14/165.02 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_a,V_P_2,V_xs_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_nth__length__takeWhile,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile__nth,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) % 165.14/165.02 => hAPP(hAPP(c_List_Onth(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_j_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_map__upds__def,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,V_m_2,T_b,T_a] : c_Map_Omap__upds(T_a,T_b,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_a,T_b,V_m_2,hAPP(c_Map_Omap__of(T_a,T_b),hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile__not__last,axiom, % 165.14/165.02 ! [T_a,V_xs_2] : % 165.14/165.02 ( V_xs_2 != c_List_Olist_ONil(T_a) % 165.14/165.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.02 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),c_List_Olast(T_a,V_xs_2))),V_xs_2) = c_List_Obutlast(T_a,V_xs_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 165.14/165.02 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 165.14/165.02 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(T_a,tc_HOL_Obool,T_b),hAPP(c_Orderings_Oord__class_Oless(T_a),V_t_2)),V_f_2),V_xs_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transfer__nat__int__list__return__embed,axiom, % 165.14/165.02 ! [V_l] : % 165.14/165.02 ( c_List_Onat__list(V_l) % 165.14/165.02 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__remdups__concat,axiom, % 165.14/165.02 ! [V_xss_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,c_List_Oconcat(T_a,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2)),c_List_Oset(T_a))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_distinct__remdups,axiom, % 165.14/165.02 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__remdups__leq,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_remdups__map__remdups,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oremdups(T_b,V_xs_2))) = c_List_Oremdups(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_set__remdups,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_remdups_Osimps_I1_J,axiom, % 165.14/165.02 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 165.14/165.02 % 165.14/165.02 fof(fact_remdups__eq__nil__right__iff,axiom, % 165.14/165.02 ! [V_x_2,T_a] : % 165.14/165.02 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2) % 165.14/165.02 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_remdups__eq__nil__iff,axiom, % 165.14/165.02 ! [V_x_2,T_a] : % 165.14/165.02 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a) % 165.14/165.02 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__remdups,axiom, % 165.14/165.02 ! [V_l,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_distinct__remdups__id,axiom, % 165.14/165.02 ! [V_xs,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 165.14/165.02 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_remdups__id__iff__distinct,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2 % 165.14/165.02 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__remdups__eq,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) % 165.14/165.02 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_remdups__remdups,axiom, % 165.14/165.02 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 165.14/165.02 % 165.14/165.02 fof(fact_remdups__filter,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : c_List_Oremdups(T_a,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oremdups(T_a,V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_remove1__remdups,axiom, % 165.14/165.02 ! [V_x,V_xs,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 165.14/165.02 => 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)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_embed__list__def,axiom, % 165.14/165.02 ! [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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_remdups_Osimps_I2_J,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_Oremdups(T_a,V_xs_2) ) % 165.14/165.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => c_List_Oremdups(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Oremdups(T_a,V_xs_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__remdups__card__conv,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile__neq__rev,axiom, % 165.14/165.02 ! [V_x_2,V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Otl(T_a),c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_dropWhile__neq__rev,axiom, % 165.14/165.02 ! [V_x_2,V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => c_List_OdropWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_a),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_List_Orev(T_a),c_List_OtakeWhile(T_a,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_distinct__dropWhile,axiom, % 165.14/165.02 ! [V_P_2,V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.02 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_dropWhile_Osimps_I2_J,axiom, % 165.14/165.02 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 165.14/165.02 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = c_List_OdropWhile(T_a,V_P_2,V_xs_2) ) % 165.14/165.02 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__dropWhile,axiom, % 165.14/165.02 ! [V_P_2,V_xs_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_dropWhile_Osimps_I1_J,axiom, % 165.14/165.02 ! [V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 165.14/165.02 % 165.14/165.02 fof(fact_dropWhile__eq__Nil__conv,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.02 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a) % 165.14/165.02 <=> ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__dropWhile__le,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile__dropWhile__id,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)) = V_xs_2 ). % 165.14/165.02 % 165.14/165.02 fof(fact_hd__dropWhile,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.02 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a) % 165.14/165.02 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_dropWhile__map,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_b,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_OdropWhile(T_b,hAPP(c_Fun_Ocomp(T_a,tc_HOL_Obool,T_b,V_P_2),V_f_2),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_dropWhile__append1,axiom, % 165.14/165.02 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_ys_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_dropWhile__eq__Cons__conv,axiom, % 165.14/165.02 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] : % 165.14/165.02 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 165.14/165.02 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)) % 165.14/165.02 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_dropWhile__eq__drop,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : c_List_OdropWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_dropWhile__nth,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) % 165.14/165.02 => hAPP(hAPP(c_List_Onth(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_listsum__map__filter,axiom, % 165.14/165.02 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] : % 165.14/165.02 ( class_Groups_Omonoid__add(T_b) % 165.14/165.02 => ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => ( ~ hBOOL(hAPP(V_P_2,B_x)) % 165.14/165.02 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) % 165.14/165.02 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__nth__monoI,axiom, % 165.14/165.02 ! [V_xs,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( ! [B_i,B_j] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 165.14/165.02 => ( 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))) % 165.14/165.02 => 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))) ) ) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_n__lists_Osimps_I2_J,axiom, % 165.14/165.02 ! [V_xs_2,V_n_2,T_a] : c_Enum_On__lists(T_a,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_a),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(T_a)),c_List_Omap(T_a,tc_List_Olist(T_a))),hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olist_OCons(T_a)))),V_xs_2)),c_Enum_On__lists(T_a,V_n_2,V_xs_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__sublists,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_distinct__n__lists,axiom, % 165.14/165.02 ! [V_n,V_xs,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 165.14/165.02 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_distinct__set__sublists,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 165.14/165.02 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool)),c_List_Oset(T_a)),c_Enum_Osublists(T_a,V_xs_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__n__lists,axiom, % 165.14/165.02 ! [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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__n__lists__elem,axiom, % 165.14/165.02 ! [V_xs_2,V_n_2,V_ys_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)))) % 165.14/165.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sublists__powset,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_Osublists(T_a,V_xs_2))) = hAPP(c_Set_OPow(T_a),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sublists_Osimps_I1_J,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_n__lists__Nil,axiom, % 165.14/165.02 ! [T_a,V_n] : % 165.14/165.02 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.02 => 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))) ) % 165.14/165.02 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.02 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_n__lists_Osimps_I1_J,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sublists_Osimps_I2_J,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,T_a] : c_Enum_Osublists(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_a)),tc_fun(tc_List_Olist(tc_List_Olist(T_a)),tc_List_Olist(tc_List_Olist(T_a))),tc_List_Olist(tc_List_Olist(T_a))),c_List_Oappend(tc_List_Olist(T_a))),hAPP(c_List_Omap(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(c_List_Olist_OCons(T_a),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_a))))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_set__n__lists,axiom, % 165.14/165.02 ! [V_xs_2,V_n_2,T_a] : hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_a)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_a),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_a)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_a)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_a)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_a)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool))),c_List_Oset(T_a))),hAPP(c_List_Oset(T_a),V_xs_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_product_Osimps_I2_J,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,V_x_2,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_a,T_b)),hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__the__def,axiom, % 165.14/165.02 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_product_Osimps_I1_J,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_distinct__product,axiom, % 165.14/165.02 ! [V_ys,T_b,V_xs,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 165.14/165.02 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 165.14/165.02 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_product__list__set,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,T_b,T_a] : hAPP(c_List_Oset(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),hAPP(c_List_Oset(T_a),V_xs_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_List_Oset(T_b),V_ys_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_map__of__zip__enum__inject,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,T_a,T_b] : % 165.14/165.02 ( ( class_Enum_Oenum(T_b) % 165.14/165.02 & class_Enum_Oenum(T_a) ) % 165.14/165.02 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)) % 165.14/165.02 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Enum_Oenum__class_Oenum(T_b)) % 165.14/165.02 => ( hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_xs_2))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_a),T_a,T_b,c_Option_Othe(T_a)),hAPP(c_Map_Omap__of(T_b,T_a),hAPP(hAPP(c_List_Ozip(T_b,T_a),c_Enum_Oenum__class_Oenum(T_b)),V_ys_2))) % 165.14/165.02 => V_xs_2 = V_ys_2 ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sort__foldl__insort,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))),c_List_Olist_ONil(T_a)),V_xs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__prod__def,axiom, % 165.14/165.02 ! [T_b,T_a] : % 165.14/165.02 ( ( class_Enum_Oenum(T_a) % 165.14/165.02 & class_Enum_Oenum(T_b) ) % 165.14/165.02 => c_Enum_Oenum__class_Oenum(tc_prod(T_a,T_b)) = c_Enum_Oproduct(T_a,T_b,c_Enum_Oenum__class_Oenum(T_a),c_Enum_Oenum__class_Oenum(T_b)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__distinct,axiom, % 165.14/165.02 ! [T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__option__def,axiom, % 165.14/165.02 ! [T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => c_Enum_Oenum__class_Oenum(tc_Option_Ooption(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(T_a)),c_Option_Ooption_ONone(T_a)),hAPP(hAPP(c_List_Omap(T_a,tc_Option_Ooption(T_a)),c_Option_Ooption_OSome(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_distinct__sort,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_a,T_b] : % 165.14/165.02 ( class_Orderings_Olinorder(T_b) % 165.14/165.02 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))) % 165.14/165.02 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_filter__sort,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] : % 165.14/165.02 ( class_Orderings_Olinorder(T_b) % 165.14/165.02 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__sort,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_a,T_b] : % 165.14/165.02 ( class_Orderings_Olinorder(T_b) % 165.14/165.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__sort,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sort__key__simps_I1_J,axiom, % 165.14/165.02 ! [V_f_2,T_a,T_b] : % 165.14/165.02 ( class_Orderings_Olinorder(T_b) % 165.14/165.02 => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_set__sort,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_a,T_b] : % 165.14/165.02 ( class_Orderings_Olinorder(T_b) % 165.14/165.02 => hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_a),V_xs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__UNIV,axiom, % 165.14/165.02 ! [T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_UNIV__enum,axiom, % 165.14/165.02 ! [T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_in__enum,axiom, % 165.14/165.02 ! [V_x_2,T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__sort__key,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_b,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Olinorder__class_Osort__key(T_b,T_a,V_f_2,V_xs_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sort__key__simps_I2_J,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 165.14/165.02 ( class_Orderings_Olinorder(T_b) % 165.14/165.02 => c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__fun__code,axiom, % 165.14/165.02 ! [T_b,T_a] : % 165.14/165.02 ( ( class_Enum_Oenum(T_a) % 165.14/165.02 & class_HOL_Oequal(T_a) % 165.14/165.02 & class_Enum_Oenum(T_b) ) % 165.14/165.02 => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__fun__def,axiom, % 165.14/165.02 ! [T_b,T_a] : % 165.14/165.02 ( ( class_Enum_Oenum(T_a) % 165.14/165.02 & class_Enum_Oenum(T_b) ) % 165.14/165.02 => c_Enum_Oenum__class_Oenum(tc_fun(T_a,T_b)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_a,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),c_Enum_On__lists(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)),c_Enum_Oenum__class_Oenum(T_b))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => c_List_Olinorder__class_Osorted__list__of__set(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),c_List_Oremdups(T_a,V_xs_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_all__n__lists__def,axiom, % 165.14/165.02 ! [V_n_2,V_P_2,T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2) % 165.14/165.02 <=> ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a))))) % 165.14/165.02 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_ex__n__lists__def,axiom, % 165.14/165.02 ! [V_n_2,V_P_2,T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2) % 165.14/165.02 <=> ? [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n_2,c_Enum_Oenum__class_Oenum(T_a))))) % 165.14/165.02 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__all__fun__def,axiom, % 165.14/165.02 ! [V_P_2,T_a,T_b] : % 165.14/165.02 ( ( class_Enum_Oenum(T_b) % 165.14/165.02 & class_Enum_Oenum(T_a) ) % 165.14/165.02 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 165.14/165.02 <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__ex__fun__def,axiom, % 165.14/165.02 ! [V_P_2,T_a,T_b] : % 165.14/165.02 ( ( class_Enum_Oenum(T_b) % 165.14/165.02 & class_Enum_Oenum(T_a) ) % 165.14/165.02 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 165.14/165.02 <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__ex__option__def,axiom, % 165.14/165.02 ! [V_P_2,T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2)) % 165.14/165.02 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 165.14/165.02 | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a)))) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__all__option__def,axiom, % 165.14/165.02 ! [V_P_2,T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2)) % 165.14/165.02 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 165.14/165.02 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_Option_Ooption(T_a),tc_HOL_Obool,T_a),V_P_2),c_Option_Ooption_OSome(T_a)))) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__ex,axiom, % 165.14/165.02 ! [V_P_2,T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) % 165.14/165.02 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__all,axiom, % 165.14/165.02 ! [V_P_2,T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) % 165.14/165.02 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_exists__code,axiom, % 165.14/165.02 ! [V_P_2,T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 165.14/165.02 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_all__code,axiom, % 165.14/165.02 ! [V_P_2,T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 165.14/165.02 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__ex__prod__def,axiom, % 165.14/165.02 ! [V_P_2,T_a,T_b] : % 165.14/165.02 ( ( class_Enum_Oenum(T_b) % 165.14/165.02 & class_Enum_Oenum(T_a) ) % 165.14/165.02 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2)) % 165.14/165.02 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__ex(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__all__prod__def,axiom, % 165.14/165.02 ! [V_P_2,T_a,T_b] : % 165.14/165.02 ( ( class_Enum_Oenum(T_b) % 165.14/165.02 & class_Enum_Oenum(T_a) ) % 165.14/165.02 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2)) % 165.14/165.02 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_Enum_Oenum__class_Oenum__all(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_HOL_Obool,T_b),V_P_2)),c_Product__Type_OPair(T_a,T_b))))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_order__fun_I1_J,axiom, % 165.14/165.02 ! [V_g_2,V_f_2,T_a,T_b] : % 165.14/165.02 ( ( class_Orderings_Oorder(T_b) % 165.14/165.02 & class_Enum_Oenum(T_a) ) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 165.14/165.02 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Oord__class_Oless__eq(T_b)),V_f_2)),V_g_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_order__fun_I2_J,axiom, % 165.14/165.02 ! [V_g_2,V_f_2,T_a,T_b] : % 165.14/165.02 ( ( class_Orderings_Oorder(T_b) % 165.14/165.02 & class_Enum_Oenum(T_a) ) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 165.14/165.02 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 165.14/165.02 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),hAPP(hAPP(c_COMBS(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_a),c_fequal),V_f_2)),V_g_2)))) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__ex__fun__code,axiom, % 165.14/165.02 ! [V_P_2,T_a,T_b] : % 165.14/165.02 ( ( class_Enum_Oenum(T_b) % 165.14/165.02 & class_Enum_Oenum(T_a) % 165.14/165.02 & class_HOL_Oequal(T_a) ) % 165.14/165.02 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 165.14/165.02 <=> c_Enum_Oex__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_enum__all__fun__code,axiom, % 165.14/165.02 ! [V_P_2,T_a,T_b] : % 165.14/165.02 ( ( class_Enum_Oenum(T_b) % 165.14/165.02 & class_Enum_Oenum(T_a) % 165.14/165.02 & class_HOL_Oequal(T_a) ) % 165.14/165.02 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 165.14/165.02 <=> c_Enum_Oall__n__lists(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_a,T_b),tc_HOL_Obool,tc_List_Olist(T_b)),V_P_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_Option_Ooption(T_b)),tc_fun(T_a,T_b),tc_List_Olist(T_b)),c_Fun_Ocomp(tc_Option_Ooption(T_b),T_b,T_a,c_Option_Othe(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(T_a,T_b)),tc_fun(T_a,tc_Option_Ooption(T_b)),tc_List_Olist(T_b)),c_Map_Omap__of(T_a,T_b)),hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a))))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_image__INT,axiom, % 165.14/165.02 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] : % 165.14/165.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 165.14/165.02 => ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) ) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2)) % 165.14/165.02 => hAPP(c_Set_Oimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Oimage(T_a,T_b,V_f_2)),V_B_2)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_map__of__zip__enum__is__Some,axiom, % 165.14/165.02 ! [V_x,V_ys,T_b,T_a] : % 165.14/165.02 ( class_Enum_Oenum(T_a) % 165.14/165.02 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_Enum_Oenum__class_Oenum(T_a)) % 165.14/165.02 => ? [B_y] : hAPP(hAPP(c_Map_Omap__of(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),c_Enum_Oenum__class_Oenum(T_a)),V_ys)),V_x) = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile__eq__filter,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.02 ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) % 165.14/165.02 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 165.14/165.02 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_inj__on__mapI,axiom, % 165.14/165.02 ! [V_A_2,V_f_2,T_b,T_a] : % 165.14/165.02 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_a),tc_fun(T_a,tc_HOL_Obool),c_List_Oset(T_a)),V_A_2))) % 165.14/165.02 => c_Fun_Oinj__on(tc_List_Olist(T_a),tc_List_Olist(T_b),hAPP(c_List_Omap(T_a,T_b),V_f_2),V_A_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_UnionI,axiom, % 165.14/165.02 ! [V_A_2,V_C_2,V_X_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_image__Union,axiom, % 165.14/165.02 ! [V_S_2,V_f_2,T_a,T_b] : hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_b,T_a,V_f_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_UNION__eq__Union__image,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Union__image__eq,axiom, % 165.14/165.02 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Field__Union,axiom, % 165.14/165.02 ! [V_R_2,T_a] : hAPP(c_Relation_OField(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),c_Relation_OField(T_a)),V_R_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_INT__simps_I8_J,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_INT__extend__simps_I8_J,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Union__disjoint,axiom, % 165.14/165.02 ! [V_A_2,V_C_2,T_a] : % 165.14/165.02 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.02 <=> ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2)) % 165.14/165.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_subset__Pow__Union,axiom, % 165.14/165.02 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Sup__le__iff,axiom, % 165.14/165.02 ! [V_b_2,V_A_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)),V_b_2)) % 165.14/165.02 <=> ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Union__upper,axiom, % 165.14/165.02 ! [V_A_2,V_B_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Union__empty,axiom, % 165.14/165.02 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_less__Sup__iff,axiom, % 165.14/165.02 ! [V_S_2,V_a_2,T_a] : % 165.14/165.02 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 & class_Orderings_Olinorder(T_a) ) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))) % 165.14/165.02 <=> ? [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 165.14/165.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Union__Pow__eq,axiom, % 165.14/165.02 ! [V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_OPow(T_a),V_A_2)) = V_A_2 ). % 165.14/165.02 % 165.14/165.02 fof(fact_Union__mono,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Union__quotient,axiom, % 165.14/165.02 ! [V_r_2,V_A_2,T_a] : % 165.14/165.02 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.02 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_a),V_A_2),V_r_2)) = V_A_2 ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Union__insert,axiom, % 165.14/165.02 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_finite__UnionD,axiom, % 165.14/165.02 ! [V_A_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) % 165.14/165.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Union__Un__distrib,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Union__UNIV,axiom, % 165.14/165.02 ! [T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Sigma__Union,axiom, % 165.14/165.02 ! [V_B_2,V_X_2,T_b,T_a] : hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Product__Type_OSigma(T_a,T_b)),V_B_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_vimage__Union,axiom, % 165.14/165.02 ! [V_A_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_a,T_b,V_f_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_UN__extend__simps_I8_J,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_UN__simps_I8_J,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool)),tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool))),V_B_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Union__def,axiom, % 165.14/165.02 ! [V_S_2,T_a] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Int__Union2,axiom, % 165.14/165.02 ! [V_A_2,V_B_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Int__Union,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Sup__upper,axiom, % 165.14/165.02 ! [V_A_2,V_x_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Sup__empty,axiom, % 165.14/165.02 ! [T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Sup__singleton,axiom, % 165.14/165.02 ! [V_a_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Sup__insert,axiom, % 165.14/165.02 ! [V_A_2,V_a_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Sup__UNIV,axiom, % 165.14/165.02 ! [T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Un__eq__Union,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Un__Union__image,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Union__Int__subset,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Sup__binary,axiom, % 165.14/165.02 ! [V_b_2,V_a_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Sup__fin__Sup,axiom, % 165.14/165.02 ! [V_A_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.02 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Sup__set__fold,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_xs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_finite__Union,axiom, % 165.14/165.02 ! [V_A_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) % 165.14/165.02 => ( ! [B_M] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2)) % 165.14/165.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) ) % 165.14/165.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_insert__partition,axiom, % 165.14/165.02 ! [V_F_2,V_x_2,T_a] : % 165.14/165.02 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)) % 165.14/165.02 => ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))) % 165.14/165.02 => ! [B_xa] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2))) % 165.14/165.02 => ( B_x != B_xa % 165.14/165.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) % 165.14/165.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile__eq__take__P__nth,axiom, % 165.14/165.02 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 165.14/165.02 ( ! [B_i] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) % 165.14/165.02 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) % 165.14/165.02 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_length__takeWhile__less__P__nth,axiom, % 165.14/165.02 ! [V_xs_2,T_a,V_P_2,V_j_2] : % 165.14/165.02 ( ! [B_i] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 165.14/165.02 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Sup__Inf,axiom, % 165.14/165.02 ! [V_A_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_a)))))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inf__Sup,axiom, % 165.14/165.02 ! [V_A_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fimplies),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_a))))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_finite__Inter,axiom, % 165.14/165.02 ! [V_M_2,T_a] : % 165.14/165.02 ( ? [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2)) % 165.14/165.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) ) % 165.14/165.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_InterE,axiom, % 165.14/165.02 ! [V_X_2,V_C_2,V_A_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_InterD,axiom, % 165.14/165.02 ! [V_X_2,V_C_2,V_A_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inter__eq,axiom, % 165.14/165.02 ! [V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OAll(tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),T_a),hAPP(c_COMBS(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_a,tc_HOL_Obool))),V_A_2)))),c_member(T_a)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inter__insert,axiom, % 165.14/165.02 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inter__anti__mono,axiom, % 165.14/165.02 ! [V_A_2,V_B_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inter__empty,axiom, % 165.14/165.02 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inf__less__iff,axiom, % 165.14/165.02 ! [V_a_2,V_S_2,T_a] : % 165.14/165.02 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 & class_Orderings_Olinorder(T_a) ) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2)) % 165.14/165.02 <=> ? [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 165.14/165.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inter__lower,axiom, % 165.14/165.02 ! [V_A_2,V_B_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_le__Inf__iff,axiom, % 165.14/165.02 ! [V_A_2,V_b_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2))) % 165.14/165.02 <=> ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inter__UNIV,axiom, % 165.14/165.02 ! [T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inter__def,axiom, % 165.14/165.02 ! [V_S_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_a,tc_HOL_Obool))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inf__lower,axiom, % 165.14/165.02 ! [V_A_2,V_x_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)),V_x_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inter__Un__distrib,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inf__singleton,axiom, % 165.14/165.02 ! [V_a_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inf__empty,axiom, % 165.14/165.02 ! [T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_a) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inf__UNIV,axiom, % 165.14/165.02 ! [T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_a) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inf__insert,axiom, % 165.14/165.02 ! [V_A_2,V_a_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_INTER__eq__Inter__image,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inter__image__eq,axiom, % 165.14/165.02 ! [V_A_2,V_B_2,T_b,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Un__Inter,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Int__eq__Inter,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Int__Inter__image,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inter__Un__subset,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inf__binary,axiom, % 165.14/165.02 ! [V_b_2,V_a_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inf__fin__Inf,axiom, % 165.14/165.02 ! [V_A_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.02 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inf__set__fold,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.02 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_xs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__def,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 165.14/165.02 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 165.14/165.02 & ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted_Osimps,axiom, % 165.14/165.02 ! [V_a_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2) % 165.14/165.02 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 165.14/165.02 | ? [B_xs,B_x] : % 165.14/165.02 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 165.14/165.02 & ! [B_xa] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) % 165.14/165.02 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__Cons,axiom, % 165.14/165.02 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) % 165.14/165.02 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 165.14/165.02 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__map2,axiom, % 165.14/165.02 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_bs_2)) % 165.14/165.02 <=> c_List_Olist__all2(T_a,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBB(T_b,tc_HOL_Obool,T_c)),V_P_2)),V_f_2),V_as_2,V_bs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__map1,axiom, % 165.14/165.02 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_a),V_f_2),V_as_2),V_bs_2) % 165.14/165.02 <=> c_List_Olist__all2(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,tc_HOL_Obool),T_c),V_P_2),V_f_2),V_as_2,V_bs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__eq,axiom, % 165.14/165.02 ! [T_a,V_ys_2,V_xs_2] : % 165.14/165.02 ( V_xs_2 = V_ys_2 % 165.14/165.02 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__lengthD,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 165.14/165.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__dropI,axiom, % 165.14/165.02 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2) % 165.14/165.02 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_bs_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__takeI,axiom, % 165.14/165.02 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 165.14/165.02 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_ys_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__Nil2,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b)) % 165.14/165.02 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__Nil,axiom, % 165.14/165.02 ! [V_ys_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2) % 165.14/165.02 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__rev1,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2) % 165.14/165.02 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__rev,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),hAPP(c_List_Orev(T_b),V_ys_2)) % 165.14/165.02 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__append,axiom, % 165.14/165.02 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 165.14/165.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 165.14/165.02 => ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2)) % 165.14/165.02 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 165.14/165.02 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__appendI,axiom, % 165.14/165.02 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) % 165.14/165.02 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_ca_2,V_d_2) % 165.14/165.02 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_b),V_b_2),V_d_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__nthD2,axiom, % 165.14/165.02 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__nthD,axiom, % 165.14/165.02 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),V_p_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__conv__all__nth,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 165.14/165.02 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) % 165.14/165.02 & ! [B_i] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i))) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__update__cong,axiom, % 165.14/165.02 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 165.14/165.02 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__update__cong2,axiom, % 165.14/165.02 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 165.14/165.02 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))) % 165.14/165.02 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_b,V_ys_2),V_i_2),V_y_2)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2I,axiom, % 165.14/165.02 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.02 ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_a_2),V_b_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) % 165.14/165.02 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2) % 165.14/165.02 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_SigmaE,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,V_ca_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 165.14/165.02 => ~ ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.02 => ! [B_y] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x))) % 165.14/165.02 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_card__partition,axiom, % 165.14/165.02 ! [V_k_2,V_C_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) % 165.14/165.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 165.14/165.02 => ( ! [B_c] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2)) % 165.14/165.02 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 ) % 165.14/165.02 => ( ! [B_c1] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2)) % 165.14/165.02 => ! [B_c2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2)) % 165.14/165.02 => ( B_c1 != B_c2 % 165.14/165.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) % 165.14/165.02 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_List_Oinsert__def,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.02 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) % 165.14/165.02 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_distinct__insert,axiom, % 165.14/165.02 ! [V_x,V_xs,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 165.14/165.02 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_insert__remdups,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_in__set__insert,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_List_Oset__insert,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oinsert(T_a,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_insert__Nil,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_not__in__set__insert,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_maps__def,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) = c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_concat__map__maps,axiom, % 165.14/165.02 ! [V_xs_2,V_f_2,T_b,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Omap(T_b,tc_List_Olist(T_a)),V_f_2),V_xs_2)) = c_List_Omaps(T_b,T_a,V_f_2,V_xs_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_maps__simps_I2_J,axiom, % 165.14/165.02 ! [V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_a) ). % 165.14/165.02 % 165.14/165.02 fof(fact_maps__simps_I1_J,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : c_List_Omaps(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_b,T_a,V_f_2,V_xs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_distinct__concat,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2)) % 165.14/165.02 => ( ! [B_ys] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) ) % 165.14/165.02 => ( ! [B_ys] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => ! [B_zs] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => ( B_ys != B_zs % 165.14/165.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_List_Oset(T_a),B_ys)),hAPP(c_List_Oset(T_a),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) % 165.14/165.02 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_code__numeral_Osimps_I5_J,axiom, % 165.14/165.02 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_code__numeral_Osimps_I4_J,axiom, % 165.14/165.02 ! [V_f2_2,V_f1_2,T_a] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ). % 165.14/165.02 % 165.14/165.02 fof(fact_accp__acc__eq,axiom, % 165.14/165.02 ! [V_x_2,V_r_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),V_x_2)) % 165.14/165.02 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_measures__lesseq,axiom, % 165.14/165.02 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 165.14/165.02 ( 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))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Cons__acc__listrel1I,axiom, % 165.14/165.02 ! [V_xs_2,V_r_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_acc__subset,axiom, % 165.14/165.02 ! [V_R2_2,V_R1_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R1_2),V_R2_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Oacc(T_a,V_R2_2)),c_Wellfounded_Oacc(T_a,V_R1_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_lists__accI,axiom, % 165.14/165.02 ! [V_r_2,V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_lists__accD,axiom, % 165.14/165.02 ! [V_r_2,V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,c_Wellfounded_Oacc(T_a,V_r_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_acc__downward,axiom, % 165.14/165.02 ! [V_a_2,V_r_2,V_b_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_acc_Osimps,axiom, % 165.14/165.02 ! [V_r_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 165.14/165.02 <=> ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_a_2)),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_in__measures_I1_J,axiom, % 165.14/165.02 ! [V_y_2,V_x_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,c_List_Olist_ONil(tc_fun(T_a,tc_Nat_Onat))))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_measures__def,axiom, % 165.14/165.02 ! [V_fs_2,T_a] : c_List_Omeasures(T_a,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_a),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_a,tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_a,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_a),c_List_Omap(tc_fun(T_a,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_a,tc_Nat_Onat),T_a,tc_Nat_Onat),c_COMBI(tc_fun(T_a,tc_Nat_Onat))))),V_fs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_in__measures_I2_J,axiom, % 165.14/165.02 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) % 165.14/165.02 <=> ( 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))) % 165.14/165.02 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 165.14/165.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,V_fs_2))) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_measures__less,axiom, % 165.14/165.02 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 165.14/165.02 ( 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))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_List_Omeasures(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_a,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rel__comp__def,axiom, % 165.14/165.02 ! [V_s_2,V_r_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_a),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_a),c_COMBC(T_c,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_a,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_c),tc_fun(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_a,T_c)))),c_Product__Type_OPair(T_a,T_c)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_s_2))))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_max__extp_Oequations,axiom, % 165.14/165.02 ! [V_a2_2,V_a1_2,V_R_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) % 165.14/165.02 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 165.14/165.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 165.14/165.02 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.02 & ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 165.14/165.02 => ? [B_xa] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 165.14/165.02 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rel__compI,axiom, % 165.14/165.02 ! [V_s_2,V_ca_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_b_2),V_ca_2)),V_s_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_a_2),V_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rel__comp__UNION__distrib2,axiom, % 165.14/165.02 ! [V_s_2,V_r_2,V_I_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),T_d),c_Relation_Orel__comp(T_a,T_c,T_b)),V_r_2)),V_s_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rel__comp__UNION__distrib,axiom, % 165.14/165.02 ! [V_r_2,V_I_2,T_d,V_s_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_d),hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_s_2)),V_r_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rel__comp__mono,axiom, % 165.14/165.02 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_H_2),V_s_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rel__comp__empty1,axiom, % 165.14/165.02 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rel__comp__empty2,axiom, % 165.14/165.02 ! [V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rel__comp__distrib2,axiom, % 165.14/165.02 ! [V_R_2,V_T_2,V_S_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_T_2),V_R_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rel__comp__distrib,axiom, % 165.14/165.02 ! [V_T_2,V_S_2,V_R_2,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_R_2),V_T_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_O__assoc,axiom, % 165.14/165.02 ! [V_T_2,V_S_2,V_R_2,T_d,T_b,T_c,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_c),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_d,T_b),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_d,T_c,T_b),V_S_2),V_T_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_union__comp__emptyL,axiom, % 165.14/165.02 ! [V_B_2,V_C_2,V_A_2,T_a] : % 165.14/165.02 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 165.14/165.02 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 165.14/165.02 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_union__comp__emptyR,axiom, % 165.14/165.02 ! [V_C_2,V_B_2,V_A_2,T_a] : % 165.14/165.02 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 165.14/165.02 => ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 165.14/165.02 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rel__comp__subset__Sigma,axiom, % 165.14/165.02 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2)))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_a),V_C_2)))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_max__ext__compat,axiom, % 165.14/165.02 ! [V_S_2,V_R_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_min__ext__compat,axiom, % 165.14/165.02 ! [V_S_2,V_R_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_a,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_a,V_R_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_pred__comp__rel__comp__eq,axiom, % 165.14/165.02 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_s_2)),V_x_2),V_y_2)) % 165.14/165.02 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_reduction__pairI,axiom, % 165.14/165.02 ! [V_S_2,V_R_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_R_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 165.14/165.02 => c_FunDef_Oreduction__pair(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__less__than,axiom, % 165.14/165.02 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 165.14/165.02 % 165.14/165.02 fof(fact_pred__comp_Ointros,axiom, % 165.14/165.02 ! [T_c,T_b,T_a,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2),V_a_2),V_ca_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__empty,axiom, % 165.14/165.02 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__inv__image,axiom, % 165.14/165.02 ! [V_f_2,T_b,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__lex,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__lex__prod,axiom, % 165.14/165.02 ! [V_rb_2,T_b,V_ra_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_ra_2) % 165.14/165.02 => ( c_Wellfounded_Owf(T_b,V_rb_2) % 165.14/165.02 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__lenlex,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__measure,axiom, % 165.14/165.02 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_acc__wfD,axiom, % 165.14/165.02 ! [V_x_2,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__acc__iff,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__no__loop,axiom, % 165.14/165.02 ! [V_R_2,T_a] : % 165.14/165.02 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 165.14/165.02 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__union__merge,axiom, % 165.14/165.02 ! [V_S_2,V_R_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) % 165.14/165.02 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_S_2),V_R_2))),V_S_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__comp__self,axiom, % 165.14/165.02 ! [V_R_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_R_2) % 165.14/165.02 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__lexn,axiom, % 165.14/165.02 ! [V_n_2,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_max__ext__wf,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__pair__less,axiom, % 165.14/165.02 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__mlex,axiom, % 165.14/165.02 ! [V_f_2,V_R_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_R_2) % 165.14/165.02 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_pred__comp_Oequations,axiom, % 165.14/165.02 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2),V_a1_2),V_a3_2)) % 165.14/165.02 <=> ? [B_b] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 165.14/165.02 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__finite__psubset,axiom, % 165.14/165.02 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_min__ext__wf,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__int__ge__less__than2,axiom, % 165.14/165.02 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__int__ge__less__than,axiom, % 165.14/165.02 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__irrefl,axiom, % 165.14/165.02 ! [V_a_2,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__asym,axiom, % 165.14/165.02 ! [V_x_2,V_a_2,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2)) % 165.14/165.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__not__sym,axiom, % 165.14/165.02 ! [V_x_2,V_a_2,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_x_2)),V_r_2)) % 165.14/165.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_a_2)),V_r_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__not__refl,axiom, % 165.14/165.02 ! [V_a_2,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__subset,axiom, % 165.14/165.02 ! [V_p_2,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_p_2),V_r_2)) % 165.14/165.02 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__less,axiom, % 165.14/165.02 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)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__Int2,axiom, % 165.14/165.02 ! [V_r_H_2,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__Int1,axiom, % 165.14/165.02 ! [V_r_H_2,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__measures,axiom, % 165.14/165.02 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 <=> ~ ? [B_f] : % 165.14/165.02 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wfE__pf,axiom, % 165.14/165.02 ! [V_A_2,V_R_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_R_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),V_A_2))) % 165.14/165.02 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__union__compatible,axiom, % 165.14/165.02 ! [V_S_2,V_R_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_R_2) % 165.14/165.02 => ( c_Wellfounded_Owf(T_a,V_S_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_S_2)),V_R_2)) % 165.14/165.02 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf,axiom, % 165.14/165.02 ! [T_a] : % 165.14/165.02 ( class_Orderings_Owellorder(T_a) % 165.14/165.02 => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_a)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_reduction__pair__def,axiom, % 165.14/165.02 ! [V_P_2,T_a] : % 165.14/165.02 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 165.14/165.02 <=> ( c_Wellfounded_Owf(T_a,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)) % 165.14/165.02 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_reduction__pair__lemma,axiom, % 165.14/165.02 ! [V_S_2,V_R_2,V_P_2,T_a] : % 165.14/165.02 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2))) % 165.14/165.02 => ( c_Wellfounded_Owf(T_a,V_S_2) % 165.14/165.02 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__map__pair__image,axiom, % 165.14/165.02 ! [V_f_2,T_b,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 165.14/165.02 => c_Wellfounded_Owf(T_b,hAPP(c_Set_Oimage(tc_prod(T_a,T_a),tc_prod(T_b,T_b),c_Product__Type_Omap__pair(T_a,T_b,T_a,T_b,V_f_2,V_f_2)),V_r_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__if__measure,axiom, % 165.14/165.02 ! [T_a,V_g_2,V_f_2,V_P_2] : % 165.14/165.02 ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(V_P_2,B_x)) % 165.14/165.02 => 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))) ) % 165.14/165.02 => c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,T_a),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(T_a,tc_HOL_Obool,T_a)),c_fequal)),V_g_2))))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_max__ext_Ointros,axiom, % 165.14/165.02 ! [V_R_2,V_Y_2,V_X_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) % 165.14/165.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2)) % 165.14/165.02 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.02 => ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) % 165.14/165.02 => ? [B_xa] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) % 165.14/165.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) ) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_pred__nat__def,axiom, % 165.14/165.02 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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__same__fst,axiom, % 165.14/165.02 ! [T_a,V_R_2,T_b,V_P_2] : % 165.14/165.02 ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(V_P_2,B_x)) % 165.14/165.02 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) ) % 165.14/165.02 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__pred__nat,axiom, % 165.14/165.02 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Nitpick_Ozero__frac__def,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_inj__on__Inter,axiom, % 165.14/165.02 ! [V_f_2,T_b,T_a,V_S_2] : % 165.14/165.02 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 165.14/165.02 => ( ! [B_A] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2)) % 165.14/165.02 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) ) % 165.14/165.02 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_S_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Nitpick_Oone__frac__def,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Nitpick_Ofrac__def,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Range__Collect__split,axiom, % 165.14/165.02 ! [V_P_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Set_OCollect(tc_prod(T_b,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_a,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),hAPP(c_COMBC(T_b,T_a,tc_HOL_Obool),V_P_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_RangeI,axiom, % 165.14/165.02 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Range__Un__eq,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Range__empty__iff,axiom, % 165.14/165.02 ! [V_r_2,T_a,T_b] : % 165.14/165.02 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.02 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Range__empty,axiom, % 165.14/165.02 ! [T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Range__Union,axiom, % 165.14/165.02 ! [V_S_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_b,T_a)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_finite__Range,axiom, % 165.14/165.02 ! [V_r_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Range__Id__on,axiom, % 165.14/165.02 ! [V_A_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2 ). % 165.14/165.02 % 165.14/165.02 fof(fact_snd__eq__Range,axiom, % 165.14/165.02 ! [V_R_2,T_a,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_a),T_a,c_Product__Type_Osnd(T_b,T_a)),V_R_2) = hAPP(c_Relation_ORange(T_b,T_a),V_R_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Range__iff,axiom, % 165.14/165.02 ! [V_r_2,T_b,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 165.14/165.02 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_y),V_a_2)),V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Range__insert,axiom, % 165.14/165.02 ! [V_r_2,V_b_2,V_a_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Range__Int__subset,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Range__Diff__subset,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_b,T_a),V_A_2)),hAPP(c_Relation_ORange(T_b,T_a),V_B_2))),hAPP(c_Relation_ORange(T_b,T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_RangeP__Range__eq,axiom, % 165.14/165.02 ! [V_x_2,V_r_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2)) % 165.14/165.02 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_RangeE,axiom, % 165.14/165.02 ! [V_r_2,T_b,V_b_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 165.14/165.02 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),V_b_2)),V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_RangeP_Ointros,axiom, % 165.14/165.02 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 165.14/165.02 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_RangeP_Oequations,axiom, % 165.14/165.02 ! [V_a2_2,V_r_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2)) % 165.14/165.02 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__Un,axiom, % 165.14/165.02 ! [V_s_2,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => ( c_Wellfounded_Owf(T_a,V_s_2) % 165.14/165.02 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.02 => c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Inter__subset,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_a] : % 165.14/165.02 ( ! [B_X] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) ) % 165.14/165.02 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_DomainI,axiom, % 165.14/165.02 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Domain__Un__eq,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Domain__mono,axiom, % 165.14/165.02 ! [V_s_2,V_r_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_s_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Domain__empty__iff,axiom, % 165.14/165.02 ! [V_r_2,T_b,T_a] : % 165.14/165.02 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.02 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Domain__empty,axiom, % 165.14/165.02 ! [T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_finite__Domain,axiom, % 165.14/165.02 ! [V_r_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Domain__Id__on,axiom, % 165.14/165.02 ! [V_A_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = V_A_2 ). % 165.14/165.02 % 165.14/165.02 fof(fact_fst__eq__Domain,axiom, % 165.14/165.02 ! [V_R_2,T_b,T_a] : hAPP(c_Set_Oimage(tc_prod(T_a,T_b),T_a,c_Product__Type_Ofst(T_a,T_b)),V_R_2) = hAPP(c_Relation_ODomain(T_a,T_b),V_R_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Domain__iff,axiom, % 165.14/165.02 ! [V_r_2,T_b,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 165.14/165.02 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Domain__insert,axiom, % 165.14/165.02 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Domain__Int__subset,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Domain__Diff__subset,axiom, % 165.14/165.02 ! [V_B_2,V_A_2,T_b,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_b),V_A_2)),hAPP(c_Relation_ODomain(T_a,T_b),V_B_2))),hAPP(c_Relation_ODomain(T_a,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Field__def,axiom, % 165.14/165.02 ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_a,T_a),V_r_2)),hAPP(c_Relation_ORange(T_a,T_a),V_r_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Domain__Union,axiom, % 165.14/165.02 ! [V_S_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_a,T_b)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Domain__Collect__split,axiom, % 165.14/165.02 ! [V_P_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_a),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_a),c_HOL_OEx(T_b)),V_P_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_DomainP__Domain__eq,axiom, % 165.14/165.02 ! [V_x_2,V_r_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2)) % 165.14/165.02 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_DomainE,axiom, % 165.14/165.02 ! [V_r_2,T_b,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 165.14/165.02 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),B_y)),V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_DomainP_Ointros,axiom, % 165.14/165.02 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 165.14/165.02 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_DomainP_Oequations,axiom, % 165.14/165.02 ! [V_a1_2,V_r_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2)) % 165.14/165.02 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_foldl__apply,axiom, % 165.14/165.02 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] : % 165.14/165.02 ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => hAPP(c_Fun_Ocomp(T_c,T_c,T_b,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_h_2),hAPP(V_g_2,B_x)) ) % 165.14/165.02 => hAPP(c_List_Ofoldl(T_c,T_a,hAPP(c_COMBC(T_a,T_c,T_c),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_g_2),V_s_2),V_xs_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wfP__def,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_OwfP(T_a,V_r_2) % 165.14/165.02 <=> c_Wellfounded_Owf(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wfP__empty,axiom, % 165.14/165.02 ! [T_a] : c_Wellfounded_OwfP(T_a,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBK(tc_HOL_Obool,T_a),c_fFalse))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wfP__subset,axiom, % 165.14/165.02 ! [V_p_2,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_OwfP(T_a,V_r_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),V_p_2),V_r_2)) % 165.14/165.02 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wfP__accp__iff,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_OwfP(T_a,V_r_2) % 165.14/165.02 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_accp__wfPD,axiom, % 165.14/165.02 ! [V_x_2,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_OwfP(T_a,V_r_2) % 165.14/165.02 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__in__rel,axiom, % 165.14/165.02 ! [V_R_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_R_2) % 165.14/165.02 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wfP__wf__eq,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_OwfP(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)) % 165.14/165.02 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wfP__acyclicP,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_OwfP(T_a,V_r_2) % 165.14/165.02 => c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Rep__Integ__induct,axiom, % 165.14/165.02 ! [V_P_2,V_y_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 165.14/165.02 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x))) % 165.14/165.02 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__acyclic,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_acyclic__subset,axiom, % 165.14/165.02 ! [V_r_2,V_s_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Oacyclic(T_a,V_s_2) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 165.14/165.02 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_finite__acyclic__wf,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 165.14/165.02 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 165.14/165.02 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__iff__acyclic__if__finite,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 165.14/165.02 => ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Nitpick_Owf_H__def,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Nitpick_Owf_H(T_a,V_r_2) % 165.14/165.02 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 165.14/165.02 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 165.14/165.02 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Rep__Integ__cases,axiom, % 165.14/165.02 ! [V_y_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 165.14/165.02 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_inj__on__INTER,axiom, % 165.14/165.02 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] : % 165.14/165.02 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.02 => ( ! [B_i] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2)) % 165.14/165.02 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) ) % 165.14/165.02 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_zip__obtain__same__length,axiom, % 165.14/165.02 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 165.14/165.02 ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2)) % 165.14/165.02 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2))),V_ys_2)))) ) % 165.14/165.02 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_map__of__eqI,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,T_b,T_a] : % 165.14/165.02 ( hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)) = hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_ys_2)) % 165.14/165.02 => ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(T_a,T_b),T_a),c_Product__Type_Ofst(T_a,T_b)),V_xs_2)))) % 165.14/165.02 => hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2),B_x) = hAPP(hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2),B_x) ) % 165.14/165.02 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Abs__Integ__induct,axiom, % 165.14/165.02 ! [V_x_2,V_P_2] : % 165.14/165.02 ( ! [B_y] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 165.14/165.02 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 165.14/165.02 => hBOOL(hAPP(V_P_2,V_x_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Abs__Integ__cases,axiom, % 165.14/165.02 ! [V_x_2] : % 165.14/165.02 ~ ! [B_y] : % 165.14/165.02 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 165.14/165.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wfP__SUP,axiom, % 165.14/165.02 ! [T_a,V_r_2,T_b] : % 165.14/165.02 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i)) % 165.14/165.02 => ( ! [B_i,B_j] : % 165.14/165.02 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 165.14/165.02 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Predicate_ODomainP(T_b,T_b,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_b,T_b,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 165.14/165.02 => c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))),V_r_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_dropWhile__append2,axiom, % 165.14/165.02 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 165.14/165.02 ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(V_P_2,B_x)) ) % 165.14/165.02 => c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_a,V_P_2,V_ys_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__all2__all__nthI,axiom, % 165.14/165.02 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] : % 165.14/165.02 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_b_2) % 165.14/165.02 => ( ! [B_n] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_a_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_b_2),B_n))) ) % 165.14/165.02 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_mem__splitI2,axiom, % 165.14/165.02 ! [V_ca_2,V_z_2,T_c,T_b,T_a,V_p_2] : % 165.14/165.02 ( ! [B_a,B_b] : % 165.14/165.02 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) ) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_ca_2),V_p_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_mem__splitE,axiom, % 165.14/165.02 ! [V_p_2,V_ca_2,T_c,T_b,V_z_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_ca_2),V_p_2))) % 165.14/165.02 => ~ ! [B_x,B_y] : % 165.14/165.02 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) % 165.14/165.02 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_finite__sorted__distinct__unique,axiom, % 165.14/165.02 ! [V_A_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.02 => ? [B_x] : % 165.14/165.02 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2 % 165.14/165.02 & c_List_Olinorder__class_Osorted(T_a,B_x) % 165.14/165.02 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x)) % 165.14/165.02 & ! [B_y] : % 165.14/165.02 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2 % 165.14/165.02 & c_List_Olinorder__class_Osorted(T_a,B_y) % 165.14/165.02 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) ) % 165.14/165.02 => B_y = B_x ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_takeWhile__append2,axiom, % 165.14/165.02 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 165.14/165.02 ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(V_P_2,B_x)) ) % 165.14/165.02 => c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),c_List_OtakeWhile(T_a,V_P_2,V_ys_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_insort__is__Cons,axiom, % 165.14/165.02 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] : % 165.14/165.02 ( class_Orderings_Olinorder(T_b) % 165.14/165.02 => ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 165.14/165.02 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_2),V_xs_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wfI__pf,axiom, % 165.14/165.02 ! [V_R_2,T_a] : % 165.14/165.02 ( ! [B_A] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_a,T_a,V_R_2),B_A))) % 165.14/165.02 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 165.14/165.02 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Cons__eq__filter__iff,axiom, % 165.14/165.02 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 165.14/165.02 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) % 165.14/165.02 <=> ? [B_us,B_vs] : % 165.14/165.02 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) % 165.14/165.02 & ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 165.14/165.02 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 165.14/165.02 & hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_filter__eq__Cons__iff,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] : % 165.14/165.02 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) % 165.14/165.02 <=> ? [B_us,B_vs] : % 165.14/165.02 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_vs)) % 165.14/165.02 & ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 165.14/165.02 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 165.14/165.02 & hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Sigma__mono,axiom, % 165.14/165.02 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 165.14/165.02 => ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) ) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_C_2),V_D_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_not__acc__down,axiom, % 165.14/165.02 ! [V_R_2,V_x_2,T_a] : % 165.14/165.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) % 165.14/165.02 => ~ ! [B_z] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_x_2)),V_R_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_acc_OaccI,axiom, % 165.14/165.02 ! [V_r_2,V_x_2,T_a] : % 165.14/165.02 ( ! [B_y] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_x_2)),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) ) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__ball__nth,axiom, % 165.14/165.02 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(V_P_2,B_x)) ) % 165.14/165.02 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_max__ext_Osimps,axiom, % 165.14/165.02 ! [V_R_2,V_a2_2,V_a1_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 165.14/165.02 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 165.14/165.02 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 165.14/165.02 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 165.14/165.02 & ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 165.14/165.02 => ? [B_xa] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 165.14/165.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_R_2)) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sorted_OCons,axiom, % 165.14/165.02 ! [V_x_2,V_xs_2,T_a] : % 165.14/165.02 ( class_Orderings_Olinorder(T_a) % 165.14/165.02 => ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) % 165.14/165.02 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 165.14/165.02 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_InterI,axiom, % 165.14/165.02 ! [V_A_2,V_C_2,T_a] : % 165.14/165.02 ( ! [B_X] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) ) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__no__infinite__down__chainE,axiom, % 165.14/165.02 ! [V_f_2,V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__ex__length,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.02 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 165.14/165.02 <=> ? [B_n] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_setsum__reindex__cong,axiom, % 165.14/165.02 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 165.14/165.02 ( class_Groups_Ocomm__monoid__add(T_c) % 165.14/165.02 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 165.14/165.02 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 165.14/165.02 => ( ! [B_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 165.14/165.02 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 165.14/165.02 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c),V_g_2),V_A_2) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__ex__simps_I2_J,axiom, % 165.14/165.02 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__ex__append,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 165.14/165.02 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 165.14/165.02 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 165.14/165.02 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__ex__rev,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.02 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 165.14/165.02 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__ex__iff,axiom, % 165.14/165.02 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.02 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 165.14/165.02 <=> ? [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.02 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_list__ex__simps_I1_J,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 165.14/165.02 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 165.14/165.02 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.02 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_scomp__unfold,axiom, % 165.14/165.02 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),hAPP(V_f_2,V_x_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_setsum__ivl__cong,axiom, % 165.14/165.02 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_a,T_b] : % 165.14/165.02 ( ( class_Groups_Ocomm__monoid__add(T_b) % 165.14/165.02 & class_Orderings_Oord(T_a) ) % 165.14/165.02 => ( V_a_2 = V_ca_2 % 165.14/165.02 => ( V_b_2 = V_d_2 % 165.14/165.02 => ( ! [B_x] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),B_x)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2)) % 165.14/165.02 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 165.14/165.02 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2)) ) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Pair__scomp,axiom, % 165.14/165.02 ! [V_f_2,V_x_2,T_b,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_a,T_b),hAPP(c_Product__Type_OPair(T_c,T_a),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_scomp__Pair,axiom, % 165.14/165.02 ! [V_x_2,T_c,T_b,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_c,tc_prod(T_b,T_c)),V_x_2),c_Product__Type_OPair(T_b,T_c)) = V_x_2 ). % 165.14/165.02 % 165.14/165.02 fof(fact_scomp__scomp,axiom, % 165.14/165.02 ! [V_h_2,V_g_2,V_f_2,T_f,T_e,T_b,T_d,T_c,T_a] : hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_c,T_d,T_b),hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,tc_prod(T_c,T_d)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_e,T_f,T_b),V_f_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_c,tc_fun(T_d,T_b)),tc_fun(T_f,T_b)),T_e),c_Product__Type_Oscomp(T_f,T_c,T_d,T_b)),V_g_2)),V_h_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_scomp__def,axiom, % 165.14/165.02 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_scomp__apply,axiom, % 165.14/165.02 ! [V_x_2,V_g_2,V_f_2,T_a,T_d,T_c,T_b] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,T_a),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_a),V_g_2),hAPP(V_f_2,V_x_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_iterate_Osimps,axiom, % 165.14/165.02 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 165.14/165.02 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 165.14/165.02 => hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2) ) % 165.14/165.02 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 165.14/165.02 => hAPP(c_Random_Oiterate(T_b,T_a,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_a,T_b,T_a,tc_prod(T_b,T_a)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_b,T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_less__eq,axiom, % 165.14/165.02 ! [V_n_2,V_m_2] : % 165.14/165.02 ( 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))) % 165.14/165.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__trancl,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_less__than__def,axiom, % 165.14/165.02 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 165.14/165.02 % 165.14/165.02 fof(fact_acyclic__def,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 165.14/165.02 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl_Or__into__trancl,axiom, % 165.14/165.02 ! [V_r_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__subset__Field2,axiom, % 165.14/165.02 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),hAPP(c_Relation_OField(T_a),V_r_2)),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_Relation_OField(T_a),V_r_2))))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_r__into__trancl_H,axiom, % 165.14/165.02 ! [V_r_2,V_p_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__empty,axiom, % 165.14/165.02 ! [T_a] : c_Transitive__Closure_Otrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__domain,axiom, % 165.14/165.02 ! [V_r_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__range,axiom, % 165.14/165.02 ! [V_r_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) = hAPP(c_Relation_ORange(T_a,T_a),V_r_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_finite__trancl,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 165.14/165.02 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_r__r__into__trancl,axiom, % 165.14/165.02 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_R_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_R_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__into__trancl2,axiom, % 165.14/165.02 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 165.14/165.02 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__trans,axiom, % 165.14/165.02 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__mono,axiom, % 165.14/165.02 ! [V_s_2,V_r_2,V_p_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__unfold,axiom, % 165.14/165.02 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_r_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__subset__Sigma,axiom, % 165.14/165.02 ! [V_A_2,V_r_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__Int__subset,axiom, % 165.14/165.02 ! [V_s_2,V_r_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),V_s_2)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_log_Osimps,axiom, % 165.14/165.02 ! [V_i,V_b] : % 165.14/165.02 ( ( ( 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))) % 165.14/165.02 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 165.14/165.02 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 165.14/165.02 & ( ~ ( 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))) % 165.14/165.02 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 165.14/165.02 => 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))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_minus__shift__def,axiom, % 165.14/165.02 ! [V_r,V_l,V_k] : % 165.14/165.02 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 165.14/165.02 => 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) ) % 165.14/165.02 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 165.14/165.02 => 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) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_inc__shift__def,axiom, % 165.14/165.02 ! [V_k,V_v] : % 165.14/165.02 ( ( V_v = V_k % 165.14/165.02 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 165.14/165.02 & ( V_v != V_k % 165.14/165.02 => 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)) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_select,axiom, % 165.14/165.02 ! [V_s_2,T_a,V_xs_2] : % 165.14/165.02 ( V_xs_2 != c_List_Olist_ONil(T_a) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_select__weight__member,axiom, % 165.14/165.02 ! [V_s_2,V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Product__Type_Ofst(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_a,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_select__weigth__select,axiom, % 165.14/165.02 ! [T_a,V_xs_2] : % 165.14/165.02 ( V_xs_2 != c_List_Olist_ONil(T_a) % 165.14/165.02 => c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_a,V_xs_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_select__weight__cons__zero,axiom, % 165.14/165.02 ! [V_xs_2,V_x_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_a,V_xs_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_select__weigth__drop__zero,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_a,V_xs_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_pick__member,axiom, % 165.14/165.02 ! [V_xs_2,T_a,V_i_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(c_Random_Opick(T_a,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_a),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),T_a),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_pick_Osimps,axiom, % 165.14/165.02 ! [V_xs,V_x,T_a,V_i] : % 165.14/165.02 ( ( 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))) % 165.14/165.02 => 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) ) % 165.14/165.02 & ( ~ 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))) % 165.14/165.02 => 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))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_pick__drop__zero,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : c_Random_Opick(T_a,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_a)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_a,V_xs_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_select__weight__def,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : c_Random_Oselect__weight(T_a,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_a,V_xs_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_pick__same,axiom, % 165.14/165.02 ! [V_xs_2,T_a,V_l_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.02 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Omap(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_a),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_l_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_number__of__code__numeral__def,axiom, % 165.14/165.02 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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 165.14/165.02 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.02 % 165.14/165.02 fof(fact_times__code__numeral__code,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 165.14/165.02 ! [V_m_2,V_n_2] : % 165.14/165.02 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 165.14/165.02 <=> V_n_2 = V_m_2 ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_zero__code__numeral__def,axiom, % 165.14/165.02 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_one__code__numeral__def,axiom, % 165.14/165.02 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_code__numeral_Oof__nat__inject,axiom, % 165.14/165.02 ! [V_y_2,V_x_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 165.14/165.02 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 165.14/165.02 <=> V_x_2 = V_y_2 ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_less__eq__code__numeral__code,axiom, % 165.14/165.02 ! [V_m_2,V_n_2] : % 165.14/165.02 ( 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))) % 165.14/165.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_plus__code__numeral__code,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_less__code__numeral__code,axiom, % 165.14/165.02 ! [V_m_2,V_n_2] : % 165.14/165.02 ( 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))) % 165.14/165.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_code__numeral__not__eq__zero,axiom, % 165.14/165.02 ! [V_i_2] : % 165.14/165.02 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 165.14/165.02 <=> 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)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_range,axiom, % 165.14/165.02 ! [V_s,V_k] : % 165.14/165.02 ( 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)) % 165.14/165.02 => 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)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_select__def,axiom, % 165.14/165.02 ! [V_xs_2,T_a] : c_Random_Oselect(T_a,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_a,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_a,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_a,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_a),V_xs_2)),c_Code__Numeral_Onat__of))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__insert,axiom, % 165.14/165.02 ! [V_r_2,V_x_2,V_y_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fconj),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(hAPP(c_COMBC(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),V_y_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a))),hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2)))))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_r__into__rtrancl,axiom, % 165.14/165.02 ! [V_r_2,V_p_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl_Ortrancl__refl,axiom, % 165.14/165.02 ! [V_r_2,V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__into__rtrancl,axiom, % 165.14/165.02 ! [V_r_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_listrel__rtrancl__refl,axiom, % 165.14/165.02 ! [V_r_2,V_xs_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_xs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 165.14/165.02 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_times__code__numeral__def,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_nat__of__inverse,axiom, % 165.14/165.02 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 165.14/165.02 % 165.14/165.02 fof(fact_of__nat__nat__of,axiom, % 165.14/165.02 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 165.14/165.02 % 165.14/165.02 fof(fact_nat__of__of__nat,axiom, % 165.14/165.02 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 165.14/165.02 % 165.14/165.02 fof(fact_type__definition__code__numeral,axiom, % 165.14/165.02 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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__trans,axiom, % 165.14/165.02 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 165.14/165.02 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 165.14/165.02 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__eq__or__trancl,axiom, % 165.14/165.02 ! [V_R_2,V_y_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 165.14/165.02 <=> ( V_x_2 = V_y_2 % 165.14/165.02 | ( V_x_2 != V_y_2 % 165.14/165.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__into__trancl2,axiom, % 165.14/165.02 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),V_r_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtranclD,axiom, % 165.14/165.02 ! [V_R_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 165.14/165.02 => ( V_a_2 = V_b_2 % 165.14/165.02 | ( V_a_2 != V_b_2 % 165.14/165.02 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__into__trancl1,axiom, % 165.14/165.02 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__rtrancl__trancl,axiom, % 165.14/165.02 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__trancl__trancl,axiom, % 165.14/165.02 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Image__closed__trancl,axiom, % 165.14/165.02 ! [V_X_2,V_r_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_a,V_r_2),V_X_2)),V_X_2)) % 165.14/165.02 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__mono,axiom, % 165.14/165.02 ! [V_s_2,V_r_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__subset,axiom, % 165.14/165.02 ! [V_S_2,V_R_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 165.14/165.02 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__subset__rtrancl,axiom, % 165.14/165.02 ! [V_s_2,V_r_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_s_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__Un__subset,axiom, % 165.14/165.02 ! [V_S_2,V_R_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_less__code__numeral__def,axiom, % 165.14/165.02 ! [V_m_2,V_n_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 165.14/165.02 <=> 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))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 165.14/165.02 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel1(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_nat__of__number,axiom, % 165.14/165.02 ! [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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 165.14/165.02 ! [V_l_2,V_k_2] : % 165.14/165.02 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 165.14/165.02 <=> V_k_2 = V_l_2 ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_code__numeral_Onat__of__inject,axiom, % 165.14/165.02 ! [V_y_2,V_x_2] : % 165.14/165.02 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 165.14/165.02 <=> V_x_2 = V_y_2 ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 165.14/165.02 ! [V_r_2,T_a] : c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_nat__of,axiom, % 165.14/165.02 ! [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)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_int__of__def,axiom, % 165.14/165.02 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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Domain__rtrancl,axiom, % 165.14/165.02 ! [V_R_2,T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Range__rtrancl,axiom, % 165.14/165.02 ! [V_R_2,T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__idemp,axiom, % 165.14/165.02 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_refl__rtrancl,axiom, % 165.14/165.02 ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_in__rtrancl__UnI,axiom, % 165.14/165.02 ! [V_S_2,V_R_2,V_x_2,T_a] : % 165.14/165.02 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 165.14/165.02 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) ) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__Un__rtrancl,axiom, % 165.14/165.02 ! [V_S_2,V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) = c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),V_S_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_r__comp__rtrancl__eq,axiom, % 165.14/165.02 ! [V_r_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__idemp__self__comp,axiom, % 165.14/165.02 ! [V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__unfold__right,axiom, % 165.14/165.02 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__unfold__left,axiom, % 165.14/165.02 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_r_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__rtrancl__absorb,axiom, % 165.14/165.02 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Transitive__Closure_Otrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__trancl__absorb,axiom, % 165.14/165.02 ! [V_R_2,T_a] : c_Transitive__Closure_Otrancl(T_a,c_Transitive__Closure_Ortrancl(T_a,V_R_2)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 165.14/165.02 % 165.14/165.02 fof(fact_listrel__rtrancl__trans,axiom, % 165.14/165.02 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_ys_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_zs_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_less__eq__code__numeral__def,axiom, % 165.14/165.02 ! [V_m_2,V_n_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 165.14/165.02 <=> 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))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_nat__of__code,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_nat__of__aux__def,axiom, % 165.14/165.02 ! [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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 165.14/165.02 ! [V_r_2,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_HOL_Obool)),c_List_Olistrel(T_a,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Not__Domain__rtrancl,axiom, % 165.14/165.02 ! [V_y_2,V_R_2,V_x_2,T_a] : % 165.14/165.02 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 165.14/165.02 <=> V_x_2 = V_y_2 ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_acc__downwards__aux,axiom, % 165.14/165.02 ! [V_r_2,V_a_2,V_b_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_acc__downwards,axiom, % 165.14/165.02 ! [V_b_2,V_r_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_wf__insert,axiom, % 165.14/165.02 ! [V_r_2,V_x_2,V_y_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) % 165.14/165.02 <=> ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.02 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 165.14/165.02 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__listrel1__eq__len,axiom, % 165.14/165.02 ! [V_r_2,V_y_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) % 165.14/165.02 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_y_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_acyclic__insert,axiom, % 165.14/165.02 ! [V_r_2,V_x_2,V_y_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Oacyclic(T_a,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),V_r_2)) % 165.14/165.02 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 165.14/165.02 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_listrel__reflcl__if__listrel1,axiom, % 165.14/165.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 165.14/165.02 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_List_Olistrel(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_a),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_Suc__code__numeral__def,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_minus__code__numeral__def,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_of__nat__inverse,axiom, % 165.14/165.02 ! [V_y_2] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 165.14/165.02 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_plus__code__numeral__def,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_div__code__numeral__def,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_pred__nat__trancl__eq__le,axiom, % 165.14/165.02 ! [V_n_2,V_m_2] : % 165.14/165.02 ( 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))) % 165.14/165.02 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_mod__code__numeral__def,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__subset__Sigma__aux,axiom, % 165.14/165.02 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_a),V_A_2),hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) % 165.14/165.02 => ( V_a_2 = V_b_2 % 165.14/165.02 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_code__numeral__decr,axiom, % 165.14/165.02 ! [V_k] : % 165.14/165.02 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 165.14/165.02 => 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))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_subtract__code__numeral__code,axiom, % 165.14/165.02 ! [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)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 165.14/165.02 ! [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))) ). % 165.14/165.02 % 165.14/165.02 fof(fact_minus__code__numeral__code,axiom, % 165.14/165.02 ! [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) ). % 165.14/165.02 % 165.14/165.02 fof(fact_subtract__code__numeral__def,axiom, % 165.14/165.02 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.02 % 165.14/165.02 fof(fact_irrefl__tranclI,axiom, % 165.14/165.02 ! [V_x_2,V_r_2,T_a] : % 165.14/165.02 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 165.14/165.02 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_sequence__trans,axiom, % 165.14/165.02 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] : % 165.14/165.02 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__converse,axiom, % 165.14/165.02 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__converseI,axiom, % 165.14/165.02 ! [V_r_2,V_x_2,V_y_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_rtrancl__converseD,axiom, % 165.14/165.02 ! [V_r_2,V_y_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__converseI,axiom, % 165.14/165.02 ! [V_r_2,V_y_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_trancl__converseD,axiom, % 165.14/165.02 ! [V_r_2,V_y_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_converse__iff,axiom, % 165.14/165.02 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 165.14/165.02 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_converseI,axiom, % 165.14/165.02 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_r_2)) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_converseD,axiom, % 165.14/165.02 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 165.14/165.02 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_b_2),V_a_2)),V_r_2)) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_in__listrel1__converse,axiom, % 165.14/165.02 ! [V_r_2,V_y_2,V_x_2,T_a] : % 165.14/165.02 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)))) % 165.14/165.02 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_a),tc_List_Olist(T_a))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)))) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_acyclic__converse,axiom, % 165.14/165.02 ! [V_r_2,T_a] : % 165.14/165.02 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 165.14/165.02 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_converse__UNION,axiom, % 165.14/165.02 ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_equiv__comp__eq,axiom, % 165.14/165.02 ! [V_r_2,V_A_2,T_a] : % 165.14/165.02 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 165.14/165.02 => hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2 ) ). % 165.14/165.02 % 165.14/165.02 fof(fact_converse__rel__comp,axiom, % 165.14/165.02 ! [V_s_2,V_r_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_a),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_a),V_s_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) ). % 165.14/165.02 % 165.14/165.02 fof(fact_converse__Un,axiom, % 165.14/165.02 ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_converse__INTER,axiom, % 165.14/165.03 ! [V_r_2,V_S_2,T_c,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),T_c),c_Relation_Oconverse(T_b,T_a)),V_r_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_converse__Int,axiom, % 165.14/165.03 ! [V_s_2,V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Relation_Oconverse(T_b,T_a),V_s_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_refl__on__converse,axiom, % 165.14/165.03 ! [V_r_2,V_A_2,T_a] : % 165.14/165.03 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 165.14/165.03 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_finite__converse,axiom, % 165.14/165.03 ! [V_r_2,T_b,T_a] : % 165.14/165.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 165.14/165.03 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_converse__Id__on,axiom, % 165.14/165.03 ! [V_A_2,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId__on(T_a,V_A_2)) = c_Relation_OId__on(T_a,V_A_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_converse__converse,axiom, % 165.14/165.03 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = V_r_2 ). % 165.14/165.03 % 165.14/165.03 fof(fact_Field__converse,axiom, % 165.14/165.03 ! [V_r_2,T_a] : hAPP(c_Relation_OField(T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_OField(T_a),V_r_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_listrel1__converse,axiom, % 165.14/165.03 ! [V_r_2,T_a] : c_List_Olistrel1(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_a),tc_List_Olist(T_a)),c_List_Olistrel1(T_a,V_r_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_converse__inv__image,axiom, % 165.14/165.03 ! [V_f_2,V_R_2,T_b,T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_b,T_a),hAPP(c_Relation_Oconverse(T_b,T_b),V_R_2)),V_f_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Range__converse,axiom, % 165.14/165.03 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2)) = hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Domain__converse,axiom, % 165.14/165.03 ! [V_r_2,T_b,T_a] : hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) = hAPP(c_Relation_ORange(T_b,T_a),V_r_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Range__def,axiom, % 165.14/165.03 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = hAPP(c_Relation_ODomain(T_a,T_b),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_trancl__converse,axiom, % 165.14/165.03 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) = hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_wf__converse__trancl,axiom, % 165.14/165.03 ! [V_r_2,T_a] : % 165.14/165.03 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 165.14/165.03 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Image__subset__eq,axiom, % 165.14/165.03 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2)),V_B_2)) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_B_2))))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_refl__on__comp__subset,axiom, % 165.14/165.03 ! [V_r_2,V_A_2,T_a] : % 165.14/165.03 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_comp__equivI,axiom, % 165.14/165.03 ! [V_A_2,V_r_2,T_a] : % 165.14/165.03 ( hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)),V_r_2) = V_r_2 % 165.14/165.03 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2 % 165.14/165.03 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_finite__acyclic__wf__converse,axiom, % 165.14/165.03 ! [V_r_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 165.14/165.03 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 165.14/165.03 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_converse__def,axiom, % 165.14/165.03 ! [V_r_2,T_a,T_b] : hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_a,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_a)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_b,T_a),tc_fun(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_a)))),hAPP(c_COMBC(T_b,T_a,tc_prod(T_b,T_a)),c_Product__Type_OPair(T_b,T_a))))),V_r_2))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Image__INT__eq,axiom, % 165.14/165.03 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] : % 165.14/165.03 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) % 165.14/165.03 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 165.14/165.03 => hAPP(c_Relation_OImage(T_b,T_a,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Relation_OImage(T_b,T_a,V_r_2)),V_B_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_reflcl__set__eq,axiom, % 165.14/165.03 ! [V_y_2,V_x_2,V_r_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a),c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_r_2)),c_fequal),V_x_2),V_y_2)) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a)))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_IdI,axiom, % 165.14/165.03 ! [V_a_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_a_2)),c_Relation_OId(T_a))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_converse__Id,axiom, % 165.14/165.03 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Domain__Id,axiom, % 165.14/165.03 ! [T_a] : hAPP(c_Relation_ODomain(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Range__Id,axiom, % 165.14/165.03 ! [T_a] : hAPP(c_Relation_ORange(T_a,T_a),c_Relation_OId(T_a)) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_refl__Id,axiom, % 165.14/165.03 ! [T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Relation_OId(T_a)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_single__valued__Id__on,axiom, % 165.14/165.03 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_single__valued__Id,axiom, % 165.14/165.03 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Image__Id,axiom, % 165.14/165.03 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ). % 165.14/165.03 % 165.14/165.03 fof(fact_single__valued__rel__comp,axiom, % 165.14/165.03 ! [V_s_2,T_c,V_r_2,T_b,T_a] : % 165.14/165.03 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 165.14/165.03 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 165.14/165.03 => c_Relation_Osingle__valued(T_a,T_c,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_R__O__Id,axiom, % 165.14/165.03 ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_b),V_R_2),c_Relation_OId(T_b)) = V_R_2 ). % 165.14/165.03 % 165.14/165.03 fof(fact_Id__O__R,axiom, % 165.14/165.03 ! [V_R_2,T_b,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_b),c_Relation_OId(T_a)),V_R_2) = V_R_2 ). % 165.14/165.03 % 165.14/165.03 fof(fact_single__valued__subset,axiom, % 165.14/165.03 ! [V_s_2,V_r_2,T_b,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) % 165.14/165.03 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2) % 165.14/165.03 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_pair__in__Id__conv,axiom, % 165.14/165.03 ! [V_b_2,V_a_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Relation_OId(T_a))) % 165.14/165.03 <=> V_a_2 = V_b_2 ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rtrancl__reflcl__absorb,axiom, % 165.14/165.03 ! [V_R_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_R_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rtrancl__reflcl,axiom, % 165.14/165.03 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rtrancl__empty,axiom, % 165.14/165.03 ! [T_a] : c_Transitive__Closure_Ortrancl(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) = c_Relation_OId(T_a) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rtrancl__r__diff__Id,axiom, % 165.14/165.03 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_single__valuedD,axiom, % 165.14/165.03 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] : % 165.14/165.03 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_r_2)) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_z_2)),V_r_2)) % 165.14/165.03 => V_y_2 = V_z_2 ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_single__valued__def,axiom, % 165.14/165.03 ! [V_r_2,T_b,T_a] : % 165.14/165.03 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 165.14/165.03 <=> ! [B_x,B_y] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y)),V_r_2)) % 165.14/165.03 => ! [B_z] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z)),V_r_2)) % 165.14/165.03 => B_y = B_z ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_pair__leq__def,axiom, % 165.14/165.03 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))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_trancl__reflcl,axiom, % 165.14/165.03 ! [V_r_2,T_a] : c_Transitive__Closure_Otrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_reflcl__trancl,axiom, % 165.14/165.03 ! [V_r_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_a,V_r_2)),c_Relation_OId(T_a)) = c_Transitive__Closure_Ortrancl(T_a,V_r_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rtrancl__unfold,axiom, % 165.14/165.03 ! [V_r_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_r_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_refl__reflcl,axiom, % 165.14/165.03 ! [V_r_2,T_a] : c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Id__def,axiom, % 165.14/165.03 ! [T_a] : c_Relation_OId(T_a) = hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_a,T_a)),c_HOL_OEx(T_a)),hAPP(hAPP(c_COMBC(tc_prod(T_a,T_a),tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_HOL_Obool)),tc_prod(T_a,T_a)),c_COMBB(tc_prod(T_a,T_a),tc_HOL_Obool,T_a)),c_fequal)),hAPP(hAPP(c_COMBS(T_a,T_a,tc_prod(T_a,T_a)),c_Product__Type_OPair(T_a,T_a)),c_COMBI(T_a))))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_irrefl__diff__Id,axiom, % 165.14/165.03 ! [V_r_2,T_a] : c_Relation_Oirrefl(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_single__valued__confluent,axiom, % 165.14/165.03 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] : % 165.14/165.03 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 165.14/165.03 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Image__Int__eq,axiom, % 165.14/165.03 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : % 165.14/165.03 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2)) % 165.14/165.03 => hAPP(c_Relation_OImage(T_b,T_a,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_b,T_a,V_R_2),V_B_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rtrancl__Int__subset,axiom, % 165.14/165.03 ! [V_r_2,V_s_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Relation_OId(T_a)),V_s_2)) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2)),V_r_2)),V_s_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_s_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_total__on__diff__Id,axiom, % 165.14/165.03 ! [V_r_2,V_A_2,T_a] : % 165.14/165.03 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_a))) % 165.14/165.03 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 165.14/165.03 ! [V_R_2,V_p_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_total__on__converse,axiom, % 165.14/165.03 ! [V_r_2,V_A_2,T_a] : % 165.14/165.03 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 165.14/165.03 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_single__valued__rel__pow,axiom, % 165.14/165.03 ! [V_n_2,V_R_2,T_a] : % 165.14/165.03 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2) % 165.14/165.03 => c_Relation_Osingle__valued(T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_relpow_Osimps_I1_J,axiom, % 165.14/165.03 ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_a) ). % 165.14/165.03 % 165.14/165.03 fof(fact_comp__funpow,axiom, % 165.14/165.03 ! [V_f_2,V_n_2,T_b,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_a,T_b),tc_fun(T_a,T_b)),V_n_2),c_Fun_Ocomp(T_b,T_b,T_a,V_f_2)) = c_Fun_Ocomp(T_b,T_b,T_a,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rtrancl__power,axiom, % 165.14/165.03 ! [V_R_2,V_p_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 165.14/165.03 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__pow__imp__rtrancl,axiom, % 165.14/165.03 ! [V_R_2,V_n_2,V_p_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__pow__add,axiom, % 165.14/165.03 ! [V_R_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_total__on__empty,axiom, % 165.14/165.03 ! [V_r_2,T_a] : c_Relation_Ototal__on(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_r_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_funpow__swap1,axiom, % 165.14/165.03 ! [V_x_2,V_n_2,T_a,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_wf__exp,axiom, % 165.14/165.03 ! [V_R_2,V_n_2,T_a] : % 165.14/165.03 ( c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) % 165.14/165.03 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__pow__1,axiom, % 165.14/165.03 ! [V_R_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__pow__commute,axiom, % 165.14/165.03 ! [V_n_2,V_R_2,T_a] : hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_relpow_Osimps_I2_J,axiom, % 165.14/165.03 ! [V_R_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_funpow__mult,axiom, % 165.14/165.03 ! [V_f_2,V_m_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__pow__0__I,axiom, % 165.14/165.03 ! [V_R_2,V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__pow__0__E,axiom, % 165.14/165.03 ! [V_R_2,V_y_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) % 165.14/165.03 => V_x_2 = V_y_2 ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__pow__Suc__I,axiom, % 165.14/165.03 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),V_R_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__pow__Suc__I2,axiom, % 165.14/165.03 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2)) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_funpow_Osimps_I2_J,axiom, % 165.14/165.03 ! [V_f_2,V_n_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_funpow__add,axiom, % 165.14/165.03 ! [V_f_2,V_n_2,V_m_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_a,T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_f_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_funpow_Osimps_I1_J,axiom, % 165.14/165.03 ! [V_f_2,T_a] : hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_a) ). % 165.14/165.03 % 165.14/165.03 fof(fact_trancl__power,axiom, % 165.14/165.03 ! [V_R_2,V_p_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 165.14/165.03 <=> ? [B_n] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 165.14/165.03 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_n),V_R_2))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_total__on__def,axiom, % 165.14/165.03 ! [V_r_2,V_A_2,T_a] : % 165.14/165.03 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2) % 165.14/165.03 <=> ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.03 => ! [B_xa] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 165.14/165.03 => ( B_x != B_xa % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_xa)),V_r_2)) % 165.14/165.03 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_xa),B_x)),V_r_2)) ) ) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 165.14/165.03 ! [V_R_2,T_a] : c_Transitive__Closure_Ortrancl(T_a,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool)),V_R_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_funpow__code__def,axiom, % 165.14/165.03 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__pow__E2,axiom, % 165.14/165.03 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 165.14/165.03 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.03 => V_x_2 != V_z_2 ) % 165.14/165.03 => ~ ! [B_y,B_m] : % 165.14/165.03 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) % 165.14/165.03 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rotate__def,axiom, % 165.14/165.03 ! [V_n_2,T_a] : c_List_Orotate(T_a,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_a),tc_List_Olist(T_a)),V_n_2),c_List_Orotate1(T_a)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__pow__E,axiom, % 165.14/165.03 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 165.14/165.03 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.03 => V_x_2 != V_z_2 ) % 165.14/165.03 => ~ ! [B_y,B_m] : % 165.14/165.03 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),B_m),V_R_2))) % 165.14/165.03 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2)) ) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_acyclicI,axiom, % 165.14/165.03 ! [V_r_2,T_a] : % 165.14/165.03 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 165.14/165.03 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_pos__not__random__dseq__def,axiom, % 165.14/165.03 ! [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)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rtrancl__Un__separator__converseE,axiom, % 165.14/165.03 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2)))) % 165.14/165.03 => ( ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) % 165.14/165.03 => ! [B_y] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_Q_2)) % 165.14/165.03 => B_y = B_x ) ) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rtrancl__Un__separatorE,axiom, % 165.14/165.03 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)),V_P_2),V_Q_2)))) % 165.14/165.03 => ( ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) % 165.14/165.03 => ! [B_y] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_y)),V_Q_2)) % 165.14/165.03 => B_x = B_y ) ) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_a,V_P_2))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__pow__Suc__E,axiom, % 165.14/165.03 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 165.14/165.03 => ~ ! [B_y] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) % 165.14/165.03 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),V_R_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__pow__Suc__D2,axiom, % 165.14/165.03 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 165.14/165.03 => ? [B_y] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) % 165.14/165.03 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__pow__Suc__E2,axiom, % 165.14/165.03 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) % 165.14/165.03 => ~ ! [B_y] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_y)),V_R_2)) % 165.14/165.03 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_a,T_a),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_tranclD2,axiom, % 165.14/165.03 ! [V_R_2,V_y_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 165.14/165.03 => ? [B_z] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 165.14/165.03 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),V_R_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_tranclD,axiom, % 165.14/165.03 ! [V_R_2,V_y_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 165.14/165.03 => ? [B_z] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),B_z)),V_R_2)) % 165.14/165.03 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_IdE,axiom, % 165.14/165.03 ! [V_p_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a))) % 165.14/165.03 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_nat__intermed__int__val,axiom, % 165.14/165.03 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 165.14/165.03 ( ! [B_i] : % 165.14/165.03 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 165.14/165.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 165.14/165.03 => 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))) ) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 165.14/165.03 => ? [B_i] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 165.14/165.03 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 165.14/165.03 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_in__set__conv__decomp__first,axiom, % 165.14/165.03 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.03 <=> ? [B_ys] : % 165.14/165.03 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) % 165.14/165.03 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_in__set__conv__decomp__last,axiom, % 165.14/165.03 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.03 <=> ? [B_ys,B_zs] : % 165.14/165.03 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) % 165.14/165.03 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_in__set__conv__decomp,axiom, % 165.14/165.03 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.03 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_zs)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_mod__div__decomp,axiom, % 165.14/165.03 ! [V_b,V_a,T_a] : % 165.14/165.03 ( class_Divides_Osemiring__div(T_a) % 165.14/165.03 => 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)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 165.14/165.03 ! [V_x_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.03 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 165.14/165.03 ! [V_x_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.03 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_sup__SUPR__fold__sup,axiom, % 165.14/165.03 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 165.14/165.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 165.14/165.03 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 165.14/165.03 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fold__empty,axiom, % 165.14/165.03 ! [V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ). % 165.14/165.03 % 165.14/165.03 fof(fact_fold__inf__insert,axiom, % 165.14/165.03 ! [V_a_2,V_b_2,V_A_2,T_a] : % 165.14/165.03 ( class_Lattices_Osemilattice__inf(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_folding_Oeq__fold,axiom, % 165.14/165.03 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_s_2),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fold__image__def,axiom, % 165.14/165.03 ! [V_g_2,V_f_2,T_b,T_a] : hAPP(c_Finite__Set_Ofold__image(T_a,T_b,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_b,T_a,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),V_f_2),V_g_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fold__def,axiom, % 165.14/165.03 ! [V_A_2,V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold__graph(T_b,T_a,V_f_2,V_z_2,V_A_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_min__max_Ofold__sup__insert,axiom, % 165.14/165.03 ! [V_a_2,V_b_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_min__max_Ofold__inf__insert,axiom, % 165.14/165.03 ! [V_a_2,V_b_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_inf__Inf__fold__inf,axiom, % 165.14/165.03 ! [V_B_2,V_A_2,T_a] : % 165.14/165.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_B_2),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fold__sup__insert,axiom, % 165.14/165.03 ! [V_a_2,V_b_2,V_A_2,T_a] : % 165.14/165.03 ( class_Lattices_Osemilattice__sup(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_union__fold__insert,axiom, % 165.14/165.03 ! [V_B_2,V_A_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)),V_B_2),V_A_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_sup__Sup__fold__sup,axiom, % 165.14/165.03 ! [V_B_2,V_A_2,T_a] : % 165.14/165.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_B_2),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_inf__INFI__fold__inf,axiom, % 165.14/165.03 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 165.14/165.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),V_B_2),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 165.14/165.03 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_a_2),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 165.14/165.03 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 165.14/165.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),V_xs_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_sup__le__fold__sup,axiom, % 165.14/165.03 ! [V_b_2,V_a_2,V_A_2,T_a] : % 165.14/165.03 ( class_Lattices_Osemilattice__sup(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_b_2),V_A_2))) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fold__inf__le__inf,axiom, % 165.14/165.03 ! [V_b_2,V_a_2,V_A_2,T_a] : % 165.14/165.03 ( class_Lattices_Osemilattice__inf(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2))) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 165.14/165.03 ! [V_b_2,V_a_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a_2),V_b_2))) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_min__max_Osup__le__fold__sup,axiom, % 165.14/165.03 ! [V_b_2,V_a_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_b_2),V_A_2))) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Sup__fold__sup,axiom, % 165.14/165.03 ! [V_A_2,T_a] : % 165.14/165.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),c_Orderings_Obot__class_Obot(T_a)),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Inf__fold__inf,axiom, % 165.14/165.03 ! [V_A_2,T_a] : % 165.14/165.03 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),c_Orderings_Otop__class_Otop(T_a)),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fold1__eq__fold__idem,axiom, % 165.14/165.03 ! [V_a_2,V_A_2,T_a] : % 165.14/165.03 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 165.14/165.03 ! [V_a_2,V_A_2,T_a] : % 165.14/165.03 ( class_Lattices_Olattice(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_a_2),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 165.14/165.03 ! [V_a_2,V_A_2,T_a] : % 165.14/165.03 ( class_Lattices_Olattice(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_a_2),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Min_Oeq__fold__idem_H,axiom, % 165.14/165.03 ! [V_a_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Max_Oeq__fold__idem_H,axiom, % 165.14/165.03 ! [V_a_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 165.14/165.03 ! [V_a_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_a_2),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 165.14/165.03 ! [V_a_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_a_2),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_minus__fold__remove,axiom, % 165.14/165.03 ! [V_B_2,V_A_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a),hAPP(c_COMBC(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_Oinsert(T_a)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_B_2),V_A_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_folding__one_Oeq__fold_H,axiom, % 165.14/165.03 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.03 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,V_f_2),V_x_2),V_A_2) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_SUPR__fold__sup,axiom, % 165.14/165.03 ! [V_f_2,V_A_2,T_a,T_b] : % 165.14/165.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_INFI__fold__inf,axiom, % 165.14/165.03 ! [V_f_2,V_A_2,T_a,T_b] : % 165.14/165.03 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_a),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fold1__eq__fold,axiom, % 165.14/165.03 ! [V_a_2,V_A_2,T_a] : % 165.14/165.03 ( class_Groups_Oab__semigroup__mult(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.03 => hAPP(c_Finite__Set_Ofold1(T_a,c_Groups_Otimes__class_Otimes(T_a)),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)),V_a_2),V_A_2) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 165.14/165.03 ! [V_x_2,V_A_2,T_a] : % 165.14/165.03 ( class_Lattices_Olattice(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.03 => c_Big__Operators_Olattice__class_OSup__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_x_2),V_A_2) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 165.14/165.03 ! [V_x_2,V_A_2,T_a] : % 165.14/165.03 ( class_Lattices_Olattice(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.03 => c_Big__Operators_Olattice__class_OInf__fin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_x_2),V_A_2) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Min_Oeq__fold_H,axiom, % 165.14/165.03 ! [V_x_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.03 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_x_2),V_A_2) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Max_Oeq__fold_H,axiom, % 165.14/165.03 ! [V_x_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.03 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_x_2),V_A_2) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofold__rec,axiom, % 165.14/165.03 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 165.14/165.03 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm,axiom, % 165.14/165.03 ! [T_a] : % 165.14/165.03 ( class_Groups_Oab__semigroup__mult(T_a) % 165.14/165.03 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 165.14/165.03 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 165.14/165.03 => V_y_2 = V_x_2 ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 165.14/165.03 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => c_Finite__Set_Ofun__left__comm(T_c,T_b,hAPP(hAPP(c_COMBB(T_a,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 165.14/165.03 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => 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)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm__insort,axiom, % 165.14/165.03 ! [T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => c_Finite__Set_Ofun__left__comm(T_a,tc_List_Olist(T_a),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 165.14/165.03 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 165.14/165.03 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofold__equality,axiom, % 165.14/165.03 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 165.14/165.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 165.14/165.03 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofold__insert,axiom, % 165.14/165.03 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2)) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 165.14/165.03 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 165.14/165.03 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_a,hAPP(c_COMBC(T_a,T_b,T_b),V_f_2),V_y_2),c_List_Oremdups(T_a,V_xs_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 165.14/165.03 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 165.14/165.03 => ? [B_y_H] : % 165.14/165.03 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 165.14/165.03 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 165.14/165.03 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] : % 165.14/165.03 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)),V_v_2)) % 165.14/165.03 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 165.14/165.03 => ~ ! [B_y] : % 165.14/165.03 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 165.14/165.03 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 165.14/165.03 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b_2),V_ca_2))) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 165.14/165.03 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 165.14/165.03 ( class_Orderings_Olinorder(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_ca_2),V_A_2))) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_inf__le__fold__inf,axiom, % 165.14/165.03 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 165.14/165.03 ( class_Lattices_Osemilattice__inf(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_ca_2),V_A_2))) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_fold__sup__le__sup,axiom, % 165.14/165.03 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 165.14/165.03 ( class_Lattices_Osemilattice__sup(T_a) % 165.14/165.03 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 165.14/165.03 => ( ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b_2),V_ca_2))) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_wf__eq__minimal,axiom, % 165.14/165.03 ! [V_r_2,T_a] : % 165.14/165.03 ( c_Wellfounded_Owf(T_a,V_r_2) % 165.14/165.03 <=> ! [B_Q] : % 165.14/165.03 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 165.14/165.03 => ? [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 165.14/165.03 & ! [B_y] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_y),B_x)),V_r_2)) % 165.14/165.03 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_transfer__nat__int__set__cong,axiom, % 165.14/165.03 ! [V_P_H_2,V_P_2] : % 165.14/165.03 ( ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 165.14/165.03 => ( hBOOL(hAPP(V_P_2,B_x)) % 165.14/165.03 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 165.14/165.03 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Int__Collect__mono,axiom, % 165.14/165.03 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 165.14/165.03 => ( ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.03 => ( hBOOL(hAPP(V_P_2,B_x)) % 165.14/165.03 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_a),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_a),V_Q_2)))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_UnionE,axiom, % 165.14/165.03 ! [V_C_2,V_A_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 165.14/165.03 => ~ ! [B_X] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) % 165.14/165.03 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_converseE,axiom, % 165.14/165.03 ! [V_r_2,V_yx_2,T_b,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_yx_2),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 165.14/165.03 => ~ ! [B_x,B_y] : % 165.14/165.03 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x) % 165.14/165.03 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),B_x),B_y)),V_r_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rel__compE,axiom, % 165.14/165.03 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_c,T_b),V_r_2),V_s_2))) % 165.14/165.03 => ~ ! [B_x,B_y,B_z] : % 165.14/165.03 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),B_x),B_y)),V_r_2)) % 165.14/165.03 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),B_z)),V_s_2)) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Nitpick_Oplus__frac__def,axiom, % 165.14/165.03 ! [V_r_2,V_q_2,T_a] : c_Nitpick_Oplus__frac(T_a,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_a),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_a),V_q_2),hAPP(c_Nitpick_Odenom(T_a),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_a),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_a),tc_Int_Oint),c_Nitpick_Ofrac(T_a)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_a),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_a),V_r_2)))))),c_COMBI(tc_Int_Oint))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_setprod__pos,axiom, % 165.14/165.03 ! [V_f_2,V_A_2,T_a,T_b] : % 165.14/165.03 ( class_Rings_Olinordered__semidom(T_b) % 165.14/165.03 => ( ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Nitpick_Otimes__frac__def,axiom, % 165.14/165.03 ! [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))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Nitpick_Oof__frac__def,axiom, % 165.14/165.03 ! [V_q,T_a,T_b] : % 165.14/165.03 ( ( class_Rings_Oinverse(T_b) % 165.14/165.03 & class_Rings_Oring__1(T_b) ) % 165.14/165.03 => 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))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 165.14/165.03 ! [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)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 165.14/165.03 ! [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))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Nitpick_Oless__frac__def,axiom, % 165.14/165.03 ! [V_r_2,V_q_2,T_a] : % 165.14/165.03 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 165.14/165.03 ! [V_r_2,V_q_2,T_a] : % 165.14/165.03 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),c_Nitpick_Oplus__frac(T_a,V_q_2,c_Nitpick_Ouminus__frac(T_a,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Nitpick_Odenom__def,axiom, % 165.14/165.03 ! [T_a] : c_Nitpick_Odenom(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Nitpick_Onum__def,axiom, % 165.14/165.03 ! [T_a] : c_Nitpick_Onum(T_a) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_a,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_a)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_list__all__length,axiom, % 165.14/165.03 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.03 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 165.14/165.03 <=> ! [B_n] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))) % 165.14/165.03 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_internal__split__def,axiom, % 165.14/165.03 ! [T_c,T_b,T_a] : c_Product__Type_Ointernal__split(T_a,T_b,T_c) = c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Ball__set__list__all,axiom, % 165.14/165.03 ! [V_P_2,V_xs_2,T_a] : % 165.14/165.03 ( ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.03 => hBOOL(hAPP(V_P_2,B_x)) ) % 165.14/165.03 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_list__all__simps_I1_J,axiom, % 165.14/165.03 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 165.14/165.03 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 165.14/165.03 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.03 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_list__all__simps_I2_J,axiom, % 165.14/165.03 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_list__all__append,axiom, % 165.14/165.03 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 165.14/165.03 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 165.14/165.03 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 165.14/165.03 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_list__all__rev,axiom, % 165.14/165.03 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.03 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 165.14/165.03 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_list__all__iff,axiom, % 165.14/165.03 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.03 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 165.14/165.03 <=> ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.03 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_list__all__iff__raw,axiom, % 165.14/165.03 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.03 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 165.14/165.03 <=> ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.03 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_internal__split__conv,axiom, % 165.14/165.03 ! [V_b_2,V_a_2,V_ca_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_b,T_c,T_a),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_b_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_list__ex1__simps_I2_J,axiom, % 165.14/165.03 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 165.14/165.03 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 165.14/165.03 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.03 => c_List_Olist__all(T_a,hAPP(hAPP(c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2) ) % 165.14/165.03 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.03 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_setprod__nonneg,axiom, % 165.14/165.03 ! [V_f_2,V_A_2,T_a,T_b] : % 165.14/165.03 ( class_Rings_Olinordered__semidom(T_b) % 165.14/165.03 => ( ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_A_2))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_list__ex1__simps_I1_J,axiom, % 165.14/165.03 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_exists1__code,axiom, % 165.14/165.03 ! [V_P_2,T_a] : % 165.14/165.03 ( class_Enum_Oenum(T_a) % 165.14/165.03 => ( ? [B_x] : % 165.14/165.03 ( hBOOL(hAPP(V_P_2,B_x)) % 165.14/165.03 & ! [B_y] : % 165.14/165.03 ( hBOOL(hAPP(V_P_2,B_y)) % 165.14/165.03 => B_y = B_x ) ) % 165.14/165.03 <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_list__ex1__iff,axiom, % 165.14/165.03 ! [V_xs_2,V_P_2,T_a] : % 165.14/165.03 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2) % 165.14/165.03 <=> ? [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.03 & hBOOL(hAPP(V_P_2,B_x)) % 165.14/165.03 & ! [B_y] : % 165.14/165.03 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.03 & hBOOL(hAPP(V_P_2,B_y)) ) % 165.14/165.03 => B_y = B_x ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_bool_Osize_I2_J,axiom, % 165.14/165.03 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(fact_bool_Osize_I1_J,axiom, % 165.14/165.03 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(fact_finite__less__ub,axiom, % 165.14/165.03 ! [V_u_2,V_f_2] : % 165.14/165.03 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 165.14/165.03 => 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)))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_measure__function__int,axiom, % 165.14/165.03 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))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_measure__snd,axiom, % 165.14/165.03 ! [T_b,V_f_2,T_a] : % 165.14/165.03 ( c_FunDef_Ois__measure(T_a,V_f_2) % 165.14/165.03 => c_FunDef_Ois__measure(tc_prod(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_b,T_a)),V_f_2),c_Product__Type_Osnd(T_b,T_a))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_is__measure_Ointros,axiom, % 165.14/165.03 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_is__measure_Oequations,axiom, % 165.14/165.03 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_is__measure_Osimps,axiom, % 165.14/165.03 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_measure__size,axiom, % 165.14/165.03 ! [T_a] : % 165.14/165.03 ( class_Nat_Osize(T_a) % 165.14/165.03 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_measure__fst,axiom, % 165.14/165.03 ! [T_b,V_f_2,T_a] : % 165.14/165.03 ( c_FunDef_Ois__measure(T_a,V_f_2) % 165.14/165.03 => c_FunDef_Ois__measure(tc_prod(T_a,T_b),hAPP(hAPP(c_COMBB(T_a,tc_Nat_Onat,tc_prod(T_a,T_b)),V_f_2),c_Product__Type_Ofst(T_a,T_b))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_equal__fun__def,axiom, % 165.14/165.03 ! [V_g_2,V_f_2,T_a,T_b] : % 165.14/165.03 ( ( class_HOL_Oequal(T_b) % 165.14/165.03 & class_Enum_Oenum(T_a) ) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 165.14/165.03 <=> ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) % 165.14/165.03 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_transfer__morphism__int__nat,axiom, % 165.14/165.03 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)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__equal,axiom, % 165.14/165.03 ! [T_a] : % 165.14/165.03 ( class_HOL_Oequal(T_a) % 165.14/165.03 => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_equal__eq,axiom, % 165.14/165.03 ! [V_y_2,V_x_2,T_a] : % 165.14/165.03 ( class_HOL_Oequal(T_a) % 165.14/165.03 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2)) % 165.14/165.03 <=> V_x_2 = V_y_2 ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_equal__refl,axiom, % 165.14/165.03 ! [V_x,T_a] : % 165.14/165.03 ( class_HOL_Oequal(T_a) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_equal,axiom, % 165.14/165.03 ! [T_a] : % 165.14/165.03 ( class_HOL_Oequal(T_a) % 165.14/165.03 => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_bool_Osize_I3_J,axiom, % 165.14/165.03 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(fact_bool_Osize_I4_J,axiom, % 165.14/165.03 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(fact_size__code,axiom, % 165.14/165.03 ! [V_xq_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),T_a),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 165.14/165.03 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 165.14/165.03 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 165.14/165.03 => hAPP(c_New__DSequence_Opos__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_a) ) % 165.14/165.03 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 165.14/165.03 => hAPP(c_New__DSequence_Opos__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_f_2),V_i_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I12_J,axiom, % 165.14/165.03 ! [V_k1_2] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin)) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I8_J,axiom, % 165.14/165.03 ! [V_k2_2] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2))) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I11_J,axiom, % 165.14/165.03 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I7_J,axiom, % 165.14/165.03 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I9_J,axiom, % 165.14/165.03 ! [V_k1_2] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls)) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I3_J,axiom, % 165.14/165.03 ! [V_k2_2] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2))) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I15_J,axiom, % 165.14/165.03 ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OBit0(V_k2))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I14_J,axiom, % 165.14/165.03 ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OBit1(V_k2))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_equal__int__def,axiom, % 165.14/165.03 ! [V_l_2,V_k_2] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) % 165.14/165.03 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__number__of__int__code,axiom, % 165.14/165.03 ! [V_l_2,V_k_2] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I6_J,axiom, % 165.14/165.03 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I16_J,axiom, % 165.14/165.03 ! [V_k2_2,V_k1_2] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I1_J,axiom, % 165.14/165.03 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I13_J,axiom, % 165.14/165.03 ! [V_k2_2,V_k1_2] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I10_J,axiom, % 165.14/165.03 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I4_J,axiom, % 165.14/165.03 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I2_J,axiom, % 165.14/165.03 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__code_I5_J,axiom, % 165.14/165.03 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_lazy__sequence__size__code,axiom, % 165.14/165.03 ! [V_xq_2,V_s_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_a,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_a),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 165.14/165.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Opos__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__int__refl,axiom, % 165.14/165.03 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_seq__case,axiom, % 165.14/165.03 ! [V_xq_2,V_g_2,V_f_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f_2,V_g_2,V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(T_a,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),T_a),V_g_2)),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_yieldn__def,axiom, % 165.14/165.03 ! [T_a] : c_Lazy__Sequence_Oyieldn(T_a) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_a),T_a,c_Lazy__Sequence_Oyield(T_a)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_New__DSequence_Opos__empty__def,axiom, % 165.14/165.03 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 165.14/165.03 % 165.14/165.03 fof(fact_New__DSequence_Opos__bind__def,axiom, % 165.14/165.03 ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Opos__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_f_2),V_i_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_pos__empty__def,axiom, % 165.14/165.03 ! [V_seed_2,V_size_2,V_nrandom_2,T_a] : c_New__Random__Sequence_Opos__empty(T_a,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_a) ). % 165.14/165.03 % 165.14/165.03 fof(fact_pos__bind__def,axiom, % 165.14/165.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 165.14/165.03 ! [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))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 165.14/165.03 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 165.14/165.03 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact__01,axiom, % 165.14/165.03 ! [V_xq,V_x,T_a] : hAPP(c_Lazy__Sequence_Oyield(T_a),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq)) = hAPP(c_Option_Ooption_OSome(tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_Product__Type_OPair(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_x),V_xq)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_lazy__sequence_Oinject,axiom, % 165.14/165.03 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] : % 165.14/165.03 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H_2,V_lazy__sequence_H_2) % 165.14/165.03 <=> ( V_a_2 = V_a_H_2 % 165.14/165.03 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_pos__map__def,axiom, % 165.14/165.03 ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Opos__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),T_b,c_New__Random__Sequence_Opos__single(T_a)),V_f_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 165.14/165.03 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 165.14/165.03 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 165.14/165.03 => hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_a) ) % 165.14/165.03 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 165.14/165.03 => hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_f_2),V_i_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 165.14/165.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Oneg__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_pos__single__def,axiom, % 165.14/165.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_a,V_x_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_New__DSequence_Opos__single__def,axiom, % 165.14/165.03 ! [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) ). % 165.14/165.03 % 165.14/165.03 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 165.14/165.03 ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Oneg__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_f_2),V_i_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_neg__bind__def,axiom, % 165.14/165.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact__02,axiom, % 165.14/165.03 ! [V_s2_2,V_s1_2,T_b,T_a] : c_Lazy__Sequence_Oproduct(T_a,T_b,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_a,tc_prod(T_a,T_b),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_a),c_Lazy__Sequence_Obind(T_b,tc_prod(T_a,T_b),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_b),c_Lazy__Sequence_Osingle(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_neg__map__def,axiom, % 165.14/165.03 ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Oneg__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),T_b,c_New__Random__Sequence_Oneg__single(T_a)),V_f_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_small__lazy__list_Osimps,axiom, % 165.14/165.03 ! [V_d_2,T_a] : % 165.14/165.03 ( class_Lazy__Sequence_Osmall__lazy(T_a) % 165.14/165.03 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_a),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_a),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),c_Lazy__Sequence_Oproduct(T_a,tc_List_Olist(T_a),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_a)))),c_List_Olist_OCons(T_a))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_a)))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_small__lazy__prod__def,axiom, % 165.14/165.03 ! [V_d,T_b,T_a] : % 165.14/165.03 ( ( class_Lazy__Sequence_Osmall__lazy(T_a) % 165.14/165.03 & class_Lazy__Sequence_Osmall__lazy(T_b) ) % 165.14/165.03 => 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)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact__03,axiom, % 165.14/165.03 ! [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)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_neg__single__def,axiom, % 165.14/165.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_a,V_x_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_New__DSequence_Opos__union__def,axiom, % 165.14/165.03 ! [V_i_2,V_yq_2,V_xq_2,T_a] : hAPP(c_New__DSequence_Opos__union(T_a,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_a,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_New__DSequence_Oneg__single__def,axiom, % 165.14/165.03 ! [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) ). % 165.14/165.03 % 165.14/165.03 fof(fact_pos__union__def,axiom, % 165.14/165.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_a] : c_New__Random__Sequence_Opos__union(T_a,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_a,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_small__lazy_H_Osimps,axiom, % 165.14/165.03 ! [V_i,V_d] : % 165.14/165.03 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 165.14/165.03 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 165.14/165.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 165.14/165.03 => 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)))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_small__lazy_H_Opsimps,axiom, % 165.14/165.03 ! [V_i_2,V_d_2] : % 165.14/165.03 ( 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))) % 165.14/165.03 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 165.14/165.03 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 165.14/165.03 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 165.14/165.03 => 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)))) ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_small__lazy__int__def,axiom, % 165.14/165.03 ! [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)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_small__lazy_H_Opinduct,axiom, % 165.14/165.03 ! [V_P_2,V_a1_2,V_a0_2] : % 165.14/165.03 ( 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))) % 165.14/165.03 => ( ! [B_d,B_i] : % 165.14/165.03 ( 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))) % 165.14/165.03 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 165.14/165.03 => hBOOL(hAPP(hAPP(V_P_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) % 165.14/165.03 => hBOOL(hAPP(hAPP(V_P_2,B_d),B_i)) ) ) % 165.14/165.03 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_hb__flat_Osimps_I2_J,axiom, % 165.14/165.03 ! [V_xqq_2,V_xq_2,T_a] : c_Lazy__Sequence_Ohb__flat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_xq_2,V_xqq_2)) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(T_a),hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)),tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)),c_Lazy__Sequence_Ohit__bound(T_a),c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))),V_xq_2),c_Lazy__Sequence_Ohb__flat(T_a,V_xqq_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_New__DSequence_Oneg__union__def,axiom, % 165.14/165.03 ! [V_i_2,V_y_2,V_x_2,T_a] : hAPP(c_New__DSequence_Oneg__union(T_a,V_x_2,V_y_2),V_i_2) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(T_a),hAPP(V_x_2,V_i_2),hAPP(V_y_2,V_i_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_hb__bind__def,axiom, % 165.14/165.03 ! [V_f_2,V_xq_2,T_a,T_b] : c_Lazy__Sequence_Ohb__bind(T_b,T_a,V_xq_2,V_f_2) = c_Lazy__Sequence_Ohb__flat(T_a,c_Lazy__Sequence_Ohb__map(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)),V_f_2,V_xq_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_hb__map_Osimps_I2_J,axiom, % 165.14/165.03 ! [V_xq_2,V_x_2,V_f_2,T_a,T_b] : c_Lazy__Sequence_Ohb__map(T_b,T_a,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(T_b),V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(T_a),hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_x_2),c_Lazy__Sequence_Ohb__map(T_b,T_a,V_f_2,V_xq_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_neg__union__def,axiom, % 165.14/165.03 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_a] : c_New__Random__Sequence_Oneg__union(T_a,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__union(T_a,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_New__DSequence_Oneg__map__def,axiom, % 165.14/165.03 ! [V_i_2,V_xq_2,V_f_2,T_a,T_b] : c_New__DSequence_Oneg__map(T_b,T_a,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Ohb__map(T_b,T_a,V_f_2,hAPP(V_xq_2,V_i_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_length__splice,axiom, % 165.14/165.03 ! [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)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_acyclicP__converse,axiom, % 165.14/165.03 ! [V_r_2,T_a] : % 165.14/165.03 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Predicate_Oconversep(T_a,T_a,V_r_2)))) % 165.14/165.03 <=> c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),V_r_2))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_converse__join,axiom, % 165.14/165.03 ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_splice_Osimps_I3_J,axiom, % 165.14/165.03 ! [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))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_splice__Nil2,axiom, % 165.14/165.03 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 165.14/165.03 % 165.14/165.03 fof(fact_splice_Osimps_I1_J,axiom, % 165.14/165.03 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 165.14/165.03 % 165.14/165.03 fof(fact_conversep__noteq,axiom, % 165.14/165.03 ! [V_y_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot)),c_fequal)),V_x_2),V_y_2)) % 165.14/165.03 <=> V_x_2 != V_y_2 ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_conversepD,axiom, % 165.14/165.03 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_conversep_Ointros,axiom, % 165.14/165.03 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_b_2),V_a_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_conversep_Oequations,axiom, % 165.14/165.03 ! [V_a1_2,V_a2_2,V_r_2,T_b,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a2_2),V_a1_2)) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_conversep__iff,axiom, % 165.14/165.03 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_conversep__conversep,axiom, % 165.14/165.03 ! [V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Oconversep(T_a,T_b,V_r_2)) = V_r_2 ). % 165.14/165.03 % 165.14/165.03 fof(fact_conversep__eq,axiom, % 165.14/165.03 ! [T_a] : c_Predicate_Oconversep(T_a,T_a,c_fequal) = c_fequal ). % 165.14/165.03 % 165.14/165.03 fof(fact_converse__meet,axiom, % 165.14/165.03 ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_converse__pred__comp,axiom, % 165.14/165.03 ! [V_s_2,V_r_2,T_c,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Opred__comp(T_b,T_c,T_a,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_a,T_c,T_b,c_Predicate_Oconversep(T_c,T_a,V_s_2),c_Predicate_Oconversep(T_b,T_c,V_r_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_conversep__converse__eq,axiom, % 165.14/165.03 ! [V_y_2,V_x_2,V_r_2,T_b,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2),V_y_2)) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_splice_Osimps_I2_J,axiom, % 165.14/165.03 ! [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) ). % 165.14/165.03 % 165.14/165.03 fof(fact_tl__replicate,axiom, % 165.14/165.03 ! [V_x,T_a,V_n] : % 165.14/165.03 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.03 => 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) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_eq__comp__r,axiom, % 165.14/165.03 ! [V_R_2,T_a] : c_Predicate_Opred__comp(T_a,T_a,T_a,c_fequal,c_Predicate_Opred__comp(T_a,T_a,T_a,V_R_2,c_fequal)) = V_R_2 ). % 165.14/165.03 % 165.14/165.03 fof(fact_in__set__replicate,axiom, % 165.14/165.03 ! [V_y_2,V_n_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_y_2)))) % 165.14/165.03 <=> ( V_x_2 = V_y_2 % 165.14/165.03 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_map__replicate,axiom, % 165.14/165.03 ! [V_x_2,V_n_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_a,V_n_2,hAPP(V_f_2,V_x_2)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_replicate__add,axiom, % 165.14/165.03 ! [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)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_nth__replicate,axiom, % 165.14/165.03 ! [V_x,T_a,V_n,V_i] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 165.14/165.03 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_replicate__eq__replicate,axiom, % 165.14/165.03 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_a] : % 165.14/165.03 ( c_List_Oreplicate(T_a,V_m_2,V_x_2) = c_List_Oreplicate(T_a,V_n_2,V_y_2) % 165.14/165.03 <=> ( V_m_2 = V_n_2 % 165.14/165.03 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.03 => V_x_2 = V_y_2 ) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_hd__replicate,axiom, % 165.14/165.03 ! [V_x,T_a,V_n] : % 165.14/165.03 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.03 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_drop__replicate,axiom, % 165.14/165.03 ! [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) ). % 165.14/165.03 % 165.14/165.03 fof(fact_last__replicate,axiom, % 165.14/165.03 ! [V_x,T_a,V_n] : % 165.14/165.03 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.03 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_take__replicate,axiom, % 165.14/165.03 ! [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) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Ball__set__replicate,axiom, % 165.14/165.03 ! [V_P_2,V_a_2,V_n_2,T_a] : % 165.14/165.03 ( ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2)))) % 165.14/165.03 => hBOOL(hAPP(V_P_2,B_x)) ) % 165.14/165.03 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 165.14/165.03 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_Bex__set__replicate,axiom, % 165.14/165.03 ! [V_P_2,V_a_2,V_n_2,T_a] : % 165.14/165.03 ( ? [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2)))) % 165.14/165.03 & hBOOL(hAPP(V_P_2,B_x)) ) % 165.14/165.03 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 165.14/165.03 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_rev__replicate,axiom, % 165.14/165.03 ! [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) ). % 165.14/165.03 % 165.14/165.03 fof(fact_append__replicate__commute,axiom, % 165.14/165.03 ! [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)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_concat__replicate__trivial,axiom, % 165.14/165.03 ! [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) ). % 165.14/165.03 % 165.14/165.03 fof(fact_replicate__empty,axiom, % 165.14/165.03 ! [V_x_2,V_n_2,T_a] : % 165.14/165.03 ( c_List_Oreplicate(T_a,V_n_2,V_x_2) = c_List_Olist_ONil(T_a) % 165.14/165.03 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_empty__replicate,axiom, % 165.14/165.03 ! [V_x_2,V_n_2,T_a] : % 165.14/165.03 ( c_List_Olist_ONil(T_a) = c_List_Oreplicate(T_a,V_n_2,V_x_2) % 165.14/165.03 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_replicate__0,axiom, % 165.14/165.03 ! [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) ). % 165.14/165.03 % 165.14/165.03 fof(fact_filter__replicate,axiom, % 165.14/165.03 ! [V_n_2,T_a,V_x_2,V_P_2] : % 165.14/165.03 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.03 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = c_List_Oreplicate(T_a,V_n_2,V_x_2) ) % 165.14/165.03 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 165.14/165.03 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = c_List_Olist_ONil(T_a) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_replicate__app__Cons__same,axiom, % 165.14/165.03 ! [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)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_replicate__Suc,axiom, % 165.14/165.03 ! [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)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_replicate__append__same,axiom, % 165.14/165.03 ! [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)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_map__replicate__const,axiom, % 165.14/165.03 ! [V_lst_2,V_k_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_k_2)),V_lst_2) = c_List_Oreplicate(T_a,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_lst_2),V_k_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_length__replicate,axiom, % 165.14/165.03 ! [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 ). % 165.14/165.03 % 165.14/165.03 fof(fact_replicate__length__filter,axiom, % 165.14/165.03 ! [V_xs_2,V_x_2,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_a,hAPP(c_fequal,V_x_2)),V_xs_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_zip__replicate,axiom, % 165.14/165.03 ! [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)) ). % 165.14/165.03 % 165.14/165.03 fof(fact_map__replicate__trivial,axiom, % 165.14/165.03 ! [V_i_2,V_x_2,T_a] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),hAPP(c_COMBK(T_a,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_a,V_i_2,V_x_2) ). % 165.14/165.03 % 165.14/165.03 fof(fact_set__replicate__conv__if,axiom, % 165.14/165.03 ! [V_x_2,T_a,V_n_2] : % 165.14/165.03 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.03 => hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 165.14/165.03 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.03 => hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_set__replicate,axiom, % 165.14/165.03 ! [V_x_2,T_a,V_n_2] : % 165.14/165.03 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 165.14/165.03 => hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_set__replicate__Suc,axiom, % 165.14/165.03 ! [V_x_2,V_n_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 165.14/165.03 % 165.14/165.03 fof(fact_field__le__epsilon,axiom, % 165.14/165.03 ! [V_y,V_x,T_a] : % 165.14/165.03 ( class_Fields_Olinordered__field(T_a) % 165.14/165.03 => ( ! [B_e] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 165.14/165.03 => 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))) ) % 165.14/165.03 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_refl__on__INTER,axiom, % 165.14/165.03 ! [V_r_2,V_A_2,T_b,V_S_2,T_a] : % 165.14/165.03 ( ! [B_x] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 165.14/165.03 => c_Relation_Orefl__on(T_b,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) ) % 165.14/165.03 => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_List_Omember__def,axiom, % 165.14/165.03 ! [V_x_2,V_xs_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_List_Omember(T_a),V_xs_2),V_x_2)) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_in__set__member,axiom, % 165.14/165.03 ! [V_xs_2,V_x_2,T_a] : % 165.14/165.03 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 165.14/165.03 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_a),V_xs_2),V_x_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(fact_member__set,axiom, % 165.14/165.03 ! [T_a] : c_List_Omember(T_a) = c_List_Oset(T_a) ). % 165.14/165.03 % 165.14/165.03 %----Arity declarations (237) % 165.14/165.03 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 165.14/165.03 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Lattices_Obounded__lattice(T_1) % 165.14/165.03 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 165.14/165.03 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Lattices_Obounded__lattice(T_1) % 165.14/165.03 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Lattices_Obounded__lattice(T_1) % 165.14/165.03 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Lattices_Olattice(T_1) % 165.14/165.03 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Lattices_Olattice(T_1) % 165.14/165.03 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Lattices_Odistrib__lattice(T_1) % 165.14/165.03 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Lattices_Oboolean__algebra(T_1) % 165.14/165.03 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Orderings_Opreorder,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Orderings_Opreorder(T_1) % 165.14/165.03 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Finite__Set_Ofinite,axiom, % 165.14/165.03 ! [T_1,T_2] : % 165.14/165.03 ( ( class_Finite__Set_Ofinite(T_2) % 165.14/165.03 & class_Finite__Set_Ofinite(T_1) ) % 165.14/165.03 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Lattices_Olattice,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Lattices_Olattice(T_1) % 165.14/165.03 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Orderings_Oorder,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Orderings_Oorder(T_1) % 165.14/165.03 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Orderings_Otop,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Orderings_Otop(T_1) % 165.14/165.03 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Orderings_Oord,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Orderings_Oord(T_1) % 165.14/165.03 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Orderings_Obot,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Orderings_Obot(T_1) % 165.14/165.03 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Groups_Ouminus,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Groups_Ouminus(T_1) % 165.14/165.03 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Groups_Ominus,axiom, % 165.14/165.03 ! [T_2,T_1] : % 165.14/165.03 ( class_Groups_Ominus(T_1) % 165.14/165.03 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__HOL_Oequal,axiom, % 165.14/165.03 ! [T_1,T_2] : % 165.14/165.03 ( ( class_Enum_Oenum(T_2) % 165.14/165.03 & class_HOL_Oequal(T_1) ) % 165.14/165.03 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_fun__Enum_Oenum,axiom, % 165.14/165.03 ! [T_1,T_2] : % 165.14/165.03 ( ( class_Enum_Oenum(T_2) % 165.14/165.03 & class_Enum_Oenum(T_1) ) % 165.14/165.03 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Com__Ocom__HOL_Oequal,axiom, % 165.14/165.03 class_HOL_Oequal(tc_Com_Ocom) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Com__Ocom__Nat_Osize,axiom, % 165.14/165.03 class_Nat_Osize(tc_Com_Ocom) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 165.14/165.03 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 165.14/165.03 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 165.14/165.03 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 165.14/165.03 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 165.14/165.03 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 165.14/165.03 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 165.14/165.03 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 165.14/165.03 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 165.14/165.03 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 165.14/165.03 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 165.14/165.03 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 165.14/165.03 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 165.14/165.03 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 165.14/165.03 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 165.14/165.03 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 165.14/165.03 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 165.14/165.03 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 165.14/165.03 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom, % 165.14/165.03 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 165.14/165.03 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 165.14/165.03 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 165.14/165.03 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 165.14/165.03 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 165.14/165.03 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 165.14/165.03 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 165.14/165.03 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 165.14/165.03 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 165.14/165.03 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 165.14/165.03 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 165.14/165.03 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 165.14/165.03 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 165.14/165.03 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 165.14/165.03 class_Divides_Osemiring__div(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 165.14/165.03 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 165.14/165.03 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 165.14/165.03 class_Groups_Oab__group__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 165.14/165.03 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 165.14/165.03 class_Rings_Oordered__ring(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 165.14/165.03 class_Orderings_Opreorder(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 165.14/165.03 class_Orderings_Olinorder(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 165.14/165.03 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 165.14/165.03 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 165.14/165.03 class_Groups_Omonoid__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 165.14/165.03 class_Smallcheck_Osmall(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 165.14/165.03 class_Rings_Osemiring__1(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 165.14/165.03 class_Rings_Osemiring__0(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 165.14/165.03 class_Lattices_Olattice(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 165.14/165.03 class_Groups_Ogroup__add(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 165.14/165.03 class_Divides_Oring__div(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 165.14/165.03 class_Rings_Omult__zero(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 165.14/165.03 class_Orderings_Oorder(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 165.14/165.03 class_Int_Oring__char__0(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 165.14/165.03 class_Int_Onumber__ring(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 165.14/165.03 class_Rings_Osemiring(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Orderings_Oord,axiom, % 165.14/165.03 class_Orderings_Oord(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 165.14/165.03 class_Groups_Ouminus(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 165.14/165.03 class_Groups_Osgn__if(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 165.14/165.03 class_Groups_Oabs__if(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 165.14/165.03 class_Rings_Oring__1(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Ominus,axiom, % 165.14/165.03 class_Groups_Ominus(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Power_Opower,axiom, % 165.14/165.03 class_Power_Opower(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Ozero,axiom, % 165.14/165.03 class_Groups_Ozero(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Oring,axiom, % 165.14/165.03 class_Rings_Oring(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Rings_Oidom,axiom, % 165.14/165.03 class_Rings_Oidom(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Int_Onumber,axiom, % 165.14/165.03 class_Int_Onumber(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__Groups_Oone,axiom, % 165.14/165.03 class_Groups_Oone(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Int__Oint__HOL_Oequal,axiom, % 165.14/165.03 class_HOL_Oequal(tc_Int_Oint) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 165.14/165.03 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 165.14/165.03 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 165.14/165.03 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 165.14/165.03 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 165.14/165.03 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 165.14/165.03 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 165.14/165.03 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 165.14/165.03 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 165.14/165.03 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 165.14/165.03 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 165.14/165.03 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 165.14/165.03 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 165.14/165.03 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 165.14/165.03 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 165.14/165.03 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 165.14/165.03 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 165.14/165.03 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 165.14/165.03 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 165.14/165.03 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 165.14/165.03 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 165.14/165.03 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 165.14/165.03 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 165.14/165.03 class_Orderings_Owellorder(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 165.14/165.03 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 165.14/165.03 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 165.14/165.03 class_Orderings_Opreorder(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 165.14/165.03 class_Orderings_Olinorder(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 165.14/165.03 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 165.14/165.03 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 165.14/165.03 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 165.14/165.03 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 165.14/165.03 class_Lattices_Olattice(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 165.14/165.03 class_Rings_Omult__zero(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 165.14/165.03 class_Orderings_Oorder(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 165.14/165.03 class_Rings_Osemiring(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 165.14/165.03 class_Orderings_Oord(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 165.14/165.03 class_Orderings_Obot(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 165.14/165.03 class_Groups_Ominus(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Power_Opower,axiom, % 165.14/165.03 class_Power_Opower(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 165.14/165.03 class_Groups_Ozero(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Int_Onumber,axiom, % 165.14/165.03 class_Int_Onumber(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Groups_Oone,axiom, % 165.14/165.03 class_Groups_Oone(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__HOL_Oequal,axiom, % 165.14/165.03 class_HOL_Oequal(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Nat__Onat__Nat_Osize,axiom, % 165.14/165.03 class_Nat_Osize(tc_Nat_Onat) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 165.14/165.03 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 165.14/165.03 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 165.14/165.03 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 165.14/165.03 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 165.14/165.03 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 165.14/165.03 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 165.14/165.03 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 165.14/165.03 class_Orderings_Opreorder(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 165.14/165.03 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 165.14/165.03 class_Lattices_Olattice(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 165.14/165.03 class_Orderings_Oorder(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 165.14/165.03 class_Orderings_Otop(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 165.14/165.03 class_Orderings_Oord(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 165.14/165.03 class_Orderings_Obot(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 165.14/165.03 class_Groups_Ouminus(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 165.14/165.03 class_Groups_Ominus(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__HOL_Oequal,axiom, % 165.14/165.03 class_HOL_Oequal(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 165.14/165.03 class_Enum_Oenum(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_HOL__Obool__Nat_Osize,axiom, % 165.14/165.03 class_Nat_Osize(tc_HOL_Obool) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Com__Ostate__HOL_Oequal,axiom, % 165.14/165.03 class_HOL_Oequal(tc_Com_Ostate) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Com__Ostate__Nat_Osize,axiom, % 165.14/165.03 class_Nat_Osize(tc_Com_Ostate) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Com__Ovname__HOL_Oequal,axiom, % 165.14/165.03 class_HOL_Oequal(tc_Com_Ovname) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Com__Ovname__Nat_Osize,axiom, % 165.14/165.03 class_Nat_Osize(tc_Com_Ovname) ). % 165.14/165.03 % 165.14/165.03 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom, % 165.14/165.03 ! [T_1] : % 165.14/165.03 ( class_Lazy__Sequence_Osmall__lazy(T_1) % 165.14/165.03 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_List__Olist__HOL_Oequal,axiom, % 165.14/165.03 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ). % 165.14/165.03 % 165.14/165.03 fof(arity_List__Olist__Nat_Osize,axiom, % 165.14/165.03 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 165.14/165.03 % 165.14/165.03 fof(arity_sum__Finite__Set_Ofinite,axiom, % 165.14/165.03 ! [T_1,T_2] : % 165.14/165.03 ( ( class_Finite__Set_Ofinite(T_2) % 165.14/165.03 & class_Finite__Set_Ofinite(T_1) ) % 165.14/165.03 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_sum__HOL_Oequal,axiom, % 165.14/165.03 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ). % 165.14/165.03 % 165.14/165.03 fof(arity_sum__Enum_Oenum,axiom, % 165.14/165.03 ! [T_1,T_2] : % 165.14/165.03 ( ( class_Enum_Oenum(T_2) % 165.14/165.03 & class_Enum_Oenum(T_1) ) % 165.14/165.03 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_sum__Nat_Osize,axiom, % 165.14/165.03 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 165.14/165.03 ! [T_1] : % 165.14/165.03 ( class_Finite__Set_Ofinite(T_1) % 165.14/165.03 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Option__Ooption__HOL_Oequal,axiom, % 165.14/165.03 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 165.14/165.03 ! [T_1] : % 165.14/165.03 ( class_Enum_Oenum(T_1) % 165.14/165.03 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Option__Ooption__Nat_Osize,axiom, % 165.14/165.03 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 165.14/165.03 % 165.14/165.03 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom, % 165.14/165.03 ! [T_1,T_2] : % 165.14/165.03 ( ( class_Lazy__Sequence_Osmall__lazy(T_2) % 165.14/165.03 & class_Lazy__Sequence_Osmall__lazy(T_1) ) % 165.14/165.03 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_prod__Finite__Set_Ofinite,axiom, % 165.14/165.03 ! [T_1,T_2] : % 165.14/165.03 ( ( class_Finite__Set_Ofinite(T_2) % 165.14/165.03 & class_Finite__Set_Ofinite(T_1) ) % 165.14/165.03 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_prod__Smallcheck_Osmall,axiom, % 165.14/165.03 ! [T_1,T_2] : % 165.14/165.03 ( ( class_Smallcheck_Osmall(T_2) % 165.14/165.03 & class_Smallcheck_Osmall(T_1) ) % 165.14/165.03 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_prod__HOL_Oequal,axiom, % 165.14/165.03 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ). % 165.14/165.03 % 165.14/165.03 fof(arity_prod__Enum_Oenum,axiom, % 165.14/165.03 ! [T_1,T_2] : % 165.14/165.03 ( ( class_Enum_Oenum(T_2) % 165.14/165.03 & class_Enum_Oenum(T_1) ) % 165.14/165.03 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 165.14/165.03 % 165.14/165.03 fof(arity_prod__Nat_Osize,axiom, % 165.14/165.03 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom, % 165.14/165.03 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 165.14/165.03 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 165.14/165.03 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom, % 165.14/165.03 class_HOL_Oequal(tc_Product__Type_Ounit) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 165.14/165.03 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 165.14/165.03 class_Nat_Osize(tc_Product__Type_Ounit) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom, % 165.14/165.03 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 165.14/165.03 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom, % 165.14/165.03 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 165.14/165.03 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 165.14/165.03 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 165.14/165.03 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 165.14/165.03 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 165.14/165.03 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 165.14/165.03 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 165.14/165.03 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 165.14/165.03 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 165.14/165.03 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 165.14/165.03 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 165.14/165.03 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 165.14/165.03 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 165.14/165.03 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 165.14/165.03 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 165.14/165.03 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 165.14/165.03 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 165.14/165.03 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 165.14/165.03 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 165.14/165.03 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 165.14/165.03 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 165.14/165.03 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 165.14/165.03 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 165.14/165.03 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 165.14/165.03 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 165.14/165.03 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 165.14/165.03 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 165.14/165.03 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 165.14/165.03 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 165.14/165.03 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 165.14/165.03 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 165.14/165.03 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 165.14/165.03 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 165.14/165.03 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 165.14/165.03 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 165.14/165.03 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 165.14/165.03 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 165.14/165.03 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom, % 165.14/165.03 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 165.14/165.03 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom, % 165.14/165.03 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 165.14/165.03 % 165.14/165.03 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 165.14/165.03 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 165.14/165.03 % 165.14/165.03 %----Helper facts (20) % 165.14/165.03 fof(help_c__COMBI__1,axiom, % 165.14/165.03 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 165.14/165.03 % 165.14/165.03 fof(help_c__COMBK__1,axiom, % 165.14/165.03 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 165.14/165.03 % 165.14/165.03 fof(help_c__COMBB__1,axiom, % 165.14/165.03 ! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(hAPP(hAPP(c_COMBB(T_b,T_a,T_c),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__COMBC__1,axiom, % 165.14/165.03 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__COMBS__1,axiom, % 165.14/165.03 ! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBS(T_b,T_c,T_a),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fequal__1,axiom, % 165.14/165.03 ! [V_y_2,V_x_2] : % 165.14/165.03 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 165.14/165.03 | V_x_2 = V_y_2 ) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fequal__2,axiom, % 165.14/165.03 ! [V_y_2,V_x_2] : % 165.14/165.03 ( V_x_2 != V_y_2 % 165.14/165.03 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fFalse__1,axiom, % 165.14/165.03 ~ hBOOL(c_fFalse) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fTrue__1,axiom, % 165.14/165.03 hBOOL(c_fTrue) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fNot__1,axiom, % 165.14/165.03 ! [V_P_2] : % 165.14/165.03 ( ~ hBOOL(hAPP(c_fNot,V_P_2)) % 165.14/165.03 | ~ hBOOL(V_P_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fNot__2,axiom, % 165.14/165.03 ! [V_P_2] : % 165.14/165.03 ( ~ ~ hBOOL(V_P_2) % 165.14/165.03 | hBOOL(hAPP(c_fNot,V_P_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fconj__1,axiom, % 165.14/165.03 ! [V_Q_2,V_P_2] : % 165.14/165.03 ( ~ hBOOL(V_P_2) % 165.14/165.03 | ~ hBOOL(V_Q_2) % 165.14/165.03 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fconj__2,axiom, % 165.14/165.03 ! [V_Q_2,V_P_2] : % 165.14/165.03 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 165.14/165.03 | hBOOL(V_P_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fconj__3,axiom, % 165.14/165.03 ! [V_Q_2,V_P_2] : % 165.14/165.03 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 165.14/165.03 | hBOOL(V_Q_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fdisj__1,axiom, % 165.14/165.03 ! [V_Q_2,V_P_2] : % 165.14/165.03 ( ~ hBOOL(V_P_2) % 165.14/165.03 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fdisj__2,axiom, % 165.14/165.03 ! [V_P_2,V_Q_2] : % 165.14/165.03 ( ~ hBOOL(V_Q_2) % 165.14/165.03 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fdisj__3,axiom, % 165.14/165.03 ! [V_Q_2,V_P_2] : % 165.14/165.03 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) % 165.14/165.03 | hBOOL(V_P_2) % 165.14/165.03 | hBOOL(V_Q_2) ) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fimplies__1,axiom, % 165.14/165.03 ! [V_Q_2,V_P_2] : % 165.14/165.03 ( hBOOL(V_P_2) % 165.14/165.03 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fimplies__2,axiom, % 165.14/165.03 ! [V_P_2,V_Q_2] : % 165.14/165.03 ( ~ hBOOL(V_Q_2) % 165.14/165.03 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 165.14/165.03 % 165.14/165.03 fof(help_c__fimplies__3,axiom, % 165.14/165.03 ! [V_Q_2,V_P_2] : % 165.14/165.03 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) % 165.14/165.03 | ~ hBOOL(V_P_2) % 165.14/165.03 | hBOOL(V_Q_2) ) ). % 165.14/165.03 % 165.14/165.03 %----Conjectures (5) % 165.14/165.03 fof(conj_0,hypothesis, % 165.14/165.03 c_Hoare__Mirabelle_Ostate__not__singleton ). % 165.14/165.03 % 165.14/165.03 fof(conj_1,hypothesis, % 165.14/165.03 c_Com_OWT__bodies ). % 165.14/165.03 % 165.14/165.03 fof(conj_2,hypothesis, % 165.14/165.03 hBOOL(hAPP(c_Com_OWT,v_c)) ). % 165.14/165.03 % 165.14/165.03 fof(conj_3,hypothesis, % 165.14/165.03 hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ). % 165.14/165.03 % 165.14/165.03 fof(conj_4,conjecture, % 165.14/165.03 c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Hoare__Mirabelle_OMGT),c_Com_Ocom_OBODY)),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 165.14/165.03 % 165.14/165.03 %------------------------------------------------------------------------------ % 165.14/165.03 %------------------------------------------- % 165.14/165.03 % Proof found % 165.14/165.03 % SZS status Theorem for theBenchmark % 165.14/165.03 % SZS output start Proof % 165.14/165.03 %ClaNum:10136(EqnAxiom:2837) % 165.14/165.03 %VarNum:69695(SingletonVarNum:20346) % 165.14/165.03 %MaxLitNum:8 % 165.14/165.03 %MaxfuncDepth:13 % 165.14/165.03 %SharedTerms:1082 % 165.14/165.03 %goalClause: 4560 % 165.14/165.03 %singleGoalClaCount:1 % 165.14/165.03 [2838]P1(a5000) % 165.14/165.03 [2839]P4(a5000) % 165.14/165.03 [2843]P24(a195) % 165.14/165.03 [2844]P25(a862) % 165.14/165.03 [2845]P25(a868) % 165.14/165.03 [2846]P104(a862) % 165.14/165.03 [2847]P104(a868) % 165.14/165.03 [2848]P104(a1) % 165.14/165.03 [2849]P104(a102) % 165.14/165.03 [2850]P105(a862) % 165.14/165.03 [2851]P105(a868) % 165.14/165.03 [2852]P105(a1) % 165.14/165.03 [2853]P105(a102) % 165.14/165.03 [2854]P106(a868) % 165.14/165.03 [2855]P106(a1) % 165.14/165.03 [2856]P106(a102) % 165.14/165.03 [2857]P107(a862) % 165.14/165.03 [2858]P107(a868) % 165.14/165.03 [2859]P107(a1) % 165.14/165.03 [2860]P107(a102) % 165.14/165.03 [2861]P26(a862) % 165.14/165.03 [2862]P26(a868) % 165.14/165.03 [2863]P26(a1) % 165.14/165.03 [2864]P27(a862) % 165.14/165.03 [2865]P27(a871) % 165.14/165.03 [2866]P99(a862) % 165.14/165.03 [2867]P99(a868) % 165.14/165.03 [2868]P99(a1) % 165.14/165.03 [2869]P64(a862) % 165.14/165.03 [2870]P65(a862) % 165.14/165.03 [2871]P65(a868) % 165.14/165.03 [2872]P65(a1) % 165.14/165.03 [2873]P65(a102) % 165.14/165.03 [2874]P77(a1) % 165.14/165.03 [2875]P66(a1) % 165.14/165.03 [2876]P67(a1) % 165.14/165.03 [2877]P81(a862) % 165.14/165.03 [2878]P82(a862) % 165.14/165.03 [2879]P82(a1) % 165.14/165.03 [2880]P100(a862) % 165.14/165.03 [2881]P100(a868) % 165.14/165.03 [2882]P100(a1) % 165.14/165.03 [2883]P97(a862) % 165.14/165.03 [2884]P97(a868) % 165.14/165.03 [2885]P97(a1) % 165.14/165.03 [2886]P78(a868) % 165.14/165.03 [2887]P78(a1) % 165.14/165.03 [2888]P78(a102) % 165.14/165.03 [2889]P68(a868) % 165.14/165.03 [2890]P68(a1) % 165.14/165.03 [2891]P68(a102) % 165.14/165.03 [2892]P69(a868) % 165.14/165.03 [2893]P69(a1) % 165.14/165.03 [2894]P69(a102) % 165.14/165.03 [2895]P70(a868) % 165.14/165.03 [2896]P70(a1) % 165.14/165.03 [2897]P70(a102) % 165.14/165.03 [2898]P83(a868) % 165.14/165.03 [2899]P83(a1) % 165.14/165.03 [2900]P83(a102) % 165.14/165.03 [2901]P84(a868) % 165.14/165.03 [2902]P84(a1) % 165.14/165.03 [2903]P84(a102) % 165.14/165.03 [2904]P86(a868) % 165.14/165.03 [2905]P86(a1) % 165.14/165.03 [2906]P86(a102) % 165.14/165.03 [2907]P108(a1) % 165.14/165.03 [2908]P112(a868) % 165.14/165.03 [2909]P112(a1) % 165.14/165.03 [2910]P112(a102) % 165.14/165.03 [2911]P73(a868) % 165.14/165.03 [2912]P73(a1) % 165.14/165.03 [2913]P73(a102) % 165.14/165.03 [2914]P113(a868) % 165.14/165.03 [2915]P113(a1) % 165.14/165.03 [2916]P113(a102) % 165.14/165.03 [2917]P123(a868) % 165.14/165.03 [2918]P123(a1) % 165.14/165.03 [2919]P114(a868) % 165.14/165.03 [2920]P114(a1) % 165.14/165.03 [2921]P114(a102) % 165.14/165.03 [2922]P124(a868) % 165.14/165.03 [2923]P124(a1) % 165.14/165.03 [2924]P124(a102) % 165.14/165.03 [2925]P125(a1) % 165.14/165.03 [2926]P115(a1) % 165.14/165.03 [2927]P71(a868) % 165.14/165.03 [2928]P71(a1) % 165.14/165.03 [2929]P71(a102) % 165.14/165.03 [2930]P79(a868) % 165.14/165.03 [2931]P79(a1) % 165.14/165.03 [2932]P79(a102) % 165.14/165.03 [2933]P137(a1) % 165.14/165.03 [2934]P126(a1) % 165.14/165.03 [2935]P118(a1) % 165.14/165.03 [2936]P109(a862) % 165.14/165.03 [2937]P98(a862) % 165.14/165.03 [2938]P74(a868) % 165.14/165.03 [2939]P74(a1) % 165.14/165.03 [2940]P74(a102) % 165.14/165.03 [2941]P140(a868) % 165.14/165.03 [2942]P140(a1) % 165.14/165.03 [2943]P140(a102) % 165.14/165.03 [2944]P127(a868) % 165.14/165.03 [2945]P127(a1) % 165.14/165.03 [2946]P127(a102) % 165.14/165.03 [2947]P90(a868) % 165.14/165.03 [2948]P90(a1) % 165.14/165.03 [2949]P90(a102) % 165.14/165.03 [2950]P80(a868) % 165.14/165.03 [2951]P80(a1) % 165.14/165.03 [2952]P80(a102) % 165.14/165.03 [2953]P75(a1) % 165.14/165.03 [2954]P139(a1) % 165.14/165.03 [2955]P128(a868) % 165.14/165.03 [2956]P128(a1) % 165.14/165.03 [2957]P128(a102) % 165.14/165.03 [2958]P141(a868) % 165.14/165.03 [2959]P141(a1) % 165.14/165.03 [2960]P141(a102) % 165.14/165.03 [2961]P87(a868) % 165.14/165.03 [2962]P87(a1) % 165.14/165.03 [2963]P87(a102) % 165.14/165.03 [2964]P121(a1) % 165.14/165.03 [2965]P122(a1) % 165.14/165.03 [2966]P133(a868) % 165.14/165.03 [2967]P133(a1) % 165.14/165.03 [2968]P133(a102) % 165.14/165.03 [2969]P135(a868) % 165.14/165.03 [2970]P135(a1) % 165.14/165.03 [2971]P135(a102) % 165.14/165.03 [2972]P134(a868) % 165.14/165.03 [2973]P134(a1) % 165.14/165.03 [2974]P134(a102) % 165.14/165.03 [2975]P129(a868) % 165.14/165.03 [2976]P129(a1) % 165.14/165.03 [2977]P129(a102) % 165.14/165.03 [2978]P119(a868) % 165.14/165.03 [2979]P119(a1) % 165.14/165.03 [2980]P119(a102) % 165.14/165.03 [2981]P130(a868) % 165.14/165.03 [2982]P130(a1) % 165.14/165.03 [2983]P130(a102) % 165.14/165.03 [2984]P131(a1) % 165.14/165.03 [2985]P132(a1) % 165.14/165.03 [2986]P110(a868) % 165.14/165.03 [2987]P110(a1) % 165.14/165.03 [2988]P110(a102) % 165.14/165.03 [2989]P138(a1) % 165.14/165.03 [2990]P101(a868) % 165.14/165.03 [2991]P101(a1) % 165.14/165.03 [2992]P101(a102) % 165.14/165.03 [2993]P142(a868) % 165.14/165.03 [2994]P142(a1) % 165.14/165.03 [2995]P142(a102) % 165.14/165.03 [2996]P28(a868) % 165.14/165.03 [2997]P28(a1) % 165.14/165.03 [2998]P28(a102) % 165.14/165.03 [2999]P91(a1) % 165.14/165.03 [3000]P29(a1) % 165.14/165.03 [3001]P88(a1) % 165.14/165.03 [3002]P85(a1) % 165.14/165.03 [3003]P136(a1) % 165.14/165.03 [3004]P72(a1) % 165.14/165.03 [3005]P76(a868) % 165.14/165.03 [3006]P76(a1) % 165.14/165.03 [3007]P76(a102) % 165.14/165.03 [3008]P30(a862) % 165.14/165.03 [3009]P92(a1) % 165.14/165.03 [3010]P93(a868) % 165.14/165.03 [3011]P93(a1) % 165.14/165.03 [3012]P93(a102) % 165.14/165.03 [3013]P143(a871) % 165.14/165.03 [3014]P143(a1) % 165.14/165.03 [3015]P89(a868) % 165.14/165.03 [3016]P89(a1) % 165.14/165.03 [3017]P89(a102) % 165.14/165.03 [3018]P59(a862) % 165.14/165.03 [3019]P59(a871) % 165.14/165.03 [3020]P94(a862) % 165.14/165.03 [3021]P94(a863) % 165.14/165.03 [3022]P94(a864) % 165.14/165.03 [3023]P94(a868) % 165.14/165.03 [3024]P94(a871) % 165.14/165.03 [3025]P94(a1) % 165.14/165.03 [3026]P94(a328) % 165.14/165.03 [3027]P94(a102) % 165.14/165.03 [3028]P94(a866) % 165.14/165.03 [3029]P111(a868) % 165.14/165.03 [3030]P103(a862) % 165.14/165.03 [3031]P103(a863) % 165.14/165.03 [3032]P103(a864) % 165.14/165.03 [3033]P103(a868) % 165.14/165.03 [3034]P103(a871) % 165.14/165.03 [3035]P103(a328) % 165.14/165.03 [3036]P103(a102) % 165.14/165.03 [3037]P103(a866) % 165.14/165.03 [3038]P102(a871) % 165.14/165.03 [3039]P102(a1) % 165.14/165.03 [3040]P96(a862) % 165.14/165.03 [3060]P41(a868,a251) % 165.14/165.03 [3061]P41(a868,a322) % 165.14/165.03 [4441]~E(a100,a84) % 165.14/165.03 [4442]~P24(a250) % 165.14/165.03 [2840]E(f2(a1),a84) % 165.14/165.03 [2841]E(f103(a102),a3) % 165.14/165.03 [2842]E(f22(a102),a23) % 165.14/165.03 [3041]E(f196(a868),f2(a868)) % 165.14/165.03 [3042]E(f32(a24),f2(a868)) % 165.14/165.03 [3043]E(f104(a868),f244(a868)) % 165.14/165.03 [3044]E(f113(a868),f245(a868)) % 165.14/165.03 [3045]E(f105(a1),f35(a1)) % 165.14/165.03 [3046]E(f85(a250),f2(a868)) % 165.14/165.03 [3047]E(f85(a195),f2(a868)) % 165.14/165.03 [3048]P31(f79(a1)) % 165.14/165.03 [3049]P31(f2(a1)) % 165.14/165.03 [3098]P24(f332(a25,a24)) % 165.14/165.03 [3099]P24(f332(a25,a873)) % 165.14/165.03 [3113]P41(f874(a868,a868),a36) % 165.14/165.03 [3470]E(f324(a868,a868,a251,a251),a36) % 165.14/165.03 [4443]~E(f79(a1),f2(a1)) % 165.14/165.03 [3050]E(f114(f2(a868)),f2(a868)) % 165.14/165.03 [3051]E(f4(f2(a102)),f2(a868)) % 165.14/165.03 [3063]E(f332(f80(a1),a84),a84) % 165.14/165.03 [3066]E(f332(a115,f2(a868)),f79(a868)) % 165.14/165.03 [3067]E(f332(a107,f79(a1)),f79(a868)) % 165.14/165.03 [3068]E(f332(a3,f79(a868)),f79(a102)) % 165.14/165.03 [3070]E(f332(a3,f2(a868)),f2(a102)) % 165.14/165.03 [3072]E(f332(f106(a1),a84),f2(a1)) % 165.14/165.03 [3073]E(f332(f106(a102),a84),f2(a102)) % 165.14/165.03 [3074]E(f332(a107,f2(a1)),f2(a868)) % 165.14/165.03 [3075]E(f332(f197(a862),a250),f2(a868)) % 165.14/165.03 [3076]E(f332(f197(a862),a195),f2(a868)) % 165.14/165.03 [3077]E(f332(f197(a863),a24),f2(a868)) % 165.14/165.03 [3078]E(f332(f106(a868),a84),f2(a868)) % 165.14/165.03 [3082]E(f332(f80(a1),f79(a1)),a100) % 165.14/165.03 [3089]E(f332(f80(a1),f2(a1)),f2(a1)) % 165.14/165.03 [3091]E(f332(f197(a102),f2(a102)),f2(a868)) % 165.14/165.03 [3092]E(f332(f103(a1),f79(a868)),f79(a1)) % 165.14/165.03 [3093]E(f332(f103(a1),f2(a868)),f2(a1)) % 165.14/165.03 [3100]E(f332(f208(a863),a877),f332(a26,a878)) % 165.14/165.03 [3109]E(f332(a107,f79(a1)),f332(a115,f2(a868))) % 165.14/165.03 [3110]E(f332(f180(a865,a863),a27),a26) % 165.14/165.03 [3111]E(f323(f874(a868,a868),a36),a37) % 165.14/165.03 [3112]E(f325(f874(a868,a868),a36),a69) % 165.14/165.03 [3134]E(f332(f253(a868),f2(a868)),f196(f875(a868,a862))) % 165.14/165.03 [3135]E(f332(f254(a868),f2(a868)),f255(f875(a868,a862))) % 165.14/165.03 [3143]P42(f196(f875(a1,a862))) % 165.14/165.03 [3179]E(f332(f332(f22(a102),f2(a102)),f79(a102)),f2(a102)) % 165.14/165.03 [3258]P24(f332(f332(f247(a1),a100),f2(a1))) % 165.14/165.03 [3283]P24(f332(f332(f246(a1),f2(a1)),f79(a1))) % 165.14/165.03 [3285]P24(f332(f332(f247(a1),f2(a1)),f79(a1))) % 165.14/165.03 [3461]P24(f332(f62(a865),f186(a865,a863,a26))) % 165.14/165.03 [3500]E(f332(f332(f289(a868,a868,a868),a322),f308(a868,a322)),a251) % 165.14/165.03 [3540]P44(a1,a868,a107,f332(f246(a1),f2(a1))) % 165.14/165.03 [3544]E(f332(f332(f42(a868,f875(a868,a862)),f255(f875(a868,a862))),f253(a868)),f255(f875(a868,a862))) % 165.14/165.03 [3545]E(f332(f332(f42(a868,f875(a868,a862)),f255(f875(a868,a862))),f254(a868)),f255(f875(a868,a862))) % 165.14/165.03 [3546]E(f332(f332(f42(a868,f875(a868,a862)),f255(f875(a868,a862))),f301(a868)),f255(f875(a868,a862))) % 165.14/165.03 [3547]E(f332(f332(f43(a868,f875(a868,a862)),f255(f875(a868,a862))),f304(a868)),f196(f875(a868,a862))) % 165.14/165.03 [3563]P21(a868,a1,f103(a1),f255(f875(a868,a862))) % 165.14/165.03 [3576]P44(a868,a1,f103(a1),f332(f16(a862,a868),a195)) % 165.14/165.03 [3712]E(f332(f74(a868,a102,a1,a3),a107),f106(a102)) % 165.14/165.03 [3941]P55(a102,a868,a19,a3,f255(f875(a868,a862))) % 165.14/165.03 [3950]P55(a1,f875(f874(a868,a868),a862),a109,a90,a101) % 165.14/165.03 [4216]E(f272(a1,a1,a1,a1,f35(a1),f80(a1)),a51) % 165.14/165.03 [4466]~E(f332(f106(a1),a100),f332(f106(a1),a84)) % 165.14/165.03 [4467]~P24(f332(a201,f79(a1))) % 165.14/165.03 [4468]~P24(f332(a201,f2(a1))) % 165.14/165.03 [4517]~P24(f332(f332(f247(a1),a84),f2(a1))) % 165.14/165.03 [3126]E(f332(f332(f22(a1),a100),a100),a84) % 165.14/165.03 [3141]E(f332(f103(a1),f332(a115,f2(a868))),f79(a1)) % 165.14/165.03 [3209]E(f332(f38(a871),f255(f875(a871,a862))),f79(a868)) % 165.14/165.03 [3230]P24(f332(a201,f332(f106(a1),a100))) % 165.14/165.03 [3232]P24(f332(f332(f246(a1),a100),a84)) % 165.14/165.03 [3234]P24(f332(f332(f247(a1),a100),a84)) % 165.14/165.03 [3295]E(f332(f332(f310(a868),f2(a868)),f196(f875(a868,a862))),f332(f301(a868),f2(a868))) % 165.14/165.03 [3352]P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),a84))) % 165.14/165.03 [3364]E(f332(f311(a868,a868,a115),f255(f875(a868,a862))),f332(f304(a868),f2(a868))) % 165.14/165.03 [3404]P6(f874(a868,a868),f255(f875(f874(a868,a868),a862)),a111) % 165.14/165.03 [3720]E(f332(f74(a868,a1,a102,f103(a1)),a19),a20) % 165.14/165.03 [3782]P41(a868,f332(f252(f874(a868,a868)),f332(f271(a868,a868,a862),f247(a868)))) % 165.14/165.03 [4506]~P24(f332(a201,f332(f106(a1),a84))) % 165.14/165.03 [4507]~P24(f332(f332(f246(a1),a84),a100)) % 165.14/165.03 [4508]~P24(f332(f332(f247(a1),a84),a84)) % 165.14/165.03 [4509]~P24(f332(f332(f247(a1),a84),a100)) % 165.14/165.03 [4510]~P24(f332(f332(f247(a1),a100),a100)) % 165.14/165.03 [4511]~P24(f332(f332(f92(a1),a84),a100)) % 165.14/165.03 [4512]~P24(f332(f332(f92(a1),a100),a84)) % 165.14/165.03 [4527]~P24(f332(f62(a868),f255(f875(a868,a862)))) % 165.14/165.03 [4528]~P24(f332(f62(a1),f255(f875(a1,a862)))) % 165.14/165.03 [4560]~P20(a864,f196(f875(f867(a864),a862)),f332(f311(a865,f867(a864),f332(f332(f8(a863,f867(a864),a865),a94),a28)),f186(a865,a863,a26))) % 165.14/165.03 [4387]E(f332(f271(a1,a1,a862),f332(f332(f8(f875(a1,a862),f875(a1,a862),a1),f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f247(a1),f2(a1))))),f332(f332(f7(a1,a1,f875(a1,a862)),f332(f332(f8(f875(a1,f875(a1,a862)),f875(a1,f875(a1,a862)),a1),f7(a1,a1,a862)),f332(f332(f8(f875(a1,a1),f875(a1,f875(a1,a862)),a1),f332(f8(a1,f875(a1,a862),a1),a329)),a229))),f79(a1)))),a225) % 165.14/165.03 [3442]E(f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100),f332(f80(a1),a100)) % 165.14/165.03 [3483]E(f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100),f332(f332(f22(a1),a84),a100)) % 165.14/165.03 [3645]E(f332(f332(f61(f874(a868,a868)),f255(f875(f874(a868,a868),a862))),a111),a101) % 165.14/165.03 [3674]E(f332(f106(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f79(a1)) % 165.14/165.03 [3675]E(f332(f106(a102),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f79(a102)) % 165.14/165.03 [3676]E(f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f79(a868)) % 165.14/165.03 [3680]E(f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(a115,f2(a868))) % 165.14/165.03 [4075]E(f332(f332(f113(f875(f874(f874(a868,a868),f874(a868,a868)),a862)),a36),f308(f874(a868,a868),f196(f875(f874(f874(a868,a868),f874(a868,a868)),a862)))),a71) % 165.14/165.03 [4146]E(f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),f79(a868)),f2(a868))),f196(f875(f874(a868,a868),a862))))),f79(a1)) % 165.14/165.03 [4147]E(f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),f2(a868)),f2(a868))),f196(f875(f874(a868,a868),a862))))),f2(a1)) % 165.14/165.03 [4162]E(f332(f252(f874(a868,a868)),f332(f271(a868,a868,a862),f332(f332(f8(a868,f875(a868,a862),a868),f332(f7(a868,a868,a862),a329)),a115))),a322) % 165.14/165.03 [4132]E(f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),f332(a115,f332(a115,f2(a868)))) % 165.14/165.03 [4135]E(f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),f332(f332(f81(a868),f79(a868)),f79(a868))) % 165.14/165.03 [4136]E(f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),f332(f38(a862),f255(f875(a862,a862)))) % 165.14/165.03 [4202]P31(f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))) % 165.14/165.03 [4274]P22(f875(f874(a868,a868),a862),f332(f332(f267(f875(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),a862),f875(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),a862)),a37),a70)) % 165.14/165.03 [4275]P22(f875(f874(a868,a868),a862),f332(f332(f267(f875(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),a862),f875(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),a862)),a69),a72)) % 165.14/165.03 [4315]E(f332(f332(f113(f875(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),a862)),f325(f874(a868,a868),a71)),f332(f332(f310(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),f196(f875(f874(a868,a868),a862))),f196(f875(f874(a868,a868),a862)))),f196(f875(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),a862)))),a72) % 165.14/165.03 [4316]E(f332(f332(f113(f875(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),a862)),f323(f874(a868,a868),a71)),f332(f332(f310(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),f196(f875(f874(a868,a868),a862))),f196(f875(f874(a868,a868),a862)))),f196(f875(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),a862)))),a70) % 165.14/165.03 [4204]E(f332(a107,f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(a115,f332(a115,f2(a868)))) % 165.14/165.03 [4251]E(f332(f103(a1),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))) % 165.14/165.03 [4286]P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))) % 165.14/165.03 [4287]E(f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),a100)),f332(a115,f332(a115,f332(a115,f2(a868))))) % 165.14/165.03 [4329]P31(f332(f106(a1),f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),a100))) % 165.14/165.03 [4357]E(f332(f103(a1),f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),a100))),f332(f106(a1),f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),a100))) % 165.14/165.03 [4372]P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),a100)))) % 165.14/165.03 [3062]P5(x30621,a329) % 165.14/165.03 [3471]P21(a868,a868,a115,x34711) % 165.14/165.03 [3052]P94(f867(x30521)) % 165.14/165.03 [3053]P94(f872(x30531)) % 165.14/165.03 [3054]P94(f869(x30541)) % 165.14/165.03 [3055]P94(f870(x30551)) % 165.14/165.03 [3056]P103(f867(x30561)) % 165.14/165.03 [3057]P103(f872(x30571)) % 165.14/165.03 [3058]P103(f869(x30581)) % 165.14/165.03 [3059]P103(f870(x30591)) % 165.14/165.03 [3079]P41(a1,f108(x30791)) % 165.14/165.03 [3080]P41(a1,f110(x30801)) % 165.14/165.03 [3131]P41(f875(x31311,a862),f307(x31311)) % 165.14/165.03 [3155]E(f256(x31551,x31551,a329),a329) % 165.14/165.03 [3170]E(f45(a1,x31701,x31701),f2(a1)) % 165.14/165.03 [3227]P11(x32271,f875(x32271,a862),f310(x32271)) % 165.14/165.03 [4445]~E(f332(a28,x44451),a24) % 165.14/165.03 [4447]~E(f332(a115,x44471),x44471) % 165.14/165.03 [4457]~E(f332(a115,x44571),f2(a868)) % 165.14/165.03 [3064]E(f332(f197(a868),x30641),x30641) % 165.14/165.03 [3065]E(f332(f106(a1),x30651),x30651) % 165.14/165.03 [3081]E(f332(a90,f333(x30811)),x30811) % 165.14/165.03 [3094]E(f117(x30941,f116(x30941)),f116(x30941)) % 165.14/165.03 [3095]E(f153(x30951,f116(x30951)),f116(x30951)) % 165.14/165.03 [3101]E(f32(f332(a28,x31011)),f2(a868)) % 165.14/165.03 [3106]E(f332(f169(x31061),f116(x31061)),f116(x31061)) % 165.14/165.03 [3107]E(f332(f173(x31071),f116(x31071)),f116(x31071)) % 165.14/165.03 [3108]E(f332(f170(x31081),f116(x31081)),f116(x31081)) % 165.14/165.03 [3114]E(f332(f106(a1),x31141),f332(f105(a1),x31141)) % 165.14/165.03 [3115]E(f332(a90,f332(a109,x31151)),x31151) % 165.14/165.03 [3117]E(f332(a3,f332(a19,x31171)),x31171) % 165.14/165.03 [3118]E(f332(a19,f332(a3,x31181)),x31181) % 165.14/165.03 [3119]P31(f332(f103(a1),x31191)) % 165.14/165.03 [3124]E(f332(f197(f872(x31241)),f209(x31241)),f2(a868)) % 165.14/165.03 [3125]E(f332(f197(f869(x31251)),f116(x31251)),f2(a868)) % 165.14/165.03 [3130]E(f332(f197(a863),f332(a28,x31301)),f2(a868)) % 165.14/165.03 [3139]E(f239(x31391,f209(x31391)),f196(f875(x31391,a862))) % 165.14/165.03 [3146]E(f332(f332(f22(a868),x31461),f2(a868)),x31461) % 165.14/165.03 [3147]E(f332(f332(f81(a868),x31471),f2(a868)),x31471) % 165.14/165.03 [3148]E(f332(f332(f81(a1),x31481),f2(a1)),x31481) % 165.14/165.03 [3149]E(f332(f332(f82(a868),x31491),f79(a868)),x31491) % 165.14/165.03 [3150]E(f332(f332(f82(a1),x31501),f79(a1)),x31501) % 165.14/165.03 [3151]E(f332(f332(f245(a868),x31511),f2(a868)),x31511) % 165.14/165.03 [3152]E(f332(f332(f82(a868),x31521),f2(a868)),f2(a868)) % 165.14/165.03 [3153]E(f332(f332(f39(a1),x31531),f2(a1)),f2(a1)) % 165.14/165.03 [3154]E(f332(f332(f244(a868),x31541),f2(a868)),f2(a868)) % 165.14/165.03 [3161]E(f332(f174(x31611),f116(x31611)),f196(f875(x31611,a862))) % 165.14/165.03 [3165]P24(f332(f138(x31651),f116(x31651))) % 165.14/165.03 [3171]E(f332(f210(x31711,x31711),f5(x31711)),f35(f872(x31711))) % 165.14/165.03 [3172]E(f332(f210(x31721,x31721),f35(x31721)),f35(f872(x31721))) % 165.14/165.03 [3173]E(f332(f155(x31731,x31731),f5(x31731)),f35(f869(x31731))) % 165.14/165.03 [3174]E(f332(f155(x31741,x31741),f35(x31741)),f35(f869(x31741))) % 165.14/165.03 [3175]E(f45(a1,x31751,f2(a1)),x31751) % 165.14/165.03 [3176]E(f332(f246(a868),f332(a115,x31761)),f332(f247(a868),x31761)) % 165.14/165.03 [3177]E(f332(f253(a868),f332(a115,x31771)),f332(f301(a868),x31771)) % 165.14/165.03 [3178]E(f332(f254(a868),f332(a115,x31781)),f332(f304(a868),x31781)) % 165.14/165.03 [3180]E(f45(a1,f2(a1),x31801),f2(a1)) % 165.14/165.03 [3193]E(f332(f332(f81(a868),x31931),f79(a868)),f332(a115,x31931)) % 165.14/165.03 [3203]E(f332(f302(a868,x32031),f2(a868)),f196(f875(a868,a862))) % 165.14/165.03 [3215]E(f303(a868,f2(a868),x32151),f332(f301(a868),x32151)) % 165.14/165.03 [3261]E(f332(f332(f22(a868),f332(a115,x32611)),f79(a868)),x32611) % 165.14/165.03 [3274]E(f47(f2(a1),x32741),f332(f332(f267(a1,a1),f2(a1)),f2(a1))) % 165.14/165.03 [3326]P24(f332(f332(f247(a868),x33261),f332(a115,x33261))) % 165.14/165.03 [3338]P24(f332(f332(f247(a868),f2(a868)),f332(a115,x33381))) % 165.14/165.03 [3631]E(f332(f332(f22(a102),f332(a3,f332(a115,f332(a19,x36311)))),f79(a102)),x36311) % 165.14/165.03 [3704]P24(f332(f332(f246(a1),f332(f80(a1),f332(f103(a1),x37041))),f2(a1))) % 165.14/165.03 [3856]P24(f332(f332(f247(a1),f332(f80(a1),f332(f103(a1),f332(a115,x38561)))),f2(a1))) % 165.14/165.03 [4473]~E(f255(f875(x44731,a862)),f196(f875(x44731,a862))) % 165.14/165.03 [4520]~P24(f332(f332(f247(a868),x45201),f2(a868))) % 165.14/165.03 [4536]~P24(f332(f332(f247(a1),f332(f103(a1),x45361)),f2(a1))) % 165.14/165.03 [3129]E(f182(x31291,f116(f869(x31291))),f116(f869(x31291))) % 165.14/165.03 [3132]E(f332(f332(f82(a1),a84),x31321),a84) % 165.14/165.03 [3133]E(f332(f332(f81(a1),a84),x31331),x31331) % 165.14/165.03 [3136]E(f332(a107,f332(f103(a1),x31361)),x31361) % 165.14/165.03 [3137]E(f332(f332(f22(a1),x31371),a84),x31371) % 165.14/165.03 [3138]E(f332(f332(f81(a1),x31381),a84),x31381) % 165.14/165.03 [3140]E(f332(f332(f22(a868),x31401),x31401),f2(a868)) % 165.14/165.03 [3144]E(f332(f80(a1),f332(f80(a1),x31441)),x31441) % 165.14/165.03 [3145]E(f332(f38(a868),f332(f253(a868),x31451)),x31451) % 165.14/165.03 [3156]E(f332(f332(f81(a868),f2(a868)),x31561),x31561) % 165.14/165.03 [3157]E(f332(f332(f81(a1),f2(a1)),x31571),x31571) % 165.14/165.03 [3158]E(f332(f332(f82(a868),f79(a868)),x31581),x31581) % 165.14/165.03 [3159]E(f332(f332(f82(a1),f79(a1)),x31591),x31591) % 165.14/165.03 [3160]E(f332(f332(f245(a868),f2(a868)),x31601),x31601) % 165.14/165.03 [3166]E(f332(f332(f22(a868),f2(a868)),x31661),f2(a868)) % 165.14/165.03 [3167]E(f332(f332(f82(a868),f2(a868)),x31671),f2(a868)) % 165.14/165.03 [3168]E(f332(f332(f39(a1),f2(a1)),x31681),f2(a1)) % 165.14/165.03 [3169]E(f332(f332(f244(a868),f2(a868)),x31691),f2(a868)) % 165.14/165.03 [3181]E(f126(x31811,f332(f80(a1),x31811)),f133(a1,x31811)) % 165.14/165.03 [3187]E(f332(f302(a868,f2(a868)),x31871),f332(f253(a868),x31871)) % 165.14/165.03 [3188]E(f332(f332(f82(a1),a100),x31881),f332(f80(a1),x31881)) % 165.14/165.03 [3195]E(f332(a107,f332(f106(a1),x31951)),f332(f106(a868),x31951)) % 165.14/165.03 [3196]E(f332(a19,f332(f106(a102),x31961)),f332(f106(a868),x31961)) % 165.14/165.03 [3197]E(f332(f38(a868),f332(f301(a868),x31971)),f332(a115,x31971)) % 165.14/165.03 [3207]E(f332(f332(f81(a868),f79(a868)),x32071),f332(a115,x32071)) % 165.14/165.03 [3211]E(f332(f105(a1),f332(f103(a1),x32111)),f332(f103(a1),x32111)) % 165.14/165.03 [3212]E(f332(f76(a1),f332(f103(a1),x32121)),f332(f103(a1),x32121)) % 165.14/165.03 [3217]E(f332(f38(x32171),f196(f875(x32171,a862))),f2(a868)) % 165.14/165.03 [3219]E(f332(f332(f39(a868),x32191),f332(a115,f2(a868))),x32191) % 165.14/165.03 [3228]E(f45(a868,x32281,f332(a115,f2(a868))),f2(a868)) % 165.14/165.03 [3229]E(f45(a1,x32291,f332(f106(a1),a100)),f2(a1)) % 165.14/165.03 [3245]E(f332(f332(f39(a1),x32451),f332(f106(a1),a100)),f332(f80(a1),x32451)) % 165.14/165.03 [3249]E(f140(a868,f332(f302(a868,x32491),f2(a868))),f116(a868)) % 165.14/165.03 [3250]E(f332(f332(f81(a1),x32501),f79(a1)),f332(f332(f22(a1),x32501),a100)) % 165.14/165.03 [3251]E(f332(f332(f22(a1),x32511),f79(a1)),f332(f332(f81(a1),x32511),a100)) % 165.14/165.03 [3255]P24(f332(f332(f246(a868),x32551),x32551)) % 165.14/165.03 [3256]P24(f332(f332(f246(a1),x32561),x32561)) % 165.14/165.03 [3257]P24(f332(f332(f92(a1),x32571),x32571)) % 165.14/165.03 [3262]E(f332(f80(a1),f332(f106(a1),x32621)),f332(f106(a1),f332(f80(a1),x32621))) % 165.14/165.03 [3263]P24(f332(f62(a868),f332(f253(a868),x32631))) % 165.14/165.03 [3264]P24(f332(f62(a868),f332(f301(a868),x32641))) % 165.14/165.03 [3272]E(f162(x32721,f255(f875(x32721,a862))),f255(f875(f869(x32721),a862))) % 165.14/165.03 [3277]P24(f332(f332(f246(a868),f2(a868)),x32771)) % 165.14/165.03 [3288]E(f332(f332(f81(a868),f114(x32881)),f332(a115,f2(a868))),f114(f332(a115,x32881))) % 165.14/165.03 [3289]E(f332(f252(x32891),f332(f16(a862,x32891),a250)),f196(f875(x32891,a862))) % 165.14/165.03 [3290]E(f332(f252(x32901),f332(f16(a862,x32901),a195)),f255(f875(x32901,a862))) % 165.14/165.03 [3294]E(f332(f332(f310(a868),x32941),f332(f253(a868),x32941)),f332(f253(a868),f332(a115,x32941))) % 165.14/165.03 [3306]E(f332(f332(f81(a1),f79(a1)),f332(f103(a1),x33061)),f332(f103(a1),f332(a115,x33061))) % 165.14/165.03 [3309]E(f332(f332(f152(f869(x33091)),f116(x33091)),f116(f869(x33091))),f54(x33091,f116(x33091))) % 165.14/165.03 [3329]E(f196(f875(f874(x33291,x33291),a862)),f264(x33291,f196(f875(x33291,a862)))) % 165.14/165.03 [3330]E(f332(f309(x33301),f255(f875(x33301,a862))),f255(f875(f875(x33301,a862),a862))) % 165.14/165.03 [3331]E(f332(f80(f875(x33311,a862)),f196(f875(x33311,a862))),f255(f875(x33311,a862))) % 165.14/165.03 [3332]E(f332(f80(f875(x33321,a862)),f255(f875(x33321,a862))),f196(f875(x33321,a862))) % 165.14/165.03 [3334]P24(f332(f62(x33341),f196(f875(x33341,a862)))) % 165.14/165.03 [3336]E(f332(f302(a868,x33361),f332(a115,x33361)),f332(f332(f310(a868),x33361),f196(f875(a868,a862)))) % 165.14/165.03 [3337]E(f86(f874(a868,a868),f48(x33371,f2(a868))),f332(f332(f267(a868,a868),f2(a868)),x33371)) % 165.14/165.03 [3351]E(f332(f332(f310(a868),f332(a115,x33511)),f332(f301(a868),x33511)),f332(f301(a868),f332(a115,x33511))) % 165.14/165.03 [3355]P41(x33551,f196(f875(f874(x33551,x33551),a862))) % 165.14/165.03 [3358]P24(f332(f332(f246(a1),f2(a1)),f332(f103(a1),x33581))) % 165.14/165.03 [3366]E(f332(f332(f81(a868),f332(f197(a868),x33661)),f332(a115,f2(a868))),f332(f197(a868),f332(a115,x33661))) % 165.14/165.03 [3478]P42(f332(f311(a868,a1,f103(a1)),x34781)) % 165.14/165.03 [3516]P43(x35161,f196(f875(x35161,a862)),f196(f875(f874(x35161,x35161),a862))) % 165.14/165.03 [3536]E(f332(f332(f267(a1,a1),f332(f106(a1),a100)),f332(f332(f22(a1),x35361),f79(a1))),f50(f332(f106(a1),a100),x35361)) % 165.14/165.03 [3588]P58(x35881,f332(f16(f875(x35881,a862),x35881),f332(f16(a862,x35881),a250))) % 165.14/165.03 [3794]P24(f332(f332(f334(f875(f874(a868,a868),a862)),f333(x37941)),a101)) % 165.14/165.03 [3820]P24(f332(f332(f334(f875(f874(a868,a868),a862)),f332(a109,x38201)),a101)) % 165.14/165.03 [3959]P21(x39591,f875(x39591,a862),f332(f332(f7(x39591,f875(x39591,a862),f875(x39591,a862)),f310(x39591)),f196(f875(x39591,a862))),f255(f875(x39591,a862))) % 165.14/165.03 [4470]~E(f332(f332(f81(a1),x44701),x44701),a100) % 165.14/165.03 [4505]~E(f332(a3,f332(a115,f332(a19,x45051))),f2(a102)) % 165.14/165.03 [4513]~P24(f332(a201,f332(f103(a1),x45131))) % 165.14/165.03 [4516]~P24(f332(f332(f247(a868),x45161),x45161)) % 165.14/165.03 [4529]~P24(f332(f332(f246(a868),f332(a115,x45291)),x45291)) % 165.14/165.03 [3279]E(f332(a107,f332(f80(a1),f332(f103(a1),x32791))),f2(a868)) % 165.14/165.03 [3282]E(f332(f332(f81(a1),f332(f80(a1),x32821)),x32821),f2(a1)) % 165.14/165.03 [3287]E(f332(f38(a1),f332(f302(a1,f2(a1)),x32871)),f332(a107,x32871)) % 165.14/165.03 [3299]E(f332(f332(f257(a868),f332(a115,f2(a868))),x32991),f332(a115,f2(a868))) % 165.14/165.03 [3401]E(f332(f285(x34011),f196(f875(f874(x34011,x34011),a862))),f196(f875(x34011,a862))) % 165.14/165.03 [3409]E(f40(f875(x34091,a862),f196(f875(f875(x34091,a862),a862))),f196(f875(x34091,a862))) % 165.14/165.03 [3410]E(f40(f875(x34101,a862),f255(f875(f875(x34101,a862),a862))),f255(f875(x34101,a862))) % 165.14/165.03 [3411]E(f41(f875(x34111,a862),f196(f875(f875(x34111,a862),a862))),f255(f875(x34111,a862))) % 165.14/165.03 [3412]E(f41(f875(x34121,a862),f255(f875(f875(x34121,a862),a862))),f196(f875(x34121,a862))) % 165.14/165.03 [3459]E(f332(f332(f310(f869(x34591)),f116(x34591)),f196(f875(f869(x34591),a862))),f162(x34591,f196(f875(x34591,a862)))) % 165.14/165.03 [3460]E(f332(f332(f310(f869(x34601)),f116(x34601)),f196(f875(f869(x34601),a862))),f163(x34601,f116(f875(x34601,a862)))) % 165.14/165.03 [3499]E(f332(f332(f81(a868),f4(x34991)),f332(a115,f2(a868))),f4(f332(a3,f332(a115,f332(a19,x34991))))) % 165.14/165.03 [3527]E(f332(f38(a1),f332(f311(a868,a1,f103(a1)),x35271)),f332(f38(a868),x35271)) % 165.14/165.03 [3530]P24(f332(f332(f246(a868),x35301),f332(f332(f82(a868),x35301),x35301))) % 165.14/165.03 [3567]E(f332(f311(a1,a868,a107),f303(a1,f2(a1),f332(f103(a1),x35671))),f332(f301(a868),x35671)) % 165.14/165.03 [3583]E(f332(f332(f39(a868),f332(a115,f2(a868))),f332(f106(a868),x35831)),f332(a107,f332(f332(f39(a1),f79(a1)),f332(f106(a1),x35831)))) % 165.14/165.03 [3585]E(f332(f174(a868),f140(a868,f332(f302(a868,f2(a868)),f332(a115,x35851)))),f332(f301(a868),x35851)) % 165.14/165.03 [3586]E(f332(f332(f81(a868),f332(f197(a102),x35861)),f332(a115,f2(a868))),f332(f197(a102),f332(a3,f332(a115,f332(a19,x35861))))) % 165.14/165.03 [3604]E(f332(f311(a1,a868,a107),f332(f311(a868,a1,f103(a1)),x36041)),x36041) % 165.14/165.03 [3637]E(f332(f332(f310(a868),f2(a868)),f332(f311(a868,a868,a115),f332(f253(a868),x36371))),f332(f253(a868),f332(a115,x36371))) % 165.14/165.03 [3644]P53(x36441,x36441,f308(x36441,f196(f875(f874(x36441,x36441),a862)))) % 165.14/165.03 [3650]P24(f332(a201,f332(f80(a1),f332(f103(a1),f332(a115,x36501))))) % 165.14/165.03 [3661]E(f332(f332(f22(f875(a868,a862)),f332(f254(a868),x36611)),f332(f332(f310(a868),x36611),f196(f875(a868,a862)))),f332(f254(a868),f332(a115,x36611))) % 165.14/165.03 [3677]E(f332(f332(f81(a1),f332(f332(f22(a1),a84),x36771)),f332(f332(f22(a1),a84),x36771)),f332(f332(f22(a1),a84),f332(f332(f81(a1),x36771),x36771))) % 165.14/165.03 [3693]E(f332(f332(f310(f875(x36931,a862)),f196(f875(x36931,a862))),f196(f875(f875(x36931,a862),a862))),f332(f309(x36931),f196(f875(x36931,a862)))) % 165.14/165.03 [3721]E(f332(f332(f22(f875(a868,a862)),f332(f304(a868),x37211)),f332(f332(f310(a868),f332(a115,x37211)),f196(f875(a868,a862)))),f332(f304(a868),f332(a115,x37211))) % 165.14/165.03 [3730]E(f332(f332(f310(f872(x37301)),f209(x37301)),f332(f311(x37301,f872(x37301),f208(x37301)),f255(f875(x37301,a862)))),f255(f875(f872(x37301),a862))) % 165.14/165.03 [3832]E(f332(f106(a868),f332(f332(f81(a1),x38321),x38321)),f332(f332(f87(a868,a868),f332(f106(a868),x38321)),f332(f332(f18(a868,a868,a868),f81(a868)),f5(a868)))) % 165.14/165.03 [4225]P11(x42251,f875(x42251,a862),f332(f332(f8(f875(x42251,a862),f875(f875(x42251,a862),f875(x42251,a862)),x42251),f332(f7(f875(x42251,a862),f875(x42251,a862),f875(x42251,a862)),f22(f875(x42251,a862)))),f332(f332(f7(x42251,f875(x42251,a862),f875(x42251,a862)),f310(x42251)),f196(f875(x42251,a862))))) % 165.14/165.03 [4314]E(f332(f252(f874(a1,a1)),f332(f271(a1,a1,a862),f332(f332(f8(f875(a1,a862),f875(a1,a862),a1),f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f246(a1),x43141)))),f247(a1)))),f110(x43141)) % 165.14/165.03 [4347]E(f332(f252(f874(a1,a1)),f332(f271(a1,a1,a862),f332(f332(f18(a1,f875(a1,a862),f875(a1,a862)),f332(f332(f8(f875(a862,a862),f875(f875(a1,a862),f875(a1,a862)),a1),f8(a862,a862,a1)),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f246(a1),x43471)))),f247(a1)))),f108(x43471)) % 165.14/165.03 [4402]E(f332(f252(f874(f875(x44021,a862),f875(x44021,a862))),f332(f271(f875(x44021,a862),f875(x44021,a862),a862),f332(f332(f7(f875(x44021,a862),f875(f875(x44021,a862),a862),f875(f875(x44021,a862),a862)),f332(f332(f8(f875(f875(x44021,a862),f875(a862,a862)),f875(f875(f875(x44021,a862),a862),f875(f875(x44021,a862),a862)),f875(x44021,a862)),f18(f875(x44021,a862),a862,a862)),f332(f332(f8(f875(f875(x44021,a862),a862),f875(f875(x44021,a862),f875(a862,a862)),f875(x44021,a862)),f332(f8(a862,f875(a862,a862),f875(x44021,a862)),a330)),f247(f875(x44021,a862))))),f62(x44021)))),f307(x44021)) % 165.14/165.03 [4533]~P24(f332(f62(f869(x45331)),f255(f875(f869(x45331),a862)))) % 165.14/165.03 [4538]~P24(f332(f332(f92(a1),a100),f332(f332(f81(a1),x45381),x45381))) % 165.14/165.03 [4548]~P24(f332(f332(f246(a1),f2(a1)),f332(f80(a1),f332(f103(a1),f332(a115,x45481))))) % 165.14/165.03 [3436]E(f332(f332(f22(a1),f332(f332(f81(a1),x34361),a100)),a100),x34361) % 165.14/165.03 [3452]E(f332(f174(a868),f140(a868,f332(f302(a868,f2(a868)),x34521))),f332(f253(a868),x34521)) % 165.14/165.03 [3700]E(f332(f332(f81(a1),f332(f332(f81(a1),f79(a1)),x37001)),x37001),f332(f332(f22(a1),f332(f332(f81(a1),x37001),x37001)),a100)) % 165.14/165.03 [3749]E(f332(f287(x37491,x37491),f308(x37491,f196(f875(f874(x37491,x37491),a862)))),f308(x37491,f196(f875(f874(x37491,x37491),a862)))) % 165.14/165.03 [3797]P24(f332(f332(f246(a868),x37971),f332(f332(f82(a868),x37971),f332(f332(f82(a868),x37971),x37971)))) % 165.14/165.03 [4079]P24(f332(f62(a868),f332(f252(a868),f332(f332(f7(a868,a868,a862),f246(a868)),x40791)))) % 165.14/165.03 [4080]P24(f332(f62(a868),f332(f252(a868),f332(f332(f7(a868,a868,a862),f247(a868)),x40801)))) % 165.14/165.03 [4367]E(f332(f252(f874(x43671,x43671)),f332(f332(f8(f875(x43671,a862),a862,f874(x43671,x43671)),f88(x43671)),f332(f332(f7(f874(x43671,x43671),f875(x43671,f874(x43671,x43671)),f875(x43671,a862)),f332(f332(f8(f875(f874(x43671,x43671),a862),f875(f875(x43671,f874(x43671,x43671)),f875(x43671,a862)),f874(x43671,x43671)),f8(f874(x43671,x43671),a862,x43671)),a329)),f332(f332(f18(x43671,x43671,f874(x43671,x43671)),f267(x43671,x43671)),f5(x43671))))),f308(x43671,f196(f875(f874(x43671,x43671),a862)))) % 165.14/165.03 [4535]~E(f332(f332(f22(a1),f332(f332(f81(a1),x45351),x45351)),a100),a84) % 165.14/165.03 [4537]~E(f332(f332(f81(a1),f332(f332(f81(a1),f79(a1)),x45371)),x45371),f2(a1)) % 165.14/165.03 [4545]~P24(f332(f332(f92(a1),f332(f332(f81(a1),x45451),x45451)),a100)) % 165.14/165.03 [3845]E(f332(f332(f81(a1),f332(f332(f22(a1),a100),x38451)),f332(f332(f22(a1),a100),x38451)),f332(f332(f22(a1),a100),f332(f332(f22(a1),f332(f332(f81(a1),x38451),x38451)),a100))) % 165.14/165.03 [3968]E(f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),a100),x39681)),f332(f332(f22(a1),a100),x39681))),a100),f332(f332(f22(a1),a100),f332(f332(f81(a1),x39681),x39681))) % 165.14/165.03 [4002]E(f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f81(a1),x40021),a100)),f332(f332(f81(a1),x40021),a100))),a100),f332(f332(f81(a1),f332(f332(f81(a1),x40021),x40021)),a100)) % 165.14/165.03 [4041]E(f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),a100),x40411)),f332(f332(f22(a1),a100),x40411))),a100),f332(f332(f22(a1),a84),f332(f332(f22(a1),f332(f332(f81(a1),x40411),x40411)),a100))) % 165.14/165.03 [4142]E(f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x41421),f2(a868))),f196(f875(f874(a868,a868),a862))))),f332(f103(a1),x41421)) % 165.14/165.03 [4152]E(f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),f337(x41521)),f519(x41521))),f196(f875(f874(a868,a868),a862))))),x41521) % 165.14/165.03 [4187]E(f332(f252(a1),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f246(a1),f2(a1)))),x41871)),f332(f311(a868,a1,f103(a1)),f332(f252(a868),f332(f332(f8(a1,a862,a868),x41871),f103(a1))))) % 165.14/165.03 [4233]P42(f332(f252(a1),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f246(a1),f2(a1)))),x42331))) % 165.14/165.03 [4254]P24(f332(f332(f334(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),x42541),f196(f875(f874(a868,a868),a862)))),a72)) % 165.14/165.03 [4260]E(f332(f311(a1,a868,a107),f332(f252(a1),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f246(a1),f2(a1)))),f332(f332(f8(a868,a862,a1),x42601),a107)))),f332(f252(a868),x42601)) % 165.14/165.03 [4416]E(f313(a868,f332(f332(f42(f874(a868,a868),f875(a868,a862)),f332(a109,x44161)),f332(f271(a868,a868,f875(a868,a862)),f332(f332(f7(a868,f875(a868,a862),f875(a868,f875(a868,a862))),f332(f332(f8(f875(a868,f875(f875(a868,a862),f875(a868,a862))),f875(f875(a868,a862),f875(a868,f875(a868,a862))),a868),f7(a868,f875(a868,a862),f875(a868,a862))),f332(f332(f8(f875(a868,a868),f875(a868,f875(f875(a868,a862),f875(a868,a862))),a868),f332(f8(a868,f875(f875(a868,a862),f875(a868,a862)),a868),f310(a868))),f22(a868)))),f196(f875(a868,a862)))))),f332(a107,x44161)) % 165.14/165.03 [4550]~P24(f332(f332(f92(a1),a84),f332(f332(f22(a1),f332(f332(f81(a1),x45501),x45501)),a100))) % 165.14/165.03 [3890]E(f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),x38901),x38901)),a100)),a100),f332(f332(f81(a1),x38901),x38901)) % 165.14/165.03 [3942]E(f332(f332(f22(a1),f332(f332(f22(a1),f332(f332(f81(a1),x39421),x39421)),a100)),a100),f332(f332(f81(a1),f332(f332(f22(a1),x39421),a100)),f332(f332(f22(a1),x39421),a100))) % 165.14/165.03 [4160]E(f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f81(a1),f332(f80(a1),x41601)),a100)),f332(f332(f81(a1),f332(f80(a1),x41601)),a100))),a100),f332(f80(a1),f332(f332(f22(a1),f332(f332(f81(a1),x41601),x41601)),a100))) % 165.14/165.03 [4558]~P24(f332(f332(f92(a1),f332(f332(f22(a1),f332(f332(f81(a1),x45581),x45581)),a100)),a84)) % 165.14/165.03 [4205]E(f332(f332(f81(a868),x42051),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(a115,f332(a115,x42051))) % 165.14/165.03 [4206]E(f332(f332(f82(a868),x42061),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(f332(f81(a868),x42061),x42061)) % 165.14/165.03 [4207]E(f332(f332(f39(a868),f332(f332(f81(a868),x42071),x42071)),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x42071) % 165.14/165.03 [4289]E(f45(a868,f332(a115,f332(a115,x42891)),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f45(a868,x42891,f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))) % 165.14/165.03 [4431]E(f332(a90,f332(f332(f42(f874(a868,a868),f875(f874(a868,a868),a862)),f332(a109,x44311)),f332(f271(a868,a868,f875(f874(a868,a868),a862)),f332(f332(f8(f875(a868,f875(f874(a868,a868),a862)),f875(a868,f875(f874(a868,a868),a862)),a868),f332(f8(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862),a868),f286(f874(a868,a868),f874(a868,a868),a111))),f332(f332(f7(a868,f875(f874(a868,a868),a862),f875(a868,f875(f874(a868,a868),a862))),f332(f332(f8(f875(a868,f875(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f875(f875(f874(a868,a868),a862),f875(a868,f875(f874(a868,a868),a862))),a868),f7(a868,f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f8(f875(a868,f874(a868,a868)),f875(a868,f875(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),a868),f332(f8(f874(a868,a868),f875(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),a868),f310(f874(a868,a868)))),f332(f7(a868,a868,f874(a868,a868)),f267(a868,a868))))),f196(f875(f874(a868,a868),a862))))))),f332(f80(a1),x44311)) % 165.14/165.03 [4284]E(f332(f332(f81(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x42841),f332(a115,f332(a115,x42841))) % 165.14/165.03 [4285]E(f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x42851),f332(f332(f81(a868),x42851),x42851)) % 165.14/165.03 [4319]E(f332(f332(f39(a868),f332(a115,f332(a115,x43191))),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(a115,f332(f332(f39(a868),x43191),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))) % 165.14/165.03 [4373]E(f332(f332(f81(a868),f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),a100))),x43731),f332(a115,f332(a115,f332(a115,x43731)))) % 165.14/165.03 [4439]E(f332(f271(a1,a1,f874(a1,a1)),f332(f332(f18(a1,f875(a1,f874(a1,a1)),f875(a1,f874(a1,a1))),f332(f332(f8(f875(a1,f875(f874(a1,a1),f874(a1,a1))),f875(f875(a1,f874(a1,a1)),f875(a1,f874(a1,a1))),a1),f18(a1,f874(a1,a1),f874(a1,a1))),f332(f332(f8(f875(a1,f874(a1,a1)),f875(a1,f875(f874(a1,a1),f874(a1,a1))),a1),f332(f18(a1,f874(a1,a1),f875(f874(a1,a1),f874(a1,a1))),f332(f332(f8(a862,f875(f874(a1,a1),f875(f874(a1,a1),f874(a1,a1))),a1),f99(f874(a1,a1))),f332(f332(f8(a1,a862,a1),f332(f246(a1),f2(a1))),f332(f332(f7(a1,a1,a1),f22(a1)),x44391))))),f332(f332(f7(a1,f875(a1,a1),f875(a1,f874(a1,a1))),f332(f332(f8(f875(a1,f874(a1,a1)),f875(f875(a1,a1),f875(a1,f874(a1,a1))),a1),f8(a1,f874(a1,a1),a1)),f332(f332(f8(a1,f875(a1,f874(a1,a1)),a1),f267(a1,a1)),f332(f332(f7(a1,a1,a1),f332(f332(f8(a1,f875(a1,a1),a1),f81(a1)),f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))),f79(a1))))),f332(f332(f7(a1,a1,a1),f22(a1)),x44391))))),f332(f332(f8(a1,f875(a1,f874(a1,a1)),a1),f267(a1,a1)),f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))))),f44(x44391)) % 165.14/165.03 [3102]P94(f874(x31021,x31022)) % 165.14/165.03 [3103]P94(f876(x31031,x31032)) % 165.14/165.03 [3104]P103(f874(x31041,x31042)) % 165.14/165.03 [3105]P103(f876(x31051,x31052)) % 165.14/165.03 [3122]P32(a1,f181(x31221,x31222)) % 165.14/165.03 [3123]P41(x31231,f154(x31231,x31232)) % 165.14/165.03 [3189]P35(x31891,x31892,f116(x31891)) % 165.14/165.03 [3223]P43(x32231,x32232,f264(x32231,x32232)) % 165.14/165.03 [3224]P53(x32241,x32241,f264(x32241,x32242)) % 165.14/165.03 [3502]P21(x35021,x35021,f5(x35021),x35022) % 165.14/165.03 [3503]P21(x35031,x35031,f35(x35031),x35032) % 165.14/165.03 [3511]P36(x35111,x35112,f116(x35111),f116(x35111)) % 165.14/165.03 [3512]P21(x35121,f872(x35121),f208(x35121),x35122) % 165.14/165.03 [3521]P21(f869(x35211),f869(x35211),f170(x35211),x35212) % 165.14/165.03 [4450]~E(f34(x44501,x44502),a24) % 165.14/165.03 [4451]~E(f33(x44511,x44512),a24) % 165.14/165.03 [4482]~P37(x44821,x44822,f116(x44821)) % 165.14/165.03 [4483]~P39(x44831,x44832,f116(x44831)) % 165.14/165.03 [3083]E(f332(f5(x30831),x30832),x30832) % 165.14/165.03 [3084]E(f332(f252(x30841),x30842),x30842) % 165.14/165.03 [3086]E(f332(f35(x30861),x30862),x30862) % 165.14/165.03 [3096]E(f332(f199(x30961),x30962),f118(x30961)) % 165.14/165.03 [3120]E(f86(x31201,f332(a329,x31202)),x31202) % 165.14/165.03 [3121]E(f91(x31211,f332(a329,x31212)),x31212) % 165.14/165.03 [3142]E(f332(f137(x31421,x31422),f116(x31421)),f116(x31421)) % 165.14/165.03 [3162]E(f153(x31621,f153(x31621,x31622)),f153(x31621,x31622)) % 165.14/165.03 [3163]E(f308(x31631,f308(x31631,x31632)),f308(x31631,x31632)) % 165.14/165.03 [3184]E(f332(f332(f135(x31841),x31842),f116(x31841)),x31842) % 165.14/165.03 [3190]E(f175(x31901,x31902,f116(x31901)),x31902) % 165.14/165.03 [3191]E(f175(x31911,f116(x31911),x31912),x31912) % 165.14/165.03 [3192]E(f171(x31921,f2(a868),x31922),f116(x31921)) % 165.14/165.03 [3198]E(f332(f332(f177(x31981),x31982),f116(x31981)),f116(x31981)) % 165.14/165.03 [3199]E(f332(f332(f139(x31991),x31992),f116(x31991)),f116(x31991)) % 165.14/165.03 [3201]E(f240(x32011,x32012,f209(x32011)),f2(a868)) % 165.14/165.03 [3202]E(f156(x32021,x32022,f116(x32021)),f2(a868)) % 165.14/165.03 [3204]E(f172(x32041,x32042,f116(x32041)),f116(x32041)) % 165.14/165.03 [3205]E(f179(x32051,x32052,f116(x32051)),f116(x32051)) % 165.14/165.03 [3206]E(f178(x32061,f116(x32061),x32062),f116(x32061)) % 165.14/165.03 [3210]E(f332(f174(x32101),f153(x32101,x32102)),f332(f174(x32101),x32102)) % 165.14/165.03 [3213]E(f332(f263(x32131,x32131),f264(x32131,x32132)),x32132) % 165.14/165.03 [3214]E(f332(f265(x32141,x32141),f264(x32141,x32142)),x32142) % 165.14/165.03 [3222]E(f332(f287(x32221,x32221),f264(x32221,x32222)),f264(x32221,x32222)) % 165.14/165.03 [3237]E(f308(f869(x32371),f158(x32371,x32372)),f159(x32371,f308(x32371,x32372))) % 165.14/165.03 [3239]P24(f332(f138(a1),f181(x32391,x32392))) % 165.14/165.03 [3247]E(f332(f263(x32471,x32471),f308(x32471,x32472)),f255(f875(x32471,a862))) % 165.14/165.03 [3248]E(f332(f265(x32481,x32481),f308(x32481,x32482)),f255(f875(x32481,a862))) % 165.14/165.03 [3252]P24(f332(f138(x32521),f153(x32521,x32522))) % 165.14/165.03 [3254]P24(f332(f161(x32541,x32542),f116(x32541))) % 165.14/165.03 [3260]E(f332(f174(a1),f181(x32601,x32602)),f303(a1,x32601,x32602)) % 165.14/165.03 [3275]P54(x32751,f196(f875(x32751,a862)),x32752) % 165.14/165.03 [3280]E(f332(f270(a1,a1),f46(x32801,x32802)),f45(a1,x32801,x32802)) % 165.14/165.03 [3281]E(f332(f302(a868,x32811),f332(a115,x32812)),f303(a868,x32811,x32812)) % 165.14/165.03 [3298]E(f332(f332(f152(x32981),x32982),f116(x32981)),f141(x32981,x32982,f116(x32981))) % 165.14/165.03 [3311]E(f303(a868,f332(a115,x33111),x33112),f305(a868,x33111,x33112)) % 165.14/165.03 [3314]P43(x33141,f255(f875(x33141,a862)),f308(x33141,x33142)) % 165.14/165.03 [3378]E(f332(f332(f22(a868),x33781),f332(a115,x33782)),f332(f38(a868),f306(a868,x33782,x33781))) % 165.14/165.03 [3437]E(f168(x34371,x34372,f116(x34371)),f332(f332(f267(f869(x34371),f869(x34371)),f116(x34371)),f116(x34371))) % 165.14/165.03 [3457]E(f332(f271(x34571,x34572,f874(x34571,x34572)),f267(x34571,x34572)),f35(f874(x34571,x34572))) % 165.14/165.03 [3462]P24(f332(f332(f334(f869(x34621)),f116(x34621)),f162(x34621,x34622))) % 165.14/165.03 [3463]E(f332(f197(f869(x34631)),f117(x34631,x34632)),f332(f332(f22(a868),f332(f197(f869(x34631)),x34632)),f79(a868))) % 165.14/165.03 [3472]P24(f332(f62(a868),f306(a868,x34721,x34722))) % 165.14/165.03 [3473]P24(f332(f62(a868),f305(a868,x34731,x34732))) % 165.14/165.03 [3474]P24(f332(f62(a868),f303(a868,x34741,x34742))) % 165.14/165.03 [3475]P24(f332(f62(a1),f306(a1,x34751,x34752))) % 165.14/165.03 [3476]P24(f332(f62(a1),f305(a1,x34761,x34762))) % 165.14/165.03 [3477]P24(f332(f62(a1),f303(a1,x34771,x34772))) % 165.14/165.03 [3582]E(f332(f311(a868,a868,a115),f303(a868,x35821,x35822)),f303(a868,f332(a115,x35821),f332(a115,x35822))) % 165.14/165.03 [3601]E(f332(f332(f289(x36011,x36011,x36011),f308(x36011,x36012)),f308(x36011,x36012)),f308(x36011,x36012)) % 165.14/165.03 [3635]E(f332(f332(f267(a1,a1),f332(f332(f39(a1),x36351),x36352)),f45(a1,x36351,x36352)),f46(x36351,x36352)) % 165.14/165.03 [3636]E(f332(f332(f267(a102,a102),f332(f332(f39(a102),x36361),x36362)),f45(a102,x36361,x36362)),f21(x36361,x36362)) % 165.14/165.04 [3665]E(f332(f332(f267(a868,a868),f332(f332(f39(a868),x36651),x36652)),f45(a868,x36651,x36652)),f86(f874(a868,a868),f48(x36651,x36652))) % 165.14/165.04 [3717]P24(f332(f332(f247(a868),f332(f332(f22(a868),x37171),x37172)),f332(a115,x37171))) % 165.14/165.04 [3819]E(f332(f332(f81(a1),f332(f332(f82(a1),x38191),f332(f332(f39(a1),x38192),x38191))),f45(a1,x38192,x38191)),x38192) % 165.14/165.04 [3823]E(f332(f332(f42(a868,f875(f874(f869(x38231),f869(x38231)),a862)),f255(f875(a868,a862))),f144(x38231,x38232)),f146(x38231,x38232)) % 165.14/165.04 [4054]P24(f332(f332(f334(f874(f869(x40541),f869(x40541))),f332(f332(f267(f869(x40541),f869(x40541)),f116(x40541)),f116(x40541))),f159(x40541,x40542))) % 165.14/165.04 [4172]E(f268(x41721,x41721,x41721,a329,f268(x41721,x41721,x41721,x41722,a329)),x41722) % 165.14/165.04 [4218]E(f272(x42181,x42181,x42182,x42182,f5(x42181),f5(x42182)),f35(f874(x42181,x42182))) % 165.14/165.04 [4220]E(f272(x42201,x42201,x42202,x42202,f35(x42201),f35(x42202)),f35(f874(x42201,x42202))) % 165.14/165.04 [4459]~E(f332(f208(x44591),x44592),f209(x44591)) % 165.14/165.04 [3182]E(f332(f243(x31821),f332(f208(x31821),x31822)),x31822) % 165.14/165.04 [3183]E(f332(f170(x31831),f332(f170(x31831),x31832)),x31832) % 165.14/165.04 [3185]E(f332(f332(f139(x31851),f2(a868)),x31852),x31852) % 165.14/165.04 [3200]E(f332(f332(f177(x32001),f2(a868)),x32002),f116(x32001)) % 165.14/165.04 [3208]E(f332(f332(f135(x32081),f116(x32081)),x32082),x32082) % 165.14/165.04 [3216]E(f332(f197(f872(x32161)),f332(f208(x32161),x32162)),f2(a868)) % 165.14/165.04 [3218]E(f40(f875(x32181,a862),f332(f309(x32181),x32182)),x32182) % 165.14/165.04 [3220]E(f332(f174(x32201),f332(f169(x32201),x32202)),f332(f174(x32201),x32202)) % 165.14/165.04 [3221]E(f332(f174(x32211),f332(f170(x32211),x32212)),f332(f174(x32211),x32212)) % 165.14/165.04 [3226]E(f332(f332(f22(a102),x32261),x32262),f332(f332(a23,x32261),x32262)) % 165.14/165.04 [3241]E(f332(f332(f81(a868),x32411),x32412),f332(f332(f81(a868),x32412),x32411)) % 165.14/165.04 [3242]E(f332(f332(f81(a1),x32421),x32422),f332(f332(f81(a1),x32422),x32421)) % 165.14/165.04 [3243]E(f332(f332(f82(a868),x32431),x32432),f332(f332(f82(a868),x32432),x32431)) % 165.14/165.04 [3244]E(f332(f332(f82(a1),x32441),x32442),f332(f332(f82(a1),x32442),x32441)) % 165.14/165.04 [3267]E(f332(f332(f191(x32671,x32671),f2(a868)),x32672),f35(x32671)) % 165.14/165.04 [3268]E(f332(f197(f869(x32681)),f332(f169(x32681),x32682)),f332(f197(f869(x32681)),x32682)) % 165.14/165.04 [3269]E(f332(f197(f869(x32691)),f332(f170(x32691),x32692)),f332(f197(f869(x32691)),x32692)) % 165.14/165.04 [3270]E(f178(x32701,x32702,f196(f875(a868,a862))),f116(x32701)) % 165.14/165.04 [3271]E(f332(f332(f155(x32711,x32711),f5(x32711)),x32712),x32712) % 165.14/165.04 [3273]E(f332(f266(a1,a1),f46(x32731,x32732)),f332(f332(f39(a1),x32731),x32732)) % 165.14/165.04 [3291]E(f332(f197(f869(x32911)),f153(x32911,x32912)),f332(f38(x32911),f332(f174(x32911),x32912))) % 165.14/165.04 [3292]E(f32(f33(x32921,x32922)),f332(f332(f81(a868),f32(x32922)),f332(a115,f2(a868)))) % 165.14/165.04 [3293]E(f332(f285(x32931),f332(f287(x32931,x32931),x32932)),f332(f285(x32931),x32932)) % 165.14/165.04 [3297]P24(f332(f62(x32971),f332(f174(x32971),x32972))) % 165.14/165.04 [3305]E(f332(f332(f81(a1),x33051),f332(f80(a1),x33052)),f332(f332(f22(a1),x33051),x33052)) % 165.14/165.04 [3313]P20(x33131,x33132,f196(f875(f867(x33131),a862))) % 165.14/165.04 [3315]E(f332(f311(x33151,x33151,f5(x33151)),x33152),x33152) % 165.14/165.04 [3316]E(f332(f311(x33161,x33161,f35(x33161)),x33162),x33162) % 165.14/165.04 [3317]E(f332(f312(x33171,x33171,f5(x33171)),x33172),x33172) % 165.14/165.04 [3318]E(f332(f312(x33181,x33181,f35(x33181)),x33182),x33182) % 165.14/165.04 [3319]P24(f332(f255(f875(x33191,a862)),x33192)) % 165.14/165.04 [3321]E(f332(f38(a868),f332(f302(a868,x33211),x33212)),f332(f332(f22(a868),x33212),x33211)) % 165.14/165.04 [3322]E(f332(f302(a868,f332(a115,x33221)),x33222),f306(a868,x33221,x33222)) % 165.14/165.04 [3335]E(f332(f332(f310(x33351),x33352),f196(f875(x33351,a862))),f332(f252(x33351),f332(a329,x33352))) % 165.14/165.04 [3339]E(f332(f332(f310(x33391),x33392),f196(f875(x33391,a862))),f239(x33391,f332(f208(x33391),x33392))) % 165.14/165.04 [3342]E(f308(x33421,f332(f287(x33421,x33421),x33422)),f332(f287(x33421,x33421),f308(x33421,x33422))) % 165.14/165.04 [3346]E(f332(f332(f81(a868),f332(a115,x33461)),x33462),f332(f332(f81(a868),x33461),f332(a115,x33462))) % 165.14/165.04 [3347]E(f332(f332(f22(a868),f332(a115,x33471)),f332(a115,x33472)),f332(f332(f22(a868),x33471),x33472)) % 165.14/165.04 [3353]E(f55(x33531,f2(a868),x33532),f332(f332(f152(f869(x33531)),f116(x33531)),f116(f869(x33531)))) % 165.14/165.04 [3354]E(f332(f38(a868),f305(a868,x33541,x33542)),f332(f332(f22(a868),x33542),x33541)) % 165.14/165.04 [3363]P41(x33631,f332(f332(f288(a868,x33631),a251),x33632)) % 165.14/165.04 [3365]P32(a868,f140(a868,f332(f302(a868,x33651),x33652))) % 165.14/165.04 [3367]P24(f332(f62(a868),f332(f302(a868,x33671),x33672))) % 165.14/165.04 [3368]P24(f332(f62(a1),f332(f302(a1,x33681),x33682))) % 165.14/165.04 [3371]E(f332(f287(f869(x33711),f869(x33711)),f158(x33711,x33712)),f158(x33711,f332(f287(x33711,x33711),x33712))) % 165.14/165.04 [3372]E(f332(f197(a863),f33(x33721,x33722)),f332(f332(f81(a868),f332(f197(a863),x33722)),f332(a115,f2(a868)))) % 165.14/165.04 [3374]E(f332(f302(a1,x33741),f332(f332(f81(a1),x33742),f79(a1))),f303(a1,x33741,x33742)) % 165.14/165.04 [3377]E(f332(f332(f39(a1),f332(f80(a1),x33771)),f332(f80(a1),x33772)),f332(f332(f39(a1),x33771),x33772)) % 165.14/165.04 [3385]E(f186(x33851,x33852,f332(f16(f872(x33852),x33851),f209(x33852))),f196(f875(x33851,a862))) % 165.14/165.04 [3386]E(f188(x33861,x33862,f332(f16(f872(x33862),x33861),f209(x33862))),f196(f875(x33862,a862))) % 165.14/165.04 [3387]E(f332(f332(f191(f874(x33871,x33871),a862),f79(a868)),x33872),x33872) % 165.14/165.04 [3389]E(f332(f332(f113(f875(x33891,a862)),x33892),f196(f875(x33891,a862))),x33892) % 165.14/165.04 [3390]E(f332(f332(f22(f875(x33901,a862)),x33902),f196(f875(x33901,a862))),x33902) % 165.14/165.04 [3391]E(f332(f332(f104(f875(x33911,a862)),x33912),f255(f875(x33911,a862))),x33912) % 165.14/165.04 [3392]E(f332(f266(a868,a868),f86(f874(a868,a868),f48(x33921,x33922))),f332(f332(f39(a868),x33921),x33922)) % 165.14/165.04 [3399]E(f314(x33991,f332(a20,x33992),f332(f80(a1),f332(a20,x33992))),f332(f332(f317(a1),x33991),x33992)) % 165.14/165.04 [3400]E(f303(a1,f332(f332(f81(a1),x34001),f79(a1)),x34002),f305(a1,x34001,x34002)) % 165.14/165.04 [3405]E(f332(f270(a868,a868),f86(f874(a868,a868),f48(x34051,x34052))),f45(a868,x34051,x34052)) % 165.14/165.04 [3413]E(f315(x34131,f332(a20,x34132),f332(f80(a1),f332(a20,x34132))),f316(a1,x34131,x34132)) % 165.14/165.04 [3416]P24(f332(f332(f334(x34161),x34162),f255(f875(x34161,a862)))) % 165.14/165.04 [3421]E(f332(f332(f22(a868),f332(a115,x34211)),x34212),f332(f38(a868),f303(a868,x34212,x34211))) % 165.14/165.04 [3448]E(f332(f332(f113(f875(x34481,a862)),x34482),f255(f875(x34481,a862))),f255(f875(x34481,a862))) % 165.14/165.04 [3449]E(f332(f332(f22(f875(x34491,a862)),x34492),f255(f875(x34491,a862))),f196(f875(x34491,a862))) % 165.14/165.04 [3450]E(f332(f332(f104(f875(x34501,a862)),x34502),f196(f875(x34501,a862))),f196(f875(x34501,a862))) % 165.14/165.04 [3467]E(f45(a1,f332(f80(a1),x34671),f332(f80(a1),x34672)),f332(f80(a1),f45(a1,x34671,x34672))) % 165.14/165.04 [3468]E(f45(a1,f332(f103(a1),x34681),f332(f103(a1),x34682)),f332(f103(a1),f45(a868,x34681,x34682))) % 165.14/165.04 [3479]E(f332(f197(f869(x34791)),f332(f173(x34791),x34792)),f332(f332(f22(a868),f332(f197(f869(x34791)),x34792)),f79(a868))) % 165.14/165.04 [3504]E(f332(f332(f39(a1),f45(a1,x35041,x35042)),x35042),f2(a1)) % 165.14/165.04 [3514]E(f332(a3,f45(a868,f332(a19,x35141),f332(a19,x35142))),f45(a102,x35141,x35142)) % 165.14/165.04 [3549]E(f332(a3,f332(f332(f22(a868),f332(a19,x35491)),f332(a19,x35492))),f332(f332(f22(a102),x35491),x35492)) % 165.14/165.04 [3550]E(f332(a3,f332(f332(f81(a868),f332(a19,x35501)),f332(a19,x35502))),f332(f332(f81(a102),x35501),x35502)) % 165.14/165.04 [3551]E(f332(a3,f332(f332(f82(a868),f332(a19,x35511)),f332(a19,x35512))),f332(f332(f82(a102),x35511),x35512)) % 165.14/165.04 [3552]E(f332(a3,f332(f332(f39(a868),f332(a19,x35521)),f332(a19,x35522))),f332(f332(f39(a102),x35521),x35522)) % 165.14/165.04 [3561]E(f332(f311(a868,a868,a115),f332(f302(a868,x35611),x35612)),f332(f302(a868,f332(a115,x35611)),f332(a115,x35612))) % 165.14/165.04 [3587]P24(f332(f48(x35871,x35872),f86(f874(a868,a868),f48(x35871,x35872)))) % 165.14/165.04 [3607]E(f332(f332(f81(a868),f332(f332(f81(a868),f32(x36071)),f32(x36072))),f332(a115,f2(a868))),f32(f34(x36071,x36072))) % 165.14/165.04 [3608]E(f45(a868,f332(a115,f45(a868,x36081,x36082)),x36082),f45(a868,f332(a115,x36081),x36082)) % 165.14/165.04 [3622]E(f332(f332(f42(f875(x36221,a862),f875(x36221,a862)),x36222),f5(f875(x36221,a862))),f40(f875(x36221,a862),x36222)) % 165.14/165.04 [3623]E(f332(f332(f43(f875(x36231,a862),f875(x36231,a862)),x36232),f5(f875(x36231,a862))),f41(f875(x36231,a862),x36232)) % 165.14/165.04 [3624]E(f332(f311(f869(x36241),f875(x36241,a862),f174(x36241)),f332(f174(f869(x36241)),f54(x36241,x36242))),f332(f309(x36241),f332(f174(x36241),x36242))) % 165.14/165.04 [3628]P24(f332(f332(f334(f875(x36281,a862)),x36282),f332(f309(x36281),x36282))) % 165.14/165.04 [3634]E(f45(a1,f332(f80(a1),f45(a1,x36341,x36342)),x36342),f45(a1,f332(f80(a1),x36341),x36342)) % 165.14/165.04 [3646]P24(f332(f332(f246(f875(x36461,a862)),x36462),f255(f875(x36461,a862)))) % 165.14/165.04 [3648]E(f332(f332(f289(x36481,x36481,x36481),f308(x36481,x36482)),f308(x36481,f308(x36481,x36482))),f308(x36481,x36482)) % 165.14/165.04 [3649]E(f332(f332(f113(f875(x36491,a862)),f332(f265(x36491,x36491),x36492)),f332(f263(x36491,x36491),x36492)),f332(f285(x36491),x36492)) % 165.14/165.04 [3670]E(f319(x36701,x36702,f255(f875(x36701,a862)),f255(f875(x36702,a862))),f255(f875(f876(x36701,x36702),a862))) % 165.14/165.04 [3722]P24(f332(f332(f246(a868),f45(a868,x37221,x37222)),x37221)) % 165.14/165.04 [3747]P24(f332(f332(f246(a1),f332(f80(a1),f332(f103(a1),x37471))),f332(f103(a1),x37472))) % 165.14/165.04 [3773]P24(f332(f332(f334(f875(x37731,a862)),f196(f875(x37731,a862))),f332(f309(x37731),x37732))) % 165.14/165.04 [3778]E(f308(x37781,f332(f332(f289(x37781,x37781,x37781),x37782),f308(x37781,x37782))),f308(x37781,x37782)) % 165.14/165.04 [3781]E(f332(f332(f289(x37811,x37811,x37811),f308(x37811,x37812)),x37812),f332(f332(f289(x37811,x37811,x37811),x37812),f308(x37811,x37812))) % 165.14/165.04 [3783]E(f332(a107,f332(f332(f81(a1),f332(f332(f22(a1),x37831),x37832)),f79(a1))),f332(f38(a1),f303(a1,x37832,x37831))) % 165.14/165.04 [3798]E(f332(f263(x37981,x37981),f332(f332(f289(x37981,x37981,x37981),x37982),f308(x37981,x37982))),f332(f263(x37981,x37981),x37982)) % 165.14/165.04 [3799]E(f332(f265(x37991,x37991),f332(f332(f289(x37991,x37991,x37991),x37992),f308(x37991,x37992))),f332(f265(x37991,x37991),x37992)) % 165.14/165.04 [3815]E(f332(f332(f81(a868),f332(f332(f81(a868),f332(f197(a863),x38151)),f332(f197(a863),x38152))),f332(a115,f2(a868))),f332(f197(a863),f34(x38151,x38152))) % 165.14/165.04 [3818]E(f332(f143(f869(x38181),f869(x38181),f135(x38181),f116(x38181)),f171(f869(x38181),x38182,f116(x38181))),f116(x38181)) % 165.14/165.04 [3827]P21(a868,a868,f332(f332(f7(a868,a868,a868),f81(a868)),x38271),x38272) % 165.14/165.04 [3829]P32(a868,f332(f170(a868),f332(f332(f155(f869(x38291),a868),f197(f869(x38291))),f182(x38291,x38292)))) % 165.14/165.04 [3876]P24(f332(f332(f247(a1),f332(f80(a1),f332(f103(a1),f332(a115,x38761)))),f332(f103(a1),x38762))) % 165.14/165.04 [3923]E(f332(f143(f869(x39231),x39231,f332(f7(x39231,f869(x39231),f869(x39231)),f152(x39231)),f116(x39231)),x39232),f332(f170(x39231),x39232)) % 165.14/165.04 [3975]P24(f332(f332(f246(f875(f874(f869(x39751),f869(x39751)),a862)),f159(x39751,x39752)),f308(f869(x39751),f158(x39751,x39752)))) % 165.14/165.04 [4006]P24(f332(f48(x40061,x40062),f332(f332(f267(a868,a868),f332(f332(f39(a868),x40061),x40062)),f45(a868,x40061,x40062)))) % 165.14/165.04 [4017]P24(f332(f332(f246(f875(f874(f869(x40171),f869(x40171)),a862)),f158(x40171,f308(x40171,x40172))),f308(f869(x40171),f158(x40171,x40172)))) % 165.14/165.04 [4244]E(f332(f332(f273(f874(a102,a102),a102,f874(a102,a102),f874(x42441,f874(a102,a102))),f277(f332(f167(a102),f332(f332(f155(f874(a102,x42441),a102),f266(a102,x42441)),x42442)))),f332(f332(f8(x42441,f875(f874(a102,a102),f874(x42441,f874(a102,a102))),a102),f267(x42441,f874(a102,a102))),f278(x42441,x42442))),f276(x42441,x42442)) % 165.14/165.04 [4355]E(f332(f241(a868,f874(x43551,f870(x43551)),f2(a868),f332(f271(x43551,f870(x43551),a868),f332(f16(f875(f870(x43551),a868),x43551),f332(f332(f7(f870(x43551),a868,a868),f332(f332(f8(a868,f875(a868,a868),f870(x43551)),f81(a868)),f197(f870(x43551)))),f79(a868))))),f332(f136(x43551),x43552)),f332(f197(f870(x43551)),x43552)) % 165.14/165.04 [4430]E(f332(f271(f875(f874(x44301,x44301),a862),f875(f874(x44301,x44301),a862),f875(f875(x44302,x44301),f874(f875(f874(x44302,x44302),a862),f875(f874(x44302,x44302),a862)))),f332(f332(f7(f875(f874(x44301,x44301),a862),f875(f875(f874(x44301,x44301),a862),f875(f875(x44302,x44301),f875(f874(x44302,x44302),a862))),f875(f875(f874(x44301,x44301),a862),f875(f875(x44302,x44301),f874(f875(f874(x44302,x44302),a862),f875(f874(x44302,x44302),a862))))),f332(f332(f8(f875(f875(f875(x44302,x44301),f875(f874(x44302,x44302),a862)),f875(f875(x44302,x44301),f874(f875(f874(x44302,x44302),a862),f875(f874(x44302,x44302),a862)))),f875(f875(f875(f874(x44301,x44301),a862),f875(f875(x44302,x44301),f875(f874(x44302,x44302),a862))),f875(f875(f874(x44301,x44301),a862),f875(f875(x44302,x44301),f874(f875(f874(x44302,x44302),a862),f875(f874(x44302,x44302),a862))))),f875(f874(x44301,x44301),a862)),f8(f875(f875(x44302,x44301),f875(f874(x44302,x44302),a862)),f875(f875(x44302,x44301),f874(f875(f874(x44302,x44302),a862),f875(f874(x44302,x44302),a862))),f875(f874(x44301,x44301),a862))),f332(f332(f8(f875(f875(x44302,x44301),f875(f875(f874(x44302,x44302),a862),f874(f875(f874(x44302,x44302),a862),f875(f874(x44302,x44302),a862)))),f875(f875(f875(x44302,x44301),f875(f874(x44302,x44302),a862)),f875(f875(x44302,x44301),f874(f875(f874(x44302,x44302),a862),f875(f874(x44302,x44302),a862)))),f875(f874(x44301,x44301),a862)),f18(f875(x44302,x44301),f875(f874(x44302,x44302),a862),f874(f875(f874(x44302,x44302),a862),f875(f874(x44302,x44302),a862)))),f332(f332(f8(f875(f875(x44302,x44301),f875(f874(x44302,x44302),a862)),f875(f875(x44302,x44301),f875(f875(f874(x44302,x44302),a862),f874(f875(f874(x44302,x44302),a862),f875(f874(x44302,x44302),a862)))),f875(f874(x44301,x44301),a862)),f332(f8(f875(f874(x44302,x44302),a862),f875(f875(f874(x44302,x44302),a862),f874(f875(f874(x44302,x44302),a862),f875(f874(x44302,x44302),a862))),f875(x44302,x44301)),f267(f875(f874(x44302,x44302),a862),f875(f874(x44302,x44302),a862)))),f288(x44301,x44302))))),f288(x44301,x44302))),f75(x44301,x44302)) % 165.14/165.04 [4514]~E(f332(f309(x45141),x45142),f196(f875(f875(x45141,a862),a862))) % 165.14/165.04 [4532]~P24(f332(f332(f334(x45321),x45322),f196(f875(x45321,a862)))) % 165.14/165.04 [4542]~P24(f332(f332(f247(f875(x45421,a862)),x45422),f196(f875(x45421,a862)))) % 165.14/165.04 [3324]E(f332(f332(f22(a868),x33241),f332(f332(f81(a868),x33241),x33242)),f2(a868)) % 165.14/165.04 [3327]E(f332(f332(f113(f875(x33271,a862)),x33272),x33272),x33272) % 165.14/165.04 [3328]E(f332(f332(f104(f875(x33281,a862)),x33282),x33282),x33282) % 165.14/165.04 [3356]E(f332(f332(f22(f875(x33561,a862)),x33562),x33562),f196(f875(x33561,a862))) % 165.14/165.04 [3359]E(f332(f144(x33591,x33592),f2(a868)),f196(f875(f874(f869(x33591),f869(x33591)),a862))) % 165.14/165.04 [3360]E(f332(f332(f81(a868),x33601),f332(a115,x33602)),f332(a115,f332(f332(f81(a868),x33601),x33602))) % 165.14/165.04 [3373]E(f202(f332(f103(a1),x33731),f332(f103(a1),x33732)),f332(f103(a1),f332(f332(f22(a868),x33731),x33732))) % 165.14/165.04 [3376]E(f332(f332(f39(a1),f332(f80(a1),x33761)),x33762),f332(f332(f39(a1),x33761),f332(f80(a1),x33762))) % 165.14/165.04 [3380]E(f332(f38(a1),f332(f302(a1,x33801),x33802)),f332(a107,f332(f332(f22(a1),x33802),x33801))) % 165.14/165.04 [3383]E(f332(f332(f81(a868),f332(a115,x33831)),x33832),f332(a115,f332(f332(f81(a868),x33831),x33832))) % 165.14/165.04 [3388]E(f332(f80(f875(x33881,a862)),f332(f80(f875(x33881,a862)),x33882)),x33882) % 165.14/165.04 [3402]E(f182(x34021,f332(f332(f152(f869(x34021)),f116(x34021)),x34022)),f182(x34021,x34022)) % 165.14/165.04 [3406]E(f332(f332(f81(a868),x34061),f332(f332(f82(a868),x34061),x34062)),f332(f332(f82(a868),x34061),f332(a115,x34062))) % 165.14/165.04 [3414]E(f332(f332(a23,f332(a3,x34141)),f332(a3,x34142)),f332(a3,f332(f332(f22(a868),x34141),x34142))) % 165.14/165.04 [3428]E(f332(f332(f82(a1),f332(f80(a1),x34281)),x34282),f332(f80(a1),f332(f332(f82(a1),x34281),x34282))) % 165.14/165.04 [3430]E(f332(f332(f257(a1),f332(f103(a1),x34301)),x34302),f332(f103(a1),f332(f332(f257(a868),x34301),x34302))) % 165.14/165.04 [3431]E(f332(f332(f81(a102),f332(a3,x34311)),f332(a3,x34312)),f332(a3,f332(f332(f81(a868),x34311),x34312))) % 165.14/165.04 [3432]E(f332(f332(f82(a102),f332(a3,x34321)),f332(a3,x34322)),f332(a3,f332(f332(f82(a868),x34321),x34322))) % 165.14/165.04 [3433]E(f332(f332(f244(a868),f332(a115,x34331)),f332(a115,x34332)),f332(a115,f332(f332(f244(a868),x34331),x34332))) % 165.14/165.04 [3434]E(f332(f332(f245(a868),f332(a115,x34341)),f332(a115,x34342)),f332(a115,f332(f332(f245(a868),x34341),x34342))) % 165.14/165.04 [3440]E(f332(f174(a868),f140(a868,f332(f302(a868,x34401),x34402))),f332(f302(a868,x34401),x34402)) % 165.14/165.04 [3441]E(f313(x34411,f332(f332(f310(x34411),x34412),f196(f875(x34411,a862)))),x34412) % 165.14/165.04 [3446]E(f332(f263(x34461,x34462),f196(f875(f874(x34461,x34462),a862))),f196(f875(x34462,a862))) % 165.14/165.04 [3447]E(f332(f265(x34471,x34472),f196(f875(f874(x34471,x34472),a862))),f196(f875(x34471,a862))) % 165.14/165.04 [3451]E(f332(a107,f332(f332(f22(a1),x34511),x34512)),f332(f38(a1),f305(a1,x34512,x34511))) % 165.14/165.04 [3456]E(f332(f332(f81(a868),x34561),f332(f332(f82(a868),x34562),x34561)),f332(f332(f82(a868),f332(a115,x34562)),x34561)) % 165.14/165.04 [3458]E(f332(f332(f61(x34581),f196(f875(x34581,a862))),x34582),f196(f875(f875(x34581,a862),a862))) % 165.14/165.04 [3469]E(f332(f197(f869(a868)),f140(a868,f332(f302(a868,x34691),x34692))),f332(f332(f22(a868),x34692),x34691)) % 165.14/165.04 [3484]E(f332(f332(f113(f875(x34841,a862)),f196(f875(x34841,a862))),x34842),x34842) % 165.14/165.04 [3485]E(f332(f332(f104(f875(x34851,a862)),f255(f875(x34851,a862))),x34852),x34852) % 165.14/165.04 [3486]E(f332(f332(f81(a1),f332(f80(a1),x34861)),f332(f80(a1),x34862)),f332(f80(a1),f332(f332(f81(a1),x34861),x34862))) % 165.14/165.04 [3491]E(f332(f332(f81(a1),f332(f103(a1),x34911)),f332(f103(a1),x34912)),f332(f103(a1),f332(f332(f81(a868),x34911),x34912))) % 165.14/165.04 [3492]E(f332(f332(f81(a1),f332(f106(a1),x34921)),f332(f106(a1),x34922)),f332(f106(a1),f332(f332(f81(a1),x34921),x34922))) % 165.14/165.04 [3494]E(f332(f332(f82(a1),f332(f103(a1),x34941)),f332(f103(a1),x34942)),f332(f103(a1),f332(f332(f82(a868),x34941),x34942))) % 165.14/165.04 [3495]E(f332(f332(f82(a1),f332(f106(a1),x34951)),f332(f106(a1),x34952)),f332(f106(a1),f332(f332(f82(a1),x34951),x34952))) % 165.14/165.04 [3496]E(f332(f332(f39(a1),f332(f103(a1),x34961)),f332(f103(a1),x34962)),f332(f103(a1),f332(f332(f39(a868),x34961),x34962))) % 165.14/165.04 [3515]E(f332(f332(f6(x35151,a868),f332(f16(a868,x35151),f79(a868))),x35152),f332(f38(x35151),x35152)) % 165.14/165.04 [3522]E(f332(f80(a1),f45(a1,f332(f80(a1),x35221),x35222)),f45(a1,x35221,f332(f80(a1),x35222))) % 165.14/165.04 [3524]E(f332(f174(a1),f181(x35241,f332(f332(f22(a1),x35242),f79(a1)))),f332(f302(a1,x35241),x35242)) % 165.14/165.04 [3528]P24(f332(f332(f246(a868),x35281),f332(f332(f81(a868),x35282),x35281))) % 165.14/165.04 [3529]P24(f332(f332(f246(a868),x35291),f332(f332(f81(a868),x35291),x35292))) % 165.14/165.04 [3532]E(f332(f332(f113(f875(x35321,a862)),f255(f875(x35321,a862))),x35322),f255(f875(x35321,a862))) % 165.14/165.04 [3533]E(f332(f332(f22(f875(x35331,a862)),f196(f875(x35331,a862))),x35332),f196(f875(x35331,a862))) % 165.14/165.04 [3534]E(f332(f332(f104(f875(x35341,a862)),f196(f875(x35341,a862))),x35342),f196(f875(x35341,a862))) % 165.14/165.04 [3541]E(f332(f332(f267(a1,a1),x35411),f332(f80(a1),x35412)),f332(a51,f332(f332(f267(a1,a1),x35411),x35412))) % 165.14/165.04 [3542]E(f332(f302(a1,f332(f332(f81(a1),x35421),f79(a1))),x35422),f306(a1,x35421,x35422)) % 165.14/165.04 [3553]E(f332(f332(f82(a868),x35531),f332(f332(f39(a868),x35532),x35531)),f332(f332(f22(a868),x35532),f45(a868,x35532,x35531))) % 165.14/165.04 [3554]E(f332(f332(f82(a1),x35541),f332(f332(f39(a1),x35542),x35541)),f332(f332(f22(a1),x35542),f45(a1,x35542,x35541))) % 165.14/165.04 [3558]E(f332(f174(a1),f181(f332(f332(f81(a1),x35581),f79(a1)),x35582)),f305(a1,x35581,x35582)) % 165.14/165.04 [3562]P24(f332(f332(f246(f875(x35621,a862)),x35622),x35622)) % 165.14/165.04 [3565]E(f332(f332(f113(f875(x35651,a862)),x35652),f332(f80(f875(x35651,a862)),x35652)),f255(f875(x35651,a862))) % 165.14/165.04 [3566]E(f332(f332(f104(f875(x35661,a862)),x35662),f332(f80(f875(x35661,a862)),x35662)),f196(f875(x35661,a862))) % 165.14/165.04 [3574]E(f332(f332(f22(a868),f332(f332(f22(a868),x35741),f79(a868))),x35742),f332(f332(f22(a868),x35741),f332(a115,x35742))) % 165.14/165.04 [3579]E(f332(f332(f22(f875(x35791,a862)),f255(f875(x35791,a862))),x35792),f332(f80(f875(x35791,a862)),x35792)) % 165.14/165.04 [3580]E(f332(f332(f22(a1),f332(f106(a1),x35801)),f332(f106(a1),x35802)),f332(f106(a1),f332(f332(f81(a1),x35801),f332(f80(a1),x35802)))) % 165.14/165.04 [3593]E(f332(f174(a868),f140(a868,f332(f302(a868,x35931),f332(a115,x35932)))),f303(a868,x35931,x35932)) % 165.14/165.04 [3605]E(f332(f197(f869(f869(x36051))),f54(x36051,x36052)),f332(f332(f257(a868),f332(a115,f332(a115,f2(a868)))),f332(f197(f869(x36051)),x36052))) % 165.14/165.04 [3626]E(f332(f332(f191(f874(x36261,x36261),a862),f2(a868)),x36262),f308(x36261,f196(f875(f874(x36261,x36261),a862)))) % 165.14/165.04 [3630]P24(f332(f138(a868),f140(a868,f332(f302(a868,x36301),x36302)))) % 165.14/165.04 [3647]E(f332(f311(a1,a868,a107),f303(a1,f332(f103(a1),x36471),f332(f103(a1),x36472))),f303(a868,x36471,x36472)) % 165.14/165.04 [3657]E(f193(a868,f2(a868),f5(a868),f332(f332(f22(a868),x36571),x36572)),f332(f332(f22(a868),x36571),f332(a115,x36572))) % 165.14/165.04 [3658]E(f332(a107,f332(f332(f22(a1),x36581),f332(f332(f81(a1),x36582),f79(a1)))),f332(f38(a1),f306(a1,x36582,x36581))) % 165.14/165.04 [3694]E(f332(f332(f155(a868,a868),a115),f140(a868,f332(f302(a868,x36941),x36942))),f140(a868,f332(f302(a868,f332(a115,x36941)),f332(a115,x36942)))) % 165.14/165.04 [3702]E(f332(f174(a1),f181(f332(f332(f81(a1),x37021),f79(a1)),f332(f332(f22(a1),x37022),f79(a1)))),f306(a1,x37021,x37022)) % 165.14/165.04 [3713]P24(f332(f332(f246(f875(x37131,a862)),f196(f875(x37131,a862))),x37132)) % 165.14/165.04 [3718]E(f86(x37181,f332(f332(f7(x37181,x37181,a862),a329),x37182)),x37182) % 165.14/165.04 [3719]E(f91(x37191,f332(f332(f7(x37191,x37191,a862),a329),x37192)),x37192) % 165.14/165.04 [3723]E(f332(f174(a868),f140(a868,f332(f302(a868,f332(a115,x37231)),f332(a115,x37232)))),f305(a868,x37231,x37232)) % 165.14/165.04 [3750]E(f332(f332(f269(x37501,x37502),f255(f875(x37501,a862))),f332(f16(f875(x37502,a862),x37501),f255(f875(x37502,a862)))),f255(f875(f874(x37501,x37502),a862))) % 165.14/165.04 [3785]E(f332(f252(x37851),f332(f332(f8(a862,a862,x37851),a327),x37852)),f332(f80(f875(x37851,a862)),f332(f252(x37851),x37852))) % 165.14/165.04 [3788]E(f332(f252(x37881),f332(f332(f7(x37881,x37881,a862),a329),x37882)),f332(f332(f310(x37881),x37882),f196(f875(x37881,a862)))) % 165.14/165.04 [3795]E(f332(f332(f81(a1),f332(f332(f22(a1),x37951),x37952)),f332(f332(f22(a1),x37951),x37952)),f332(f332(f22(a1),f332(f332(f81(a1),x37951),x37951)),f332(f332(f81(a1),x37952),x37952))) % 165.14/165.04 [3796]E(f332(f332(f81(a1),f332(f332(f81(a1),x37961),x37961)),f332(f332(f81(a1),x37962),x37962)),f332(f332(f81(a1),f332(f332(f81(a1),x37961),x37962)),f332(f332(f81(a1),x37961),x37962))) % 165.14/165.04 [3812]P24(f332(f332(f246(a868),f332(f38(x38121),f332(f174(x38121),x38122))),f332(f197(f869(x38121)),x38122))) % 165.14/165.04 [3813]P24(f332(f332(f246(a868),f332(f197(f869(x38131)),f153(x38131,x38132))),f332(f197(f869(x38131)),x38132))) % 165.14/165.04 [3824]E(f332(f252(x38241),f332(f332(f7(x38241,f875(x38241,a862),a862),f334(x38241)),x38242)),x38242) % 165.14/165.04 [3840]E(f332(f332(f177(x38401),f332(f332(f22(a868),f332(f197(f869(x38401)),x38402)),f79(a868))),x38402),f117(x38401,x38402)) % 165.14/165.04 [3863]E(f193(a868,f2(a868),f332(f332(f8(a868,a868,a868),a115),f332(f244(a868),x38631)),x38632),f332(f332(f244(a868),f332(a115,x38631)),x38632)) % 165.14/165.04 [3867]E(f40(f875(x38671,a862),f332(f311(f875(f874(x38671,x38671),a862),f875(x38671,a862),f285(x38671)),x38672)),f332(f285(x38671),f40(f875(f874(x38671,x38671),a862),x38672))) % 165.14/165.04 [3868]E(f193(a868,f332(a115,x38681),f332(f332(f8(a868,a868,a868),a115),f332(f245(a868),x38681)),x38682),f332(f332(f245(a868),f332(a115,x38681)),x38682)) % 165.14/165.04 [3870]E(f332(f332(f267(a1,a1),f332(f332(f39(a1),f332(f76(a1),x38701)),f332(f76(a1),x38702))),f45(a1,f332(f76(a1),x38701),f332(f76(a1),x38702))),f53(x38701,x38702)) % 165.14/165.04 [3893]P24(f332(f332(f246(f875(f875(x38931,a862),a862)),x38932),f332(f309(x38931),f40(f875(x38931,a862),x38932)))) % 165.14/165.04 [3928]E(f332(f332(f42(x39281,f875(x39281,a862)),x39282),f332(f332(f7(x39281,f875(x39281,a862),f875(x39281,a862)),f310(x39281)),f196(f875(x39281,a862)))),x39282) % 165.14/165.04 [3929]E(f332(f332(f289(x39291,x39291,x39291),f332(f287(x39291,x39291),x39292)),f308(x39291,f332(f287(x39291,x39291),x39292))),f332(f287(x39291,x39291),f332(f332(f289(x39291,x39291,x39291),x39292),f308(x39291,x39292)))) % 165.14/165.04 [3997]E(f332(f174(x39971),f332(f143(f869(x39971),f869(x39971),f135(x39971),f116(x39971)),x39972)),f332(f332(f42(f869(x39971),f875(x39971,a862)),f332(f174(f869(x39971)),x39972)),f174(x39971))) % 165.14/165.04 [4030]E(f332(f332(f113(f875(f874(x40301,x40301),a862)),f308(x40301,f196(f875(f874(x40301,x40301),a862)))),f332(f332(f289(x40301,x40301,x40301),f308(x40301,x40302)),x40302)),f308(x40301,x40302)) % 165.14/165.04 [4064]E(f332(f332(f184(x40641,x40641),x40642),x40642),f332(f332(f155(x40641,f874(x40641,x40641)),f332(f332(f18(x40641,x40641,f874(x40641,x40641)),f267(x40641,x40641)),f5(x40641))),x40642)) % 165.14/165.04 [4181]E(f332(f143(a868,f869(x41811),f332(f7(f869(x41811),a868,a868),f332(f332(f8(a868,f875(a868,a868),f869(x41811)),f245(a868)),f197(f869(x41811)))),f2(a868)),f332(f170(f869(x41811)),x41812)),f332(f197(f869(f869(x41811))),f182(x41811,x41812))) % 165.14/165.04 [4259]E(f332(f332(f288(f874(a868,f869(x42591)),f869(x42591)),f324(a868,f869(x42591),a251,f146(x42591,x42592))),f332(f332(f18(f869(x42591),f869(x42591),f874(a868,f869(x42591))),f332(f332(f8(a868,f875(f869(x42591),f874(a868,f869(x42591))),f869(x42591)),f267(a868,f869(x42591))),f197(f869(x42591)))),f5(f869(x42591)))),f147(x42591,x42592)) % 165.14/165.04 [4389]E(f332(f252(x43891),f332(f332(f8(f875(f875(x43891,a862),a862),a862,x43891),f89(f875(x43891,a862))),f332(f332(f8(f875(f875(x43891,a862),a862),f875(f875(x43891,a862),a862),x43891),f332(f18(f875(x43891,a862),a862,a862),f332(f332(f8(a862,f875(a862,a862),f875(x43891,a862)),a335),f332(f332(f7(f875(x43891,a862),f875(f875(x43891,a862),a862),a862),f334(f875(x43891,a862))),x43892)))),f334(x43891)))),f41(f875(x43891,a862),x43892)) % 165.14/165.04 [4543]~P24(f332(f332(f247(a1),f332(f103(a1),x45431)),f332(f80(a1),f332(f103(a1),x45432)))) % 165.14/165.04 [4559]~P24(f332(f332(f92(a1),f332(f332(f22(a1),f332(f332(f81(a1),x45591),x45591)),a100)),f332(f332(f81(a1),x45592),x45592))) % 165.14/165.04 [3454]E(f332(f332(f22(a868),f332(f332(f81(a868),x34541),x34542)),x34542),x34541) % 165.14/165.04 [3455]E(f332(f332(f22(a868),f332(f332(f81(a868),x34551),x34552)),x34551),x34552) % 165.14/165.04 [3523]E(f332(f332(f81(a868),f332(f332(f22(a868),x35231),x35232)),x35232),f332(f332(f245(a868),x35231),x35232)) % 165.14/165.04 [3633]E(f332(f332(f82(a868),f332(f332(f39(a868),x36331),x36332)),x36332),f332(f332(f22(a868),x36331),f45(a868,x36331,x36332))) % 165.14/165.04 [3662]E(f332(f174(a868),f140(a868,f332(f302(a868,f332(a115,x36621)),x36622))),f306(a868,x36621,x36622)) % 165.14/165.04 [3669]E(f332(f103(a1),f228(f332(a107,f332(f76(a1),x36691)),f332(a107,f332(f76(a1),x36692)))),f332(f332(a229,x36691),x36692)) % 165.14/165.04 [3671]E(f332(f332(f113(f875(x36711,a862)),f332(f80(f875(x36711,a862)),x36712)),x36712),f255(f875(x36711,a862))) % 165.14/165.04 [3672]E(f332(f332(f104(f875(x36721,a862)),f332(f80(f875(x36721,a862)),x36722)),x36722),f196(f875(x36721,a862))) % 165.14/165.04 [3690]P24(f332(f332(f246(a868),f332(f332(f22(a868),x36901),x36902)),x36901)) % 165.14/165.04 [3691]P24(f332(f332(f246(a868),f332(f332(f39(a868),x36911),x36912)),x36911)) % 165.14/165.04 [3715]P24(f332(f332(f247(a868),x37151),f332(a115,f332(f332(f81(a868),x37152),x37151)))) % 165.14/165.04 [3716]P24(f332(f332(f247(a868),x37161),f332(a115,f332(f332(f81(a868),x37161),x37162)))) % 165.14/165.04 [3734]E(f332(f332(f82(a868),f332(a107,f332(f76(a1),x37341))),f332(a107,f332(f76(a1),x37342))),f332(a107,f332(f76(a1),f332(f332(f82(a1),x37341),x37342)))) % 165.14/165.04 [3746]P24(f332(f332(f246(a1),f2(a1)),f332(f332(f257(a1),f332(f76(a1),x37461)),x37462))) % 165.14/165.04 [3817]E(f332(f286(f869(x38171),f869(x38171),f159(x38171,x38172)),f332(f332(f310(f869(x38171)),f116(x38171)),f196(f875(f869(x38171),a862)))),f332(f332(f310(f869(x38171)),f116(x38171)),f196(f875(f869(x38171),a862)))) % 165.14/165.04 [3838]E(f332(f332(f113(f875(f874(x38381,x38381),a862)),f308(x38381,x38382)),f308(x38381,f196(f875(f874(x38381,x38381),a862)))),f308(x38381,x38382)) % 165.14/165.04 [3853]E(f332(f332(f39(a1),f332(f106(a1),f332(f332(f81(a1),x38531),x38531))),f332(f106(a1),f332(f332(f81(a1),x38532),x38532))),f332(f332(f39(a1),f332(f106(a1),x38531)),f332(f106(a1),x38532))) % 165.14/165.04 [3918]E(f332(f332(f257(a1),x39181),f332(f106(a868),f332(f332(f81(a1),x39182),x39182))),f332(f332(f87(a1,a1),f332(f332(f257(a1),x39181),f332(f106(a868),x39182))),f332(f332(f18(a1,a1,a1),f82(a1)),f5(a1)))) % 165.14/165.04 [3924]E(f332(f252(f875(x39241,a862)),f332(f332(f7(f875(x39241,a862),f875(x39241,a862),a862),f246(f875(x39241,a862))),x39242)),f332(f309(x39241),x39242)) % 165.14/165.04 [3939]E(f332(f332(f155(a1,a868),a107),f332(f332(f135(a1),f332(f332(f155(a868,a1),f103(a1)),x39391)),f332(f332(f155(a868,a1),f103(a1)),x39392))),f332(f332(f135(a868),x39391),x39392)) % 165.14/165.04 [3974]E(f332(f311(a1,a1,f332(f332(f7(a1,a1,a1),f81(a1)),x39741)),f332(f302(a1,f2(a1)),f332(f332(f22(a1),x39742),x39741))),f332(f302(a1,x39741),x39742)) % 165.14/165.04 [3976]P45(x39761,f332(f332(f22(f875(f874(x39761,x39761),a862)),x39762),f308(x39761,f196(f875(f874(x39761,x39761),a862))))) % 165.14/165.04 [3995]E(f332(f197(f869(x39951)),f332(f143(f869(x39951),f869(x39951),f135(x39951),f116(x39951)),x39952)),f332(f167(a868),f332(f332(f155(f869(x39951),a868),f197(f869(x39951))),x39952))) % 165.14/165.04 [4000]P43(x40001,f255(f875(x40001,a862)),f332(f332(f113(f875(f874(x40001,x40001),a862)),x40002),f308(x40001,f196(f875(f874(x40001,x40001),a862))))) % 165.14/165.04 [4044]E(f193(a868,f2(a868),f332(f332(f8(a868,a868,a868),a115),f332(f332(f7(a868,a868,a868),f244(a868)),x40441)),x40442),f332(f332(f244(a868),x40442),f332(a115,x40441))) % 165.14/165.04 [4047]E(f193(a868,f332(a115,x40471),f332(f332(f8(a868,a868,a868),a115),f332(f332(f7(a868,a868,a868),f245(a868)),x40471)),x40472),f332(f332(f245(a868),x40472),f332(a115,x40471))) % 165.14/165.04 [4050]E(f332(f311(x40501,f869(x40501),f332(f332(f7(x40501,f869(x40501),f869(x40501)),f152(x40501)),f116(x40501))),x40502),f176(x40501,x40502,f332(f332(f310(f869(x40501)),f116(x40501)),f196(f875(f869(x40501),a862))))) % 165.14/165.04 [4051]E(f332(f332(f113(f875(f874(x40511,x40511),a862)),f332(f332(f289(x40511,x40511,x40511),x40512),f308(x40511,x40512))),f308(x40511,f196(f875(f874(x40511,x40511),a862)))),f308(x40511,x40512)) % 165.14/165.04 [4059]P24(f332(f332(f246(f875(f874(x40591,x40591),a862)),f264(x40591,x40592)),f332(f332(f269(x40591,x40591),x40592),f332(f16(f875(x40591,a862),x40591),x40592)))) % 165.14/165.04 [4062]E(f332(f311(a1,a868,a107),f332(f332(f113(f875(a1,a862)),f332(f311(a868,a1,f103(a1)),x40621)),f332(f311(a868,a1,f103(a1)),x40622))),f332(f332(f113(f875(a868,a862)),x40621),x40622)) % 165.14/165.04 [4063]E(f332(f311(a1,a868,a107),f332(f332(f104(f875(a1,a862)),f332(f311(a868,a1,f103(a1)),x40631)),f332(f311(a868,a1,f103(a1)),x40632))),f332(f332(f104(f875(a868,a862)),x40631),x40632)) % 165.14/165.04 [4067]E(f332(f252(x40671),f332(f332(f8(a862,a862,x40671),a327),f332(f332(f7(x40671,f875(x40671,a862),a862),f334(x40671)),x40672))),f332(f80(f875(x40671,a862)),x40672)) % 165.14/165.04 [4094]E(f332(f143(f869(x40941),f869(x40941),f135(x40941),f116(x40941)),f332(f332(f155(f869(x40941),f869(x40941)),f170(x40941)),f332(f170(f869(x40941)),x40942))),f332(f170(x40941),f332(f143(f869(x40941),f869(x40941),f135(x40941),f116(x40941)),x40942))) % 165.14/165.04 [4123]E(f332(f332(f42(a868,f875(f874(x41231,x41231),a862)),f255(f875(a868,a862))),f332(f332(f7(a868,f875(f874(x41231,x41231),a862),f875(f874(x41231,x41231),a862)),f191(f874(x41231,x41231),a862)),x41232)),f308(x41231,x41232)) % 165.14/165.04 [4143]E(f86(x41431,f332(f332(f8(f875(x41431,a862),a862,x41431),f332(a329,x41432)),f332(f332(f7(x41431,f875(x41431,a862),f875(x41431,a862)),f310(x41431)),f196(f875(x41431,a862))))),f313(x41431,x41432)) % 165.14/165.04 [4151]E(f332(f197(f869(x41511)),f153(x41511,f332(f143(f869(x41511),f869(x41511),f135(x41511),f116(x41511)),x41512))),f332(f38(x41511),f332(f332(f42(f869(x41511),f875(x41511,a862)),f332(f174(f869(x41511)),x41512)),f174(x41511)))) % 165.14/165.04 [4167]E(f332(f332(f113(f875(f874(x41671,x41671),a862)),x41672),f332(f332(f289(x41671,x41671,x41671),f332(f332(f289(x41671,x41671,x41671),x41672),f308(x41671,x41672))),x41672)),f332(f332(f289(x41671,x41671,x41671),x41672),f308(x41671,x41672))) % 165.14/165.04 [4191]P24(f332(f332(f246(f875(f874(x41911,x41911),a862)),f332(f332(f289(x41911,x41911,x41911),x41912),f308(x41911,x41912))),f332(f332(f269(x41911,x41911),f332(f285(x41911),x41912)),f332(f16(f875(x41911,a862),x41911),f332(f285(x41911),x41912))))) % 165.14/165.04 [4234]E(f332(f252(f869(x42341)),f332(f332(f7(f869(x42341),f875(x42341,a862),a862),f332(f332(f8(f875(x42341,a862),f875(f875(x42341,a862),a862),f869(x42341)),f246(f875(x42341,a862))),f174(x42341))),x42342)),f162(x42341,x42342)) % 165.14/165.04 [4246]E(f332(f157(f869(x42461),x42461,f116(x42461),f332(f332(f8(f869(x42461),f875(f869(x42461),f869(x42461)),x42461),f332(f7(f869(x42461),f869(x42461),f869(x42461)),f135(x42461))),f332(f332(f7(x42461,f869(x42461),f869(x42461)),f152(x42461)),f116(x42461)))),x42462),f332(f169(x42461),x42462)) % 165.14/165.04 [4288]P21(f875(x42881,x42882),f875(f874(x42881,x42882),a862),f332(f332(f8(f875(f874(x42881,x42882),a862),f875(f874(x42881,x42882),a862),f875(x42881,x42882)),f252(f874(x42881,x42882))),f332(f332(f8(f875(x42881,f875(x42882,a862)),f875(f874(x42881,x42882),a862),f875(x42881,x42882)),f271(x42881,x42882,a862)),f332(f8(x42882,f875(x42882,a862),x42881),f332(f7(x42882,x42882,a862),a329)))),f255(f875(f875(x42881,x42882),a862))) % 165.14/165.04 [4293]E(f45(a1,f332(f106(a1),f332(f332(f81(a1),x42931),x42931)),f332(f106(a1),f332(f332(f81(a1),x42932),x42932))),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f45(a1,f332(f106(a1),x42931),f332(f106(a1),x42932)))) % 165.14/165.04 [4336]E(f332(f332(f42(x43361,f875(f874(x43361,x43361),a862)),x43362),f332(f332(f7(x43361,f875(f874(x43361,x43361),a862),f875(f874(x43361,x43361),a862)),f332(f332(f8(f874(x43361,x43361),f875(f875(f874(x43361,x43361),a862),f875(f874(x43361,x43361),a862)),x43361),f310(f874(x43361,x43361))),f332(f332(f18(x43361,x43361,f874(x43361,x43361)),f267(x43361,x43361)),f5(x43361)))),f196(f875(f874(x43361,x43361),a862)))),f264(x43361,x43362)) % 165.14/165.04 [4344]E(f214(x43441,f332(f332(f267(a1,a1),f332(f80(a1),f332(f332(f74(f874(a1,a1),a1,x43441,f266(a1,a1)),f224(x43441)),x43442))),f332(f332(f74(f874(a1,a1),a1,x43441,f270(a1,a1)),f224(x43441)),x43442))),f232(x43441,x43442)) % 165.14/165.04 [4425]E(f332(f252(f875(x44251,a862)),f332(f332(f8(f875(f875(x44251,a862),a862),a862,f875(x44251,a862)),f88(f875(x44251,a862))),f332(f332(f7(f875(x44251,a862),f875(f875(x44251,a862),a862),f875(f875(x44251,a862),a862)),f332(f332(f8(f875(f875(x44251,a862),f875(a862,a862)),f875(f875(f875(x44251,a862),a862),f875(f875(x44251,a862),a862)),f875(x44251,a862)),f18(f875(x44251,a862),a862,a862)),f332(f332(f8(f875(f875(x44251,a862),a862),f875(f875(x44251,a862),f875(a862,a862)),f875(x44251,a862)),f332(f8(a862,f875(a862,a862),f875(x44251,a862)),a330)),f332(f332(f7(f875(x44251,a862),f875(f875(x44251,a862),f875(x44251,a862)),f875(f875(x44251,a862),a862)),f332(f332(f8(f875(f875(x44251,a862),a862),f875(f875(f875(x44251,a862),f875(x44251,a862)),f875(f875(x44251,a862),a862)),f875(x44251,a862)),f8(f875(x44251,a862),a862,f875(x44251,a862))),a329)),f80(f875(x44251,a862)))))),f332(f332(f8(f875(f875(x44251,a862),a862),a862,f875(x44251,a862)),f332(f334(f875(x44251,a862)),x44252)),f309(x44251))))),f332(f309(x44251),f332(f80(f875(x44251,a862)),x44252))) % 165.14/165.04 [4540]~E(f332(f332(f81(a1),x45401),x45401),f332(f332(f22(a1),f332(f332(f81(a1),x45402),x45402)),a100)) % 165.14/165.04 [4546]~P24(f332(f332(f247(a868),f332(f332(f81(a868),x45461),x45462)),x45462)) % 165.14/165.04 [4547]~P24(f332(f332(f247(a868),f332(f332(f81(a868),x45471),x45472)),x45471)) % 165.14/165.04 [3751]E(f332(f332(f22(a868),x37511),f332(f332(f82(a868),f332(f332(f39(a868),x37511),x37512)),x37512)),f45(a868,x37511,x37512)) % 165.14/165.04 [3752]E(f332(f332(f22(a1),x37521),f332(f332(f82(a1),f332(f332(f39(a1),x37521),x37522)),x37522)),f45(a1,x37521,x37522)) % 165.14/165.04 [3786]E(f332(f332(f155(a868,x37861),f332(f166(x37861),x37862)),f140(a868,f332(f302(a868,f2(a868)),f332(f197(f869(x37861)),x37862)))),x37862) % 165.14/165.04 [3849]E(f332(f286(x38491,x38491,f308(x38491,f196(f875(f874(x38491,x38491),a862)))),x38492),x38492) % 165.14/165.04 [3979]E(f308(x39791,f332(f332(f113(f875(f874(x39791,x39791),a862)),x39792),f308(x39791,f196(f875(f874(x39791,x39791),a862))))),f308(x39791,x39792)) % 165.14/165.04 [3980]E(f308(x39801,f332(f332(f22(f875(f874(x39801,x39801),a862)),x39802),f308(x39801,f196(f875(f874(x39801,x39801),a862))))),f308(x39801,x39802)) % 165.14/165.04 [4033]E(f332(f332(f22(a1),f332(f332(f22(a1),f332(f332(f81(a1),x40331),x40331)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),x40332),x40332)),a100)),f332(f332(f81(a1),f332(f332(f22(a1),x40331),x40332)),f332(f332(f22(a1),x40331),x40332))) % 165.14/165.04 [4072]E(f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f81(a1),x40721),x40722)),f332(f332(f81(a1),x40721),x40722))),a100),f332(f332(f81(a1),f332(f332(f81(a1),x40721),x40721)),f332(f332(f22(a1),f332(f332(f81(a1),x40722),x40722)),a100))) % 165.14/165.04 [4098]E(f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),x40981),x40981)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),x40982),x40982)),a100)),f332(f332(f81(a1),f332(f332(f81(a1),x40981),f332(f332(f22(a1),x40982),a100))),f332(f332(f81(a1),x40981),f332(f332(f22(a1),x40982),a100)))) % 165.14/165.04 [4108]E(f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),x41081),x41082)),f332(f332(f22(a1),x41081),x41082))),a100),f332(f332(f22(a1),f332(f332(f22(a1),f332(f332(f81(a1),x41081),x41081)),a100)),f332(f332(f81(a1),x41082),x41082))) % 165.14/165.04 [4109]E(f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f81(a1),x41091),x41092)),f332(f332(f81(a1),x41091),x41092))),a100),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),x41091),x41091)),a100)),f332(f332(f81(a1),x41092),x41092))) % 165.14/165.04 [4164]E(f332(f103(a1),f332(f332(f39(a868),f332(f332(f82(a868),f332(a107,f332(f76(a1),x41641))),f332(a107,f332(f76(a1),x41642)))),f228(f332(a107,f332(f76(a1),x41641)),f332(a107,f332(f76(a1),x41642))))),f230(x41641,x41642)) % 165.14/165.04 [4211]E(f332(f332(f273(f874(a102,a102),a102,f874(a102,a102),f874(x42111,f874(a102,a102))),f277(f332(a3,f332(f197(f869(x42111)),x42112)))),f332(f332(f8(x42111,f875(f874(a102,a102),f874(x42111,f874(a102,a102))),a102),f267(x42111,f874(a102,a102))),f332(f332(f8(a868,x42111,a102),f332(f166(x42111),x42112)),a19))),f283(x42111,x42112)) % 165.14/165.04 [4294]E(f332(f143(a868,f869(x42941),f332(f7(f869(x42941),a868,a868),f332(f332(f8(a868,f875(a868,a868),f869(x42941)),f245(a868)),f197(f869(x42941)))),f2(a868)),f332(f170(f869(x42941)),f182(x42941,x42942))),f332(f197(f869(f869(x42941))),f332(f137(f869(x42941),f332(f332(f8(a862,a862,f869(x42941)),a327),f332(f332(f7(f869(x42941),f869(x42941),a862),a329),f116(x42941)))),x42942))) % 165.14/165.04 [4300]E(f332(f332(f42(a868,f875(x43001,a862)),f255(f875(a868,a862))),f332(f332(f7(a868,f875(a868,f875(x43001,a862)),f875(x43001,a862)),f332(f332(f8(f875(a868,a862),f875(f875(a868,f875(x43001,a862)),f875(x43001,a862)),a868),f42(a868,f875(x43001,a862))),f302(a868,f2(a868)))),x43002)),f332(f332(f42(a868,f875(x43001,a862)),f255(f875(a868,a862))),x43002)) % 165.14/165.04 [4320]P24(f332(f62(a868),f332(f252(a868),f332(f332(f18(a868,a862,a862),f332(f332(f8(a862,f875(a862,a862),a868),a330),x43201)),f332(f332(f7(a868,a868,a862),f247(a868)),x43202))))) % 165.14/165.04 [4436]E(f332(f252(f874(f869(x44361),f869(x44361))),f332(f271(f869(x44361),f869(x44361),a862),f332(f332(f18(f869(x44361),f875(f869(x44361),a862),f875(f869(x44361),a862)),f332(f332(f8(f875(f869(x44361),f875(a862,a862)),f875(f875(f869(x44361),a862),f875(f869(x44361),a862)),f869(x44361)),f18(f869(x44361),a862,a862)),f332(f332(f8(f875(f869(x44361),a862),f875(f869(x44361),f875(a862,a862)),f869(x44361)),f332(f8(a862,f875(a862,a862),f869(x44361)),a331)),f332(f332(f7(f869(x44361),f875(f869(x44361),a868),f875(f869(x44361),a862)),f332(f332(f8(f875(a868,a862),f875(f875(f869(x44361),a868),f875(f869(x44361),a862)),f869(x44361)),f8(a868,a862,f869(x44361))),f332(f332(f8(a868,f875(a868,a862),f869(x44361)),f247(a868)),f197(f869(x44361))))),f197(f869(x44361)))))),f332(f332(f18(f869(x44361),f875(f869(x44361),a862),f875(f869(x44361),a862)),f332(f332(f8(f875(f869(x44361),f875(a862,a862)),f875(f875(f869(x44361),a862),f875(f869(x44361),a862)),f869(x44361)),f18(f869(x44361),a862,a862)),f332(f332(f8(f875(f869(x44361),a862),f875(f869(x44361),f875(a862,a862)),f869(x44361)),f332(f8(a862,f875(a862,a862),f869(x44361)),a330)),f332(f332(f7(f869(x44361),f875(f869(x44361),a868),f875(f869(x44361),a862)),f332(f332(f8(f875(a868,a862),f875(f875(f869(x44361),a868),f875(f869(x44361),a862)),f869(x44361)),f8(a868,a862,f869(x44361))),f332(f332(f8(a868,f875(a868,a862),f869(x44361)),a329),f197(f869(x44361))))),f197(f869(x44361)))))),f332(f332(f7(f869(x44361),f875(f874(f869(x44361),f869(x44361)),a862),f875(f869(x44361),a862)),f332(f332(f8(f875(f869(x44361),f875(f875(f874(f869(x44361),f869(x44361)),a862),a862)),f875(f875(f874(f869(x44361),f869(x44361)),a862),f875(f869(x44361),a862)),f869(x44361)),f7(f869(x44361),f875(f874(f869(x44361),f869(x44361)),a862),a862)),f332(f332(f8(f875(f869(x44361),f874(f869(x44361),f869(x44361))),f875(f869(x44361),f875(f875(f874(f869(x44361),f869(x44361)),a862),a862)),f869(x44361)),f332(f8(f874(f869(x44361),f869(x44361)),f875(f875(f874(f869(x44361),f869(x44361)),a862),a862),f869(x44361)),f334(f874(f869(x44361),f869(x44361))))),f267(f869(x44361),f869(x44361))))),f146(x44361,x44362)))))),f147(x44361,x44362)) % 165.14/165.04 [4552]~P24(f332(f332(f92(a1),f332(f332(f81(a1),x45521),x45521)),f332(f332(f22(a1),f332(f332(f81(a1),x45522),x45522)),a100))) % 165.14/165.04 [4101]E(f332(f332(f81(a1),f332(f332(f81(a1),f332(f332(f82(a1),x41011),x41012)),f332(f332(f82(a1),x41011),x41012))),x41012),f332(f332(f82(a1),f332(f332(f22(a1),f332(f332(f81(a1),x41011),x41011)),a100)),x41012)) % 165.14/165.04 [4209]E(f332(a107,f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x42091),x42092)),f196(f875(f874(a868,a868),a862)))))),f332(f332(f22(a868),x42091),x42092)) % 165.14/165.04 [4214]E(f332(f332(f289(x42141,x42141,x42141),f332(f332(f113(f875(f874(x42141,x42141),a862)),x42142),f308(x42141,f196(f875(f874(x42141,x42141),a862))))),f308(x42141,f332(f332(f113(f875(f874(x42141,x42141),a862)),x42142),f308(x42141,f196(f875(f874(x42141,x42141),a862)))))),f308(x42141,x42142)) % 165.14/165.04 [4252]E(f276(x42521,f332(f137(f874(a102,x42521),f332(f271(a102,x42521,a862),f332(f332(f8(a862,f875(x42521,a862),a102),f16(a862,x42521)),f332(f247(a102),f2(a102))))),x42522)),f276(x42521,x42522)) % 165.14/165.04 [4253]E(f278(x42531,f332(f137(f874(a102,x42531),f332(f271(a102,x42531,a862),f332(f332(f8(a862,f875(x42531,a862),a102),f16(a862,x42531)),f332(f247(a102),f2(a102))))),x42532)),f278(x42531,x42532)) % 165.14/165.04 [4255]E(f332(f80(a1),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x42551),x42552)),f196(f875(f874(a868,a868),a862)))))),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x42552),x42551)),f196(f875(f874(a868,a868),a862)))))) % 165.14/165.04 [4312]E(f332(f332(f288(f869(a868),x43121),f146(a868,a251)),f332(f332(f7(x43121,f869(f875(x43121,a868)),f869(a868)),f332(f332(f8(f875(f875(x43121,a868),a868),f875(f869(f875(x43121,a868)),f869(a868)),x43121),f155(f875(x43121,a868),a868)),f332(f7(f875(x43121,a868),x43121,a868),f5(f875(x43121,a868))))),x43122)),f154(x43121,x43122)) % 165.14/165.04 [4333]E(f332(f332(f87(a1,a868),f332(f106(a1),f332(f332(f81(a1),x43331),a100))),f332(f332(f18(a1,a868,a868),f332(f332(f7(a1,a868,f875(a868,a868)),f332(f332(f8(a862,f875(a868,f875(a868,a868)),a1),f99(a868)),a201)),f2(a868))),f332(f332(f8(a868,a868,a1),a115),f332(f332(f8(a868,a868,a1),f332(f244(a868),x43332)),a107)))),f332(f332(f244(a868),f332(a115,x43332)),f332(f106(a868),x43331))) % 165.14/165.04 [4334]E(f332(f332(f87(a1,a868),f332(f106(a1),f332(f332(f81(a1),x43341),a100))),f332(f332(f18(a1,a868,a868),f332(f332(f7(a1,a868,f875(a868,a868)),f332(f332(f8(a862,f875(a868,f875(a868,a868)),a1),f99(a868)),a201)),f332(a115,x43342))),f332(f332(f8(a868,a868,a1),a115),f332(f332(f8(a868,a868,a1),f332(f245(a868),x43342)),a107)))),f332(f332(f245(a868),f332(a115,x43342)),f332(f106(a868),x43341))) % 165.14/165.04 [4354]E(f332(f143(f869(x43541),f869(x43541),f135(x43541),f116(x43541)),f332(f332(f155(f869(x43541),f869(x43541)),f157(f869(x43541),x43541,f116(x43541),f332(f332(f8(f869(x43541),f875(f869(x43541),f869(x43541)),x43541),f16(f869(x43541),f869(x43541))),f332(f332(f7(x43541,f869(x43541),f869(x43541)),f152(x43541)),f116(x43541))))),x43542)),f332(f332(f155(f869(x43541),x43541),f142(x43541)),f332(f137(f869(x43541),f332(f332(f8(a862,a862,f869(x43541)),a327),f332(f332(f7(f869(x43541),f869(x43541),a862),a329),f116(x43541)))),x43542))) % 165.14/165.04 [4417]E(f332(f271(a1,a1,a862),f332(f332(f7(a1,f875(a1,a862),f875(a1,a862)),f332(f332(f8(f875(a1,f875(a862,a862)),f875(f875(a1,a862),f875(a1,a862)),a1),f18(a1,a862,a862)),f332(f332(f8(f875(a1,a862),f875(a1,f875(a862,a862)),a1),f332(f8(a862,f875(a862,a862),a1),a330)),f332(f332(f8(f875(a1,a1),f875(a1,a862),a1),f332(f8(a1,a862,a1),f332(a329,x44171))),f332(f332(f8(a1,f875(a1,a1),a1),f81(a1)),f332(f82(a1),x44172)))))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f332(f8(a862,a862,a1),f332(a335,f332(f332(f247(a1),f2(a1)),x44172))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f246(a1),f2(a1)))),f332(f332(f7(a1,a1,a862),f247(a1)),x44172))))),f332(f332(f8(a862,a862,a1),f332(a335,f332(a327,f332(f332(f247(a1),f2(a1)),x44172)))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f247(a1),x44172))),f332(f332(f7(a1,a1,a862),f246(a1)),f2(a1))))))),f49(x44171,x44172)) % 165.14/165.04 [4419]E(f332(f252(x44191),f332(f332(f8(f875(a868,a862),a862,x44191),f88(a868)),f332(f332(f7(x44191,f875(a868,a862),f875(a868,a862)),f332(f332(f8(f875(a868,f875(a862,a862)),f875(f875(a868,a862),f875(a868,a862)),x44191),f18(a868,a862,a862)),f332(f332(f8(f875(a868,a862),f875(a868,f875(a862,a862)),x44191),f332(f8(a862,f875(a862,a862),a868),a330)),f332(f332(f7(x44191,f875(a868,x44191),f875(a868,a862)),f332(f332(f8(f875(x44191,a862),f875(f875(a868,x44191),f875(a868,a862)),x44191),f8(x44191,a862,a868)),a329)),f332(f166(x44191),x44192))))),f332(f332(f7(a868,a868,a862),f247(a868)),f332(f197(f869(x44191)),x44192))))),f332(f174(x44191),x44192)) % 165.14/165.04 [4224]E(f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),x42241),a100)),x42242)),f332(f332(f22(a1),f332(f332(f81(a1),x42241),a100)),x42242))),a100),f332(f332(f22(a1),f332(f332(f81(a1),x42241),x42241)),f332(f332(f22(a1),f332(f332(f81(a1),x42242),x42242)),a100))) % 165.14/165.04 [4349]E(f332(f143(f869(f869(x43491)),f869(f869(x43491)),f135(f869(x43491)),f116(f869(x43491))),f332(f332(f155(f869(x43491),f869(f869(x43491))),f157(f869(f869(x43491)),x43491,f116(f869(x43491)),f332(f16(f875(f869(x43491),f869(f869(x43491))),x43491),f332(f332(f7(f869(x43491),f869(f869(x43491)),f869(f869(x43491))),f152(f869(x43491))),f116(f869(x43491)))))),x43492)),f332(f332(f155(f869(x43491),f869(x43491)),f173(x43491)),f332(f137(f869(x43491),f332(f332(f8(a862,a862,f869(x43491)),a327),f332(f332(f7(f869(x43491),f869(x43491),a862),a329),f116(x43491)))),x43492))) % 165.14/165.04 [4360]E(f332(f332(f87(a1,a868),f332(f106(a1),f332(f332(f81(a1),x43601),a100))),f332(f332(f18(a1,a868,a868),f332(f332(f7(a1,a868,f875(a868,a868)),f332(f332(f8(a862,f875(a868,f875(a868,a868)),a1),f99(a868)),a201)),f2(a868))),f332(f332(f8(a868,a868,a1),a115),f332(f332(f7(a1,a868,a868),f332(f332(f8(a868,f875(a868,a868),a1),f244(a868)),a107)),x43602)))),f332(f332(f244(a868),f332(f106(a868),x43601)),f332(a115,x43602))) % 165.14/165.04 [4361]E(f332(f332(f87(a1,a868),f332(f106(a1),f332(f332(f81(a1),x43611),a100))),f332(f332(f18(a1,a868,a868),f332(f332(f7(a1,a868,f875(a868,a868)),f332(f332(f8(a862,f875(a868,f875(a868,a868)),a1),f99(a868)),a201)),f332(a115,x43612))),f332(f332(f8(a868,a868,a1),a115),f332(f332(f7(a1,a868,a868),f332(f332(f8(a868,f875(a868,a868),a1),f245(a868)),a107)),x43612)))),f332(f332(f245(a868),f332(f106(a868),x43611)),f332(a115,x43612))) % 165.14/165.04 [4348]E(f332(f271(x43481,x43481,a862),f332(f332(f18(x43481,a862,f875(x43481,a862)),f332(f332(f8(f875(x43481,f875(a862,a862)),f875(a862,f875(x43481,a862)),x43481),f7(x43481,a862,a862)),f332(f332(f8(f875(x43481,a862),f875(x43481,f875(a862,a862)),x43481),f332(f8(a862,f875(a862,a862),x43481),a330)),a329))),x43482)),f264(x43481,x43482)) % 165.14/165.04 [4395]E(f332(f332(f39(a868),x43951),f332(f332(f81(a868),f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),a100))),x43952)),f332(f332(f39(a868),x43951),f332(a115,f332(a115,f332(a115,x43952))))) % 165.14/165.04 [4396]E(f45(a868,x43961,f332(f332(f81(a868),f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),a100))),x43962)),f45(a868,x43961,f332(a115,f332(a115,f332(a115,x43962))))) % 165.14/165.04 [4397]E(f45(a868,f332(f332(f81(a868),f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),a100))),x43971),x43972),f45(a868,f332(a115,f332(a115,f332(a115,x43971))),x43972)) % 165.14/165.04 [4410]E(f125(f332(x44101,f332(f332(f82(a102),f332(f106(a102),f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),a100))),x44102))),f332(f212(x44101),x44102)) % 165.14/165.04 [4411]E(f332(f332(f39(a868),f332(f332(f81(a868),f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),a100))),x44111)),x44112),f332(f332(f39(a868),f332(a115,f332(a115,f332(a115,x44111)))),x44112)) % 165.14/165.04 [4460]~E(f34(x44601,x44602),f332(a28,x44603)) % 165.14/165.04 [4461]~E(f33(x44611,x44612),f332(a28,x44613)) % 165.14/165.04 [4462]~E(f332(a28,x44621),f34(x44622,x44623)) % 165.14/165.04 [4463]~E(f332(a28,x44631),f33(x44632,x44633)) % 165.14/165.04 [4477]~E(f29(x44771,x44772,x44773),a24) % 165.14/165.04 [4478]~E(f31(x44781,x44782,x44783),a24) % 165.14/165.04 [4479]~E(f30(x44791,x44792,x44793),a24) % 165.14/165.04 [3164]E(f332(f200(x31641,x31642),x31643),f122(x31641,x31642)) % 165.14/165.04 [3186]E(f332(f211(x31861,x31862),x31863),f332(f127(x31861),x31862)) % 165.14/165.04 [3265]E(f332(f332(f210(x32651,x32652),x32653),f209(x32651)),f209(x32652)) % 165.14/165.04 [3266]E(f332(f332(f155(x32661,x32662),x32663),f116(x32661)),f116(x32662)) % 165.14/165.04 [3286]E(f32(f29(x32861,x32862,x32863)),f2(a868)) % 165.14/165.04 [3307]E(f332(f192(x33071,x33072,x33073),f2(a868)),x33072) % 165.14/165.04 [3308]E(f332(f197(a863),f29(x33081,x33082,x33083)),f2(a868)) % 165.14/165.04 [3310]E(f332(f332(f184(x33101,x33102),x33103),f116(x33102)),f116(f874(x33101,x33102))) % 165.14/165.04 [3325]E(f332(f197(f869(x33251)),f171(x33251,x33252,x33253)),x33252) % 165.14/165.04 [3345]E(f86(x33451,f63(x33451,x33452,x33453)),f332(f64(x33451,x33452),x33453)) % 165.14/165.04 [3349]E(f256(x33491,x33492,f256(x33492,x33491,x33493)),x33493) % 165.14/165.04 [3369]E(f332(f170(x33691),f171(x33691,x33692,x33693)),f171(x33691,x33692,x33693)) % 165.14/165.04 [3398]E(f141(x33981,x33982,f153(x33981,x33983)),f153(x33981,f141(x33981,x33982,x33983))) % 165.14/165.04 [3417]E(f332(f266(f869(x34171),f869(x34171)),f168(x34171,x34172,x34173)),f332(f137(x34171,x34172),x34173)) % 165.14/165.04 [3465]E(f332(f332(f152(x34651),x34652),f171(x34651,x34653,x34652)),f171(x34651,f332(a115,x34653),x34652)) % 165.14/165.04 [3497]E(f193(x34971,x34972,x34973,f2(a868)),x34972) % 165.14/165.04 [3498]E(f17(x34981,x34982,x34983,f2(a102)),x34982) % 165.14/165.04 [3505]E(f164(x35051,x35052,x35053,f116(x35051)),f116(x35052)) % 165.14/165.04 [3506]E(f165(x35061,x35062,x35063,f116(x35061)),f116(x35062)) % 165.14/165.04 [3513]E(f332(f332(f166(x35131),f332(f332(f152(x35131),x35132),x35133)),f2(a868)),x35132) % 165.14/165.04 [3543]E(f60(x35431,x35432,f116(x35431),x35433),f116(f874(x35431,x35432))) % 165.14/165.04 [3564]P21(x35641,x35642,x35643,f196(f875(x35641,a862))) % 165.14/165.04 [3725]E(f332(f74(x37251,x37252,x37251,x37253),f35(x37251)),x37253) % 165.14/165.04 [3908]P24(f332(f332(f334(f874(x39081,x39081)),f332(f332(f267(x39081,x39081),x39082),x39082)),f308(x39081,x39083))) % 165.14/165.04 [4553]~P24(f332(f332(f334(f874(f869(x45531),f869(x45531))),f332(f332(f267(f869(x45531),f869(x45531)),x45532),f116(x45531))),f148(x45531,x45533))) % 165.14/165.04 [4554]~P24(f332(f332(f334(f874(f869(x45541),f869(x45541))),f332(f332(f267(f869(x45541),f869(x45541)),x45542),f116(x45541))),f146(x45541,x45543))) % 165.14/165.04 [4555]~P24(f332(f332(f334(f874(f869(x45551),f869(x45551))),f332(f332(f267(f869(x45551),f869(x45551)),x45552),f116(x45551))),f158(x45551,x45553))) % 165.14/165.04 [4556]~P24(f332(f332(f334(f874(f869(x45561),f869(x45561))),f332(f332(f267(f869(x45561),f869(x45561)),f116(x45561)),x45562)),f146(x45561,x45563))) % 165.14/165.04 [4557]~P24(f332(f332(f334(f874(f869(x45571),f869(x45571))),f332(f332(f267(f869(x45571),f869(x45571)),f116(x45571)),x45572)),f158(x45571,x45573))) % 165.14/165.04 [3240]E(f332(f332(f213(x32401),x32402),x32403),f214(x32401,f227(x32402,x32403))) % 165.14/165.04 [3296]E(f332(f287(x32961,x32962),f332(f287(x32962,x32961),x32963)),x32963) % 165.14/165.04 [3320]E(f332(f332(f184(x33201,x33202),f116(x33201)),x33203),f116(f874(x33201,x33202))) % 165.14/165.04 [3323]E(f178(x33231,x33232,f332(f253(a868),x33233)),f332(f332(f177(x33231),x33233),x33232)) % 165.14/165.04 [3341]E(f153(x33411,f332(f137(x33411,x33412),x33413)),f332(f137(x33411,x33412),f153(x33411,x33413))) % 165.14/165.04 [3343]E(f332(f263(x33431,x33432),f332(f287(x33432,x33431),x33433)),f332(f265(x33432,x33431),x33433)) % 165.14/165.04 [3344]E(f332(f265(x33441,x33442),f332(f287(x33442,x33441),x33443)),f332(f263(x33442,x33441),x33443)) % 165.14/165.04 [3361]E(f332(f137(x33611,x33612),f332(f170(x33611),x33613)),f332(f170(x33611),f332(f137(x33611,x33612),x33613))) % 165.14/165.04 [3375]E(f332(f332(f139(x33751),x33752),f332(f173(x33751),x33753)),f332(f332(f139(x33751),f332(a115,x33752)),x33753)) % 165.14/165.04 [3393]E(f32(f30(x33931,x33932,x33933)),f332(f332(f81(a868),f32(x33933)),f332(a115,f2(a868)))) % 165.14/165.04 [3394]E(f332(f311(x33941,x33942,x33943),f196(f875(x33941,a862))),f196(f875(x33942,a862))) % 165.14/165.04 [3395]E(f332(f312(x33951,x33952,x33953),f196(f875(x33952,a862))),f196(f875(x33951,a862))) % 165.14/165.04 [3396]E(f332(f312(x33961,x33962,x33963),f255(f875(x33962,a862))),f255(f875(x33961,a862))) % 165.14/165.04 [3397]E(f332(f286(x33971,x33972,x33973),f196(f875(x33971,a862))),f196(f875(x33972,a862))) % 165.14/165.04 [3426]E(f332(f332(f310(x34261),x34262),f332(f174(x34261),x34263)),f332(f174(x34261),f141(x34261,x34262,x34263))) % 165.14/165.04 [3438]E(f240(x34381,x34382,f332(f208(x34381),x34383)),f332(f332(f81(a868),f332(x34382,x34383)),f332(a115,f2(a868)))) % 165.14/165.04 [3517]E(f332(f197(a863),f30(x35171,x35172,x35173)),f332(f332(f81(a868),f332(f197(a863),x35173)),f332(a115,f2(a868)))) % 165.14/165.04 [3518]E(f332(f311(f874(x35181,x35182),x35182,f270(x35181,x35182)),x35183),f332(f263(x35181,x35182),x35183)) % 165.14/165.04 [3519]E(f332(f311(f874(x35191,x35192),x35191,f266(x35191,x35192)),x35193),f332(f265(x35191,x35192),x35193)) % 165.14/165.04 [3535]E(f332(f174(x35351),f171(x35351,f332(a115,x35352),x35353)),f332(f332(f310(x35351),x35353),f196(f875(x35351,a862)))) % 165.14/165.04 [3592]E(f332(f332(f267(x35921,x35922),f332(f266(x35921,x35922),x35923)),f332(f270(x35921,x35922),x35923)),x35923) % 165.14/165.04 [3599]E(f332(f197(f870(x35991)),f128(x35991,x35992,x35993)),f332(f332(f81(a868),f332(f197(f870(x35991)),x35993)),f332(a115,f2(a868)))) % 165.14/165.04 [3600]E(f332(f332(f271(x36001,x36002,x36001),f16(x36001,x36002)),x36003),f332(f266(x36001,x36002),x36003)) % 165.14/165.04 [3620]E(f187(x36201,x36202,x36203,f332(f16(f872(x36202),x36201),f209(x36202))),x36203) % 165.14/165.04 [3621]E(f187(x36211,x36212,f332(f16(f872(x36212),x36211),f209(x36212)),x36213),x36213) % 165.14/165.04 [3678]E(f32(f31(x36781,x36782,x36783)),f332(f332(f81(a868),f332(f332(f81(a868),f32(x36782)),f32(x36783))),f332(a115,f2(a868)))) % 165.14/165.04 [3729]E(f332(f74(x37291,x37291,x37292,f35(x37291)),x37293),x37293) % 165.14/165.04 [3737]E(f332(f332(f135(x37371),f171(x37371,x37372,x37373)),f332(f332(f152(x37371),x37373),f116(x37371))),f332(f332(f152(x37371),x37373),f171(x37371,x37372,x37373))) % 165.14/165.04 [3841]E(f332(f197(a863),f31(x38411,x38412,x38413)),f332(f332(f81(a868),f332(f332(f81(a868),f332(f197(a863),x38412)),f332(f197(a863),x38413))),f332(a115,f2(a868)))) % 165.14/165.04 [3919]P24(f332(f332(f246(f875(x39191,a862)),f332(f174(x39191),f332(f137(x39191,x39192),x39193))),f332(f174(x39191),x39193))) % 165.14/165.04 [3964]P24(f332(f332(f246(f875(x39641,a862)),f332(f174(x39641),f332(f332(f177(x39641),x39642),x39643))),f332(f174(x39641),x39643))) % 165.14/165.04 [3965]P24(f332(f332(f246(f875(x39651,a862)),f332(f174(x39651),f332(f332(f139(x39651),x39652),x39653))),f332(f174(x39651),x39653))) % 165.14/165.04 [3970]P24(f332(f332(f246(f875(x39701,a862)),f332(f174(x39701),f172(x39701,x39702,x39703))),f332(f174(x39701),x39703))) % 165.14/165.04 [3971]P24(f332(f332(f246(f875(x39711,a862)),f332(f174(x39711),f178(x39711,x39712,x39713))),f332(f174(x39711),x39712))) % 165.14/165.04 [3993]P21(f874(x39931,x39932),f874(x39932,x39931),f332(f271(x39931,x39932,f874(x39932,x39931)),f332(f7(x39932,x39931,f874(x39932,x39931)),f267(x39932,x39931))),x39933) % 165.14/165.04 [4005]E(f332(f332(f332(f191(f869(x40051),f869(x40051)),f45(a868,x40052,f332(f197(f869(x40051)),x40053))),f169(x40051)),x40053),f332(f332(f332(f191(f869(x40051),f869(x40051)),x40052),f169(x40051)),x40053)) % 165.14/165.04 [4048]P24(f332(f332(f334(f874(f869(x40481),f869(x40481))),f332(f332(f267(f869(x40481),f869(x40481)),x40482),x40482)),f159(x40481,f308(x40481,x40483)))) % 165.14/165.04 [4194]E(f86(f874(x41941,x41942),f332(f332(f18(f874(x41941,x41942),x41942,a862),f332(f332(f8(x41941,f875(x41942,a862),f874(x41941,x41942)),x41943),f266(x41941,x41942))),f270(x41941,x41942))),f86(f874(x41941,x41942),f332(f271(x41941,x41942,a862),x41943))) % 165.14/165.04 [4195]E(f91(f874(x41951,x41952),f332(f332(f18(f874(x41951,x41952),x41952,a862),f332(f332(f8(x41951,f875(x41952,a862),f874(x41951,x41952)),x41953),f266(x41951,x41952))),f270(x41951,x41952))),f91(f874(x41951,x41952),f332(f271(x41951,x41952,a862),x41953))) % 165.14/165.04 [4231]E(f332(f332(f288(f874(a868,x42311),x42311),f324(a868,x42311,a251,x42312)),f332(f332(f18(x42311,x42311,f874(a868,x42311)),f332(f332(f8(a868,f875(x42311,f874(a868,x42311)),x42311),f267(a868,x42311)),x42313)),f5(x42311))),f326(x42311,x42313,x42312)) % 165.14/165.04 [4296]E(f332(f272(x42961,x42961,x42962,x42962,f5(x42961),f5(x42962)),x42963),x42963) % 165.14/165.04 [4371]E(f332(f143(f869(f869(x43711)),f869(f869(x43711)),f135(f869(x43711)),f116(f869(x43711))),f332(f332(f155(f869(x43711),f869(f869(x43711))),f332(f332(f7(f869(x43711),f869(x43711),f869(f869(x43711))),f332(f332(f8(f875(x43711,f869(x43711)),f875(f869(x43711),f869(f869(x43711))),f869(x43711)),f155(x43711,f869(x43711))),f332(f7(x43711,f869(x43711),f869(x43711)),f152(x43711)))),x43712)),f55(x43711,x43713,x43712))),f55(x43711,f332(a115,x43713),x43712)) % 165.14/165.04 [4432]E(f332(f241(a868,f874(x44321,f870(x44321)),f2(a868),f332(f271(x44321,f870(x44321),a868),f332(f332(f7(x44321,a868,f875(f870(x44321),a868)),f332(f332(f8(f875(f870(x44321),f875(a868,a868)),f875(a868,f875(f870(x44321),a868)),x44321),f7(f870(x44321),a868,a868)),f332(f332(f8(f875(f870(x44321),a868),f875(f870(x44321),f875(a868,a868)),x44321),f332(f8(a868,f875(a868,a868),f870(x44321)),f81(a868))),f332(f332(f7(x44321,f875(f870(x44321),a868),f875(f870(x44321),a868)),f332(f332(f8(f875(a868,a868),f875(f875(f870(x44321),a868),f875(f870(x44321),a868)),x44321),f8(a868,a868,f870(x44321))),f332(f332(f8(a868,f875(a868,a868),x44321),f81(a868)),x44322))),f130(x44321,x44322))))),f79(a868)))),f332(f136(x44321),x44323)),f332(f130(x44321,x44322),x44323)) % 165.14/165.04 [4435]E(f332(f332(f87(a1,x44351),f230(f332(f332(f74(f874(a1,a1),a1,x44351,f270(a1,a1)),f224(x44351)),x44352),f332(f332(f74(f874(a1,a1),a1,x44351,f270(a1,a1)),f224(x44351)),x44353))),f332(f332(f18(a1,a1,x44351),f332(f332(f8(a1,f875(a1,x44351),a1),f213(x44351)),f332(f332(f18(a1,a1,a1),f332(f332(f8(a1,f875(a1,a1),a1),f81(a1)),f332(f332(f8(a1,a1,a1),f332(f82(a1),f332(f332(f74(f874(a1,a1),a1,x44351,f266(a1,a1)),f224(x44351)),x44352))),f332(f332(f7(a1,a1,a1),f39(a1)),f332(f332(f74(f874(a1,a1),a1,x44351,f270(a1,a1)),f224(x44351)),x44352))))),f332(f332(f8(a1,a1,a1),f332(f82(a1),f332(f332(f74(f874(a1,a1),a1,x44351,f266(a1,a1)),f224(x44351)),x44353))),f332(f332(f7(a1,a1,a1),f39(a1)),f332(f332(f74(f874(a1,a1),a1,x44351,f270(a1,a1)),f224(x44351)),x44353)))))),f5(a1))),f235(x44351,x44352,x44353)) % 165.14/165.04 [4472]~E(f332(f332(f152(x44721),x44722),x44723),x44723) % 165.14/165.04 [4481]~E(f332(f332(f152(x44811),x44812),x44813),f116(x44811)) % 165.14/165.04 [4503]~E(f332(f332(f310(x45031),x45032),x45033),f196(f875(x45031,a862))) % 165.14/165.04 [4530]~E(f332(f311(x45301,f875(x45301,a862),x45302),x45303),f332(f309(x45301),x45303)) % 165.14/165.04 [3301]E(f332(f332(f160(x33011,f116(x33011)),x33012),x33013),f116(x33011)) % 165.14/165.04 [3302]E(f332(f142(x33021),f332(f332(f152(x33021),x33022),x33023)),x33022) % 165.14/165.04 [3303]E(f332(f173(x33031),f332(f332(f152(x33031),x33032),x33033)),x33033) % 165.14/165.04 [3348]E(f332(f332(f139(x33481),f79(a868)),f332(f332(f152(x33481),x33482),x33483)),x33483) % 165.14/165.04 [3382]E(f117(x33821,f332(f332(f139(x33821),x33822),x33823)),f332(f332(f139(x33821),x33822),f117(x33821,x33823))) % 165.14/165.04 [3384]E(f332(f332(f160(x33841,x33842),x33843),f332(f332(f166(x33841),x33842),x33843)),x33842) % 165.14/165.04 [3408]E(f332(f332(f310(x34081),x34082),f332(f332(f310(x34081),x34082),x34083)),f332(f332(f310(x34081),x34082),x34083)) % 165.14/165.04 [3419]E(f332(f332(f180(x34191,x34192),f116(f874(x34191,x34192))),x34193),f209(x34192)) % 165.14/165.04 [3422]E(f332(f332(f310(x34221),x34222),f332(f174(x34221),x34223)),f332(f174(x34221),f332(f332(f152(x34221),x34222),x34223))) % 165.14/165.04 [3424]E(f332(f332(f139(x34241),x34242),f332(f173(x34241),x34243)),f332(f173(x34241),f332(f332(f139(x34241),x34242),x34243))) % 165.14/165.04 [3435]E(f332(f332(f177(x34351),f79(a868)),f332(f332(f152(x34351),x34352),x34353)),f332(f332(f152(x34351),x34352),f116(x34351))) % 165.14/165.04 [3482]E(f332(f64(x34821,x34822),f332(f332(f310(x34821),x34823),f196(f875(x34821,a862)))),x34823) % 165.14/165.04 [3525]E(f332(f332(f81(a868),x35251),f332(f332(f81(a868),x35252),x35253)),f332(f332(f81(a868),x35252),f332(f332(f81(a868),x35251),x35253))) % 165.14/165.04 [3526]E(f332(f332(f81(a1),x35261),f332(f332(f81(a1),x35262),x35263)),f332(f332(f81(a1),x35262),f332(f332(f81(a1),x35261),x35263))) % 165.14/165.04 [3531]E(f332(f332(f269(x35311,x35312),f196(f875(x35311,a862))),x35313),f196(f875(f874(x35311,x35312),a862))) % 165.14/165.04 [3556]E(f332(f332(f113(f875(x35561,a862)),x35562),x35563),f332(f332(f113(f875(x35561,a862)),x35563),x35562)) % 165.14/165.04 [3557]E(f332(f332(f104(f875(x35571,a862)),x35572),x35573),f332(f332(f104(f875(x35571,a862)),x35573),x35572)) % 165.14/165.04 [3559]E(f332(f332(f135(x35591),x35592),f332(f332(f152(x35591),x35593),f116(x35591))),f332(f169(x35591),f332(f332(f152(x35591),x35593),x35592))) % 165.14/165.04 [3560]E(f332(f332(f135(x35601),f332(f170(x35601),x35602)),f332(f170(x35601),x35603)),f332(f170(x35601),f332(f332(f135(x35601),x35603),x35602))) % 165.14/165.04 [3570]E(f332(f173(x35701),f332(f332(f177(x35701),f332(a115,x35702)),x35703)),f332(f332(f177(x35701),x35702),f332(f173(x35701),x35703))) % 165.28/165.04 [3577]P24(f332(f332(f334(x35771),x35772),f332(f332(f310(x35771),x35772),x35773))) % 165.28/165.04 [3581]E(f332(f332(f43(x35811,f875(x35812,a862)),f196(f875(x35811,a862))),x35813),f255(f875(x35812,a862))) % 165.28/165.04 [3584]E(f332(f286(x35841,x35841,f264(x35841,x35842)),x35843),f332(f332(f104(f875(x35841,a862)),x35842),x35843)) % 165.28/165.04 [3598]E(f332(f197(f869(x35981)),f332(f332(f152(x35981),x35982),x35983)),f332(f332(f81(a868),f332(f197(f869(x35981)),x35983)),f332(a115,f2(a868)))) % 165.28/165.04 [3602]E(f117(x36021,f332(f332(f135(x36021),x36022),f332(f332(f152(x36021),x36023),f116(x36021)))),x36022) % 165.28/165.04 [3603]E(f145(x36031,f332(f332(f135(x36031),x36032),f332(f332(f152(x36031),x36033),f116(x36031)))),x36033) % 165.28/165.04 [3609]E(f332(f332(f135(x36091),f332(f332(f177(x36091),x36092),x36093)),f332(f332(f139(x36091),x36092),x36093)),x36093) % 165.28/165.04 [3618]E(f332(f332(f22(a868),f332(f332(f81(a868),x36181),x36182)),f332(f332(f81(a868),x36183),x36182)),f332(f332(f22(a868),x36181),x36183)) % 165.28/165.04 [3619]E(f332(f332(f22(a868),f332(f332(f81(a868),x36191),x36192)),f332(f332(f81(a868),x36191),x36193)),f332(f332(f22(a868),x36192),x36193)) % 165.28/165.04 [3627]E(f332(f332(f135(x36271),f332(f170(x36271),x36272)),f332(f332(f152(x36271),x36273),f116(x36271))),f332(f170(x36271),f332(f332(f152(x36271),x36273),x36272))) % 165.28/165.04 [3629]E(f332(f332(f81(a868),f332(f197(f869(x36291)),x36292)),f332(f197(f869(x36291)),x36293)),f332(f197(f869(x36291)),f332(f332(f135(x36291),x36292),x36293))) % 165.28/165.04 [3632]E(f332(f332(f81(a868),f332(f197(f869(x36321)),x36322)),f332(f197(f869(x36321)),x36323)),f332(f197(f869(x36321)),f175(x36321,x36322,x36323))) % 165.28/165.04 [3640]E(f332(f332(f113(f875(x36401,a862)),f332(f174(x36401),x36402)),f332(f174(x36401),x36403)),f332(f174(x36401),f332(f332(f135(x36401),x36402),x36403))) % 165.28/165.04 [3641]E(f45(a868,f332(f332(f82(a868),x36411),x36412),f332(f332(f82(a868),x36411),x36413)),f332(f332(f82(a868),x36411),f45(a868,x36412,x36413))) % 165.28/165.04 [3654]E(f332(f332(f177(x36541),f332(f332(f22(a868),x36542),f79(a868))),f332(f173(x36541),x36543)),f332(f173(x36541),f332(f332(f177(x36541),x36542),x36543))) % 165.28/165.04 [3659]E(f332(f332(f104(f875(x36591,a862)),x36592),f332(f80(f875(x36591,a862)),x36593)),f332(f332(f22(f875(x36591,a862)),x36592),x36593)) % 165.28/165.04 [3660]E(f332(f332(f22(f875(x36601,a862)),x36602),f332(f80(f875(x36601,a862)),x36603)),f332(f332(f104(f875(x36601,a862)),x36602),x36603)) % 165.28/165.04 [3682]E(f332(f332(f269(x36821,x36822),x36823),f332(f16(f875(x36822,a862),x36821),f196(f875(x36822,a862)))),f196(f875(f874(x36821,x36822),a862))) % 165.28/165.04 [3684]E(f332(f332(f22(a868),f332(f332(f82(a868),x36841),x36842)),f332(f332(f82(a868),x36841),x36843)),f332(f332(f82(a868),x36841),f332(f332(f22(a868),x36842),x36843))) % 165.28/165.04 [3685]E(f332(f332(f81(a868),f332(f332(f82(a868),x36851),x36852)),f332(f332(f82(a868),x36851),x36853)),f332(f332(f82(a868),x36851),f332(f332(f81(a868),x36852),x36853))) % 165.28/165.04 [3686]E(f332(f332(f22(a1),f332(f332(f82(a1),x36861),x36862)),f332(f332(f82(a1),x36861),x36863)),f332(f332(f82(a1),x36861),f332(f332(f22(a1),x36862),x36863))) % 165.28/165.04 [3687]E(f332(f332(f81(a1),f332(f332(f82(a1),x36871),x36872)),f332(f332(f82(a1),x36871),x36873)),f332(f332(f82(a1),x36871),f332(f332(f81(a1),x36872),x36873))) % 165.28/165.04 [3688]E(f332(f332(f82(a1),f332(f332(f257(a1),x36881),x36882)),f332(f332(f257(a1),x36881),x36883)),f332(f332(f257(a1),x36881),f332(f332(f81(a868),x36882),x36883))) % 165.28/165.04 [3703]E(f332(f332(f42(x37031,f875(x37032,a862)),x37033),f332(f16(f875(x37032,a862),x37031),f196(f875(x37032,a862)))),f196(f875(x37032,a862))) % 165.28/165.04 [3705]E(f45(a868,f332(f332(f82(a868),x37051),x37052),f332(f332(f82(a868),x37053),x37052)),f332(f332(f82(a868),f45(a868,x37051,x37053)),x37052)) % 165.28/165.04 [3709]E(f45(a1,f332(f332(f22(a1),x37091),f45(a1,x37092,x37093)),x37093),f45(a1,f332(f332(f22(a1),x37091),x37092),x37093)) % 165.28/165.04 [3710]E(f45(a1,f332(f332(f82(a1),x37101),f45(a1,x37102,x37103)),x37103),f45(a1,f332(f332(f82(a1),x37101),x37102),x37103)) % 165.28/165.04 [3711]P24(f332(f332(f246(f875(x37111,a862)),x37112),f332(f332(f310(x37111),x37113),x37112))) % 165.28/165.04 [3714]E(f332(f311(f874(x37141,x37142),x37141,f266(x37141,x37142)),f332(f174(f874(x37141,x37142)),x37143)),f186(x37141,x37142,f332(f180(x37141,x37142),x37143))) % 165.28/165.04 [3765]P24(f332(f62(x37651),f186(x37651,x37652,f332(f180(x37651,x37652),x37653)))) % 165.28/165.04 [3790]E(f332(f332(f43(f875(x37901,a862),f875(x37901,a862)),x37902),f332(f113(f875(x37901,a862)),x37903)),f332(f332(f113(f875(x37901,a862)),x37903),f41(f875(x37901,a862),x37902))) % 165.28/165.04 [3791]E(f332(f332(f42(f875(x37911,a862),f875(x37911,a862)),x37912),f332(f104(f875(x37911,a862)),x37913)),f332(f332(f104(f875(x37911,a862)),x37913),f40(f875(x37911,a862),x37912))) % 165.28/165.04 [3802]E(f332(f174(x38021),f332(f332(f332(f191(f869(x38021),f869(x38021)),x38022),f169(x38021)),x38023)),f332(f174(x38021),x38023)) % 165.28/165.04 [3806]E(f332(f332(f177(x38061),f332(f197(f869(x38061)),f179(x38061,x38062,x38063))),x38063),f179(x38061,x38062,x38063)) % 165.28/165.04 [3807]E(f186(x38071,x38072,f332(f332(f8(x38072,f872(x38072),x38071),f208(x38072)),x38073)),f255(f875(x38071,a862))) % 165.28/165.04 [3811]E(f332(f197(f869(x38111)),f332(f332(f332(f191(f869(x38111),f869(x38111)),x38112),f169(x38111)),x38113)),f332(f197(f869(x38111)),x38113)) % 165.28/165.04 [3814]E(f332(f332(f271(x38141,x38142,x38142),f332(f16(f875(x38142,x38142),x38141),f5(x38142))),x38143),f332(f270(x38141,x38142),x38143)) % 165.28/165.04 [3821]E(f45(a1,f332(f332(f22(a1),f45(a1,x38211,x38212)),x38213),x38212),f45(a1,f332(f332(f22(a1),x38211),x38213),x38212)) % 165.28/165.04 [3822]E(f45(a1,f332(f332(f257(a1),f45(a1,x38221,x38222)),x38223),x38222),f45(a1,f332(f332(f257(a1),x38221),x38223),x38222)) % 165.28/165.04 [3825]E(f332(f332(f42(f875(f874(x38251,x38252),a862),f875(x38252,a862)),x38253),f263(x38251,x38252)),f332(f263(x38251,x38252),f40(f875(f874(x38251,x38252),a862),x38253))) % 165.28/165.04 [3826]E(f332(f332(f42(f875(f874(x38261,x38262),a862),f875(x38261,a862)),x38263),f265(x38261,x38262)),f332(f265(x38261,x38262),f40(f875(f874(x38261,x38262),a862),x38263))) % 165.28/165.04 [3854]E(f332(f74(x38541,x38541,x38541,x38542),f332(f332(f191(x38541,x38541),x38543),x38542)),f332(f332(f191(x38541,x38541),f332(a115,x38543)),x38542)) % 165.28/165.04 [3864]E(f241(f872(x38641),x38642,f209(x38641),f332(f332(f8(x38641,f872(x38641),x38642),f208(x38641)),x38643)),f332(f210(x38642,x38641),x38643)) % 165.28/165.04 [3871]E(f332(f332(f139(x38711),f332(f332(f22(a868),f332(f197(f869(x38711)),x38712)),x38713)),f332(f170(x38711),x38712)),f332(f170(x38711),f332(f332(f177(x38711),x38713),x38712))) % 165.28/165.04 [3872]E(f332(f332(f177(x38721),f332(f332(f22(a868),f332(f197(f869(x38721)),x38722)),x38723)),f332(f170(x38721),x38722)),f332(f170(x38721),f332(f332(f139(x38721),x38723),x38722))) % 165.28/165.04 [3875]E(f332(f332(f81(a868),f332(f167(a868),f332(f332(f155(x38751,a868),x38752),x38753))),f332(f197(f869(x38751)),x38753)),f156(x38751,x38752,x38753)) % 165.28/165.04 [3894]E(f332(f169(x38941),f332(f332(f332(f191(f869(x38941),f869(x38941)),x38942),f169(x38941)),x38943)),f332(f332(f332(f191(f869(x38941),f869(x38941)),f332(a115,x38942)),f169(x38941)),x38943)) % 165.28/165.04 [3909]P24(f332(f332(f246(a868),f332(f197(f869(x39091)),f332(f137(x39091,x39092),x39093))),f332(f197(f869(x39091)),x39093))) % 165.28/165.04 [3927]E(f332(f332(f113(f875(f875(x39271,a862),a862)),f332(f309(x39271),x39272)),f332(f311(f875(x39271,a862),f875(x39271,a862),f332(f310(x39271),x39273)),f332(f309(x39271),x39272))),f332(f309(x39271),f332(f332(f310(x39271),x39273),x39272))) % 165.28/165.04 [3946]P20(x39461,x39462,f332(f332(f310(f867(x39461)),f332(f332(f332(f93(x39461),x39463),a24),x39463)),f196(f875(f867(x39461),a862)))) % 165.28/165.04 [3961]P24(f332(f332(f246(a868),f332(f197(f869(x39611)),f179(x39611,x39612,x39613))),f332(f197(f869(x39611)),x39613))) % 165.28/165.04 [3969]E(f332(f265(x39691,x39692),f332(f252(f874(x39691,x39692)),f332(f271(x39691,x39692,a862),x39693))),f332(f252(x39691),f332(f332(f8(f875(x39692,a862),a862,x39691),f88(x39692)),x39693))) % 165.28/165.04 [3981]E(f332(f311(a868,a868,f332(f332(f7(a868,a868,a868),f81(a868)),x39811)),f303(a868,x39812,x39813)),f303(a868,f332(f332(f81(a868),x39812),x39811),f332(f332(f81(a868),x39813),x39811))) % 165.28/165.04 [3983]P24(f332(f62(f872(x39831)),f332(f311(x39832,f872(x39831),f332(f180(x39832,x39831),x39833)),f255(f875(x39832,a862))))) % 165.28/165.04 [3996]E(f332(f311(a868,a868,f332(f332(f7(a868,a868,a868),f81(a868)),x39961)),f332(f302(a868,x39962),x39963)),f332(f302(a868,f332(f332(f81(a868),x39962),x39961)),f332(f332(f81(a868),x39963),x39961))) % 165.28/165.04 [4014]E(f332(f332(f184(x40141,x40142),f332(f332(f155(f874(x40141,x40142),x40141),f266(x40141,x40142)),x40143)),f332(f332(f155(f874(x40141,x40142),x40142),f270(x40141,x40142)),x40143)),x40143) % 165.28/165.04 [4019]E(f332(f332(f81(a868),f332(f332(f82(a868),x40191),f45(a868,f332(f332(f39(a868),x40192),x40191),x40193))),f45(a868,x40192,x40191)),f45(a868,x40192,f332(f332(f82(a868),x40191),x40193))) % 165.28/165.04 [4034]E(f332(f332(f135(x40341),x40342),f332(f143(f869(x40341),f869(x40341),f135(x40341),f116(x40341)),x40343)),f332(f143(f869(x40341),f869(x40341),f135(x40341),x40342),x40343)) % 165.28/165.04 [4052]P24(f332(f332(f334(f874(x40521,x40521)),f332(f332(f267(x40521,x40521),x40522),x40522)),f332(f332(f191(f874(x40521,x40521),a862),f2(a868)),x40523))) % 165.28/165.04 [4058]E(f332(f252(x40581),f332(f332(f8(f875(x40582,a862),a862,x40581),f88(x40582)),f332(f7(x40582,x40581,a862),x40583))),f332(f263(x40582,x40581),f332(f252(f874(x40582,x40581)),f332(f271(x40582,x40581,a862),x40583)))) % 165.28/165.04 [4076]E(f332(f332(f113(f875(x40761,a862)),f332(f332(f42(a868,f875(x40761,a862)),f303(a868,f79(a868),x40762)),x40763)),f332(x40763,f2(a868))),f332(f332(f42(a868,f875(x40761,a862)),f332(f301(a868),x40762)),x40763)) % 165.28/165.04 [4091]E(f332(f143(f869(x40911),f869(x40911),f135(x40911),f116(x40911)),f332(f332(f155(f869(x40911),f869(x40911)),f137(x40911,x40912)),x40913)),f332(f137(x40911,x40912),f332(f143(f869(x40911),f869(x40911),f135(x40911),f116(x40911)),x40913))) % 165.28/165.04 [4096]E(f332(f270(f869(x40961),f869(x40961)),f168(x40961,x40962,x40963)),f332(f137(x40961,f332(f74(a862,a862,x40961,a327),x40962)),x40963)) % 165.28/165.04 [4145]E(f332(f332(f81(a1),f332(f332(f81(a1),f332(f332(f82(a1),x41451),f332(f332(f39(a1),x41452),x41451))),f45(a1,x41452,x41451))),x41453),f332(f332(f81(a1),x41452),x41453)) % 165.28/165.04 [4183]E(f332(f332(f81(a1),f332(f332(f81(a1),f332(f332(f82(a1),f332(f332(f39(a1),x41831),x41832)),x41832)),f45(a1,x41831,x41832))),x41833),f332(f332(f81(a1),x41831),x41833)) % 165.28/165.04 [4212]E(f86(f874(x42121,x42122),f332(f271(x42121,x42122,a862),f332(f332(f8(f875(x42122,f874(x42121,x42122)),f875(x42122,a862),x42121),f332(f8(f874(x42121,x42122),a862,x42122),x42123)),f267(x42121,x42122)))),f86(f874(x42121,x42122),x42123)) % 165.28/165.04 [4213]E(f91(f874(x42131,x42132),f332(f271(x42131,x42132,a862),f332(f332(f8(f875(x42132,f874(x42131,x42132)),f875(x42132,a862),x42131),f332(f8(f874(x42131,x42132),a862,x42132),x42133)),f267(x42131,x42132)))),f91(f874(x42131,x42132),x42133)) % 165.28/165.04 [4241]P24(f332(f332(f246(f875(x42411,a862)),f40(f875(x42411,a862),f332(f332(f104(f875(f875(x42411,a862),a862)),x42412),x42413))),f332(f332(f104(f875(x42411,a862)),f40(f875(x42411,a862),x42412)),f40(f875(x42411,a862),x42413)))) % 165.28/165.04 [4242]E(f332(f170(x42421),f332(f332(f332(f191(f869(x42421),f869(x42421)),f332(f332(f22(a868),f332(f197(f869(x42421)),x42422)),f45(a868,x42423,f332(f197(f869(x42421)),x42422)))),f169(x42421)),x42422)),f332(f332(f332(f191(f869(x42421),f869(x42421)),x42423),f169(x42421)),f332(f170(x42421),x42422))) % 165.28/165.04 [4256]E(f332(f252(x42561),f332(f332(f8(a862,a862,x42561),a327),f332(f332(f7(x42561,f872(x42562),a862),f332(f332(f8(f872(x42562),f875(f872(x42562),a862),x42561),a329),x42563)),f209(x42562)))),f186(x42561,x42562,x42563)) % 165.28/165.04 [4281]P24(f332(f332(f246(a868),f332(f197(f869(x42811)),f332(f332(f139(x42811),f332(f197(f869(x42811)),f179(x42811,x42812,x42813))),x42813))),f332(f197(f869(x42811)),x42813))) % 165.28/165.04 [4322]E(f332(f252(x43221),f332(f332(f8(f875(x43222,a862),a862,x43221),f88(x43222)),f332(f332(f8(f872(x43221),f875(x43222,a862),x43221),f332(f7(x43222,f872(x43221),a862),f332(f332(f8(f872(x43221),f875(f872(x43221),a862),x43222),a329),x43223))),f208(x43221)))),f188(x43222,x43221,x43223)) % 165.28/165.04 [4544]~P24(f332(f63(x45441,x45442,f196(f875(x45441,a862))),x45443)) % 165.28/165.04 [4551]~P24(f332(f332(f334(f874(x45511,x45511)),f332(f332(f267(x45511,x45511),x45512),x45513)),f154(x45511,f116(f875(x45511,a868))))) % 165.28/165.04 [3571]E(f332(f197(f869(x35711)),f332(f332(f177(x35711),x35712),x35713)),f332(f332(f244(a868),f332(f197(f869(x35711)),x35713)),x35712)) % 165.28/165.04 [3572]E(f332(f197(f869(x35721)),f332(f332(f139(x35721),x35722),x35723)),f332(f332(f22(a868),f332(f197(f869(x35721)),x35723)),x35722)) % 165.28/165.04 [3597]E(f332(f197(f869(f869(x35971))),f55(x35971,x35972,x35973)),f332(f332(f257(a868),f332(f197(f869(x35971)),x35973)),x35972)) % 165.28/165.04 [3611]E(f332(f332(f39(a868),f332(f332(f39(a868),x36111),x36112)),x36113),f332(f332(f39(a868),x36111),f332(f332(f82(a868),x36112),x36113))) % 165.28/165.04 [3612]E(f332(f332(f22(a868),f332(f332(f22(a868),x36121),x36122)),x36123),f332(f332(f22(a868),x36121),f332(f332(f81(a868),x36122),x36123))) % 165.28/165.04 [3613]E(f332(f332(f81(a868),f332(f332(f81(a868),x36131),x36132)),x36133),f332(f332(f81(a868),x36131),f332(f332(f81(a868),x36132),x36133))) % 165.28/165.04 [3614]E(f332(f332(f81(a1),f332(f332(f81(a1),x36141),x36142)),x36143),f332(f332(f81(a1),x36141),f332(f332(f81(a1),x36142),x36143))) % 165.28/165.04 [3615]E(f332(f332(f82(a868),f332(f332(f82(a868),x36151),x36152)),x36153),f332(f332(f82(a868),x36151),f332(f332(f82(a868),x36152),x36153))) % 165.28/165.04 [3616]E(f332(f332(f82(a1),f332(f332(f82(a1),x36161),x36162)),x36163),f332(f332(f82(a1),x36161),f332(f332(f82(a1),x36162),x36163))) % 165.28/165.04 [3617]E(f332(f332(f257(a1),f332(f332(f257(a1),x36171),x36172)),x36173),f332(f332(f257(a1),x36171),f332(f332(f82(a868),x36172),x36173))) % 165.28/165.04 [3638]E(f163(x36381,f332(f332(f152(f875(x36381,a862)),x36382),x36383)),f176(x36381,x36382,f163(x36381,x36383))) % 165.28/165.04 [3683]E(f332(f332(f22(a868),f332(f332(f22(a868),x36831),x36832)),x36833),f332(f332(f22(a868),f332(f332(f22(a868),x36831),x36833)),x36832)) % 165.28/165.04 [3689]E(f332(f208(f874(x36891,f870(x36891))),f332(f332(f267(x36891,f870(x36891)),x36892),x36893)),f332(f136(x36891),f128(x36891,x36892,x36893))) % 165.28/165.04 [3692]E(f332(f332(f104(f875(x36921,a862)),x36922),f332(f332(f22(f875(x36921,a862)),x36923),x36922)),f196(f875(x36921,a862))) % 165.28/165.04 [3696]E(f332(f332(f155(a868,x36961),f332(f16(x36961,a868),x36962)),f140(a868,f332(f302(a868,f2(a868)),x36963))),f171(x36961,x36963,x36962)) % 165.28/165.04 [3735]E(f40(f875(x37351,a862),f332(f332(f310(f875(x37351,a862)),x37352),x37353)),f332(f332(f113(f875(x37351,a862)),x37352),f40(f875(x37351,a862),x37353))) % 165.28/165.04 [3736]E(f41(f875(x37361,a862),f332(f332(f310(f875(x37361,a862)),x37362),x37363)),f332(f332(f104(f875(x37361,a862)),x37362),f41(f875(x37361,a862),x37363))) % 165.28/165.04 [3738]E(f171(x37381,f332(f197(f869(x37381)),f332(f137(x37381,f332(a329,x37382)),x37383)),x37382),f332(f137(x37381,f332(a329,x37382)),x37383)) % 165.28/165.04 [3740]E(f332(f332(f22(a868),f332(f332(f82(a868),x37401),x37402)),f332(f332(f82(a868),x37403),x37402)),f332(f332(f82(a868),f332(f332(f22(a868),x37401),x37403)),x37402)) % 165.28/165.04 [3741]E(f332(f332(f81(a868),f332(f332(f82(a868),x37411),x37412)),f332(f332(f82(a868),x37413),x37412)),f332(f332(f82(a868),f332(f332(f81(a868),x37411),x37413)),x37412)) % 165.28/165.04 [3742]E(f332(f332(f22(a1),f332(f332(f82(a1),x37421),x37422)),f332(f332(f82(a1),x37423),x37422)),f332(f332(f82(a1),f332(f332(f22(a1),x37421),x37423)),x37422)) % 165.28/165.04 [3743]E(f332(f332(f81(a1),f332(f332(f82(a1),x37431),x37432)),f332(f332(f82(a1),x37433),x37432)),f332(f332(f82(a1),f332(f332(f81(a1),x37431),x37433)),x37432)) % 165.28/165.04 [3745]E(f332(f332(f244(a868),f332(f332(f22(a868),x37451),x37452)),f332(f332(f22(a868),x37453),x37452)),f332(f332(f22(a868),f332(f332(f244(a868),x37451),x37453)),x37452)) % 165.28/165.04 [3768]E(f332(f332(f104(f875(f869(x37681),a862)),f161(x37681,x37682)),f161(x37681,x37683)),f161(x37681,f332(f332(f104(f875(x37681,a862)),x37682),x37683))) % 165.28/165.04 [3770]E(f332(f332(f113(f875(x37701,a862)),x37702),f332(f332(f113(f875(x37701,a862)),x37702),x37703)),f332(f332(f113(f875(x37701,a862)),x37702),x37703)) % 165.28/165.04 [3771]E(f332(f332(f113(f875(x37711,a862)),x37712),f332(f332(f22(f875(x37711,a862)),x37713),x37712)),f332(f332(f113(f875(x37711,a862)),x37712),x37713)) % 165.28/165.04 [3772]E(f332(f332(f104(f875(x37721,a862)),x37722),f332(f332(f104(f875(x37721,a862)),x37722),x37723)),f332(f332(f104(f875(x37721,a862)),x37722),x37723)) % 165.28/165.04 [3784]E(f332(f332(f289(x37841,x37842,x37842),x37843),f308(x37842,f196(f875(f874(x37842,x37842),a862)))),x37843) % 165.28/165.04 [3787]E(f332(f332(f113(f875(x37871,a862)),f332(f332(f310(x37871),x37872),f196(f875(x37871,a862)))),x37873),f332(f332(f310(x37871),x37872),x37873)) % 165.28/165.04 [3805]E(f332(f332(f22(a868),f332(f332(f22(a868),f332(a115,x38051)),x38052)),f332(a115,x38053)),f332(f332(f22(a868),f332(f332(f22(a868),x38051),x38052)),x38053)) % 165.28/165.04 [3835]E(f332(f332(f104(f875(f875(x38351,a862),a862)),f332(f309(x38351),x38352)),f332(f309(x38351),x38353)),f332(f309(x38351),f332(f332(f104(f875(x38351,a862)),x38352),x38353))) % 165.28/165.04 [3839]E(f332(f332(f113(f875(x38391,a862)),f332(f80(f875(x38391,a862)),x38392)),x38393),f332(f80(f875(x38391,a862)),f332(f332(f22(f875(x38391,a862)),x38392),x38393))) % 165.28/165.04 [3851]E(f332(f332(f310(x38511),x38512),f332(f332(f22(f875(x38511,a862)),x38513),f332(f332(f310(x38511),x38512),f196(f875(x38511,a862))))),f332(f332(f310(x38511),x38512),x38513)) % 165.28/165.04 [3861]P24(f332(f332(f246(f875(x38611,a862)),x38612),f332(f332(f113(f875(x38611,a862)),x38613),x38612))) % 165.28/165.04 [3862]P24(f332(f332(f246(f875(x38621,a862)),x38622),f332(f332(f113(f875(x38621,a862)),x38622),x38623))) % 165.28/165.04 [3865]E(f332(f332(f104(f875(x38651,a862)),f332(f80(f875(x38651,a862)),x38652)),f332(f80(f875(x38651,a862)),x38653)),f332(f80(f875(x38651,a862)),f332(f332(f113(f875(x38651,a862)),x38652),x38653))) % 165.28/165.04 [3866]E(f332(f332(f113(f875(x38661,a862)),f332(f80(f875(x38661,a862)),x38662)),f332(f80(f875(x38661,a862)),x38663)),f332(f80(f875(x38661,a862)),f332(f332(f104(f875(x38661,a862)),x38662),x38663))) % 165.28/165.04 [3880]P24(f332(f332(f246(f875(x38801,a862)),f332(f174(x38801),x38802)),f332(f174(x38801),f332(f332(f152(x38801),x38803),x38802)))) % 165.28/165.04 [3891]E(f332(f332(f113(f875(x38911,a862)),f332(f332(f22(f875(x38911,a862)),x38912),x38913)),f332(f332(f104(f875(x38911,a862)),x38912),x38913)),x38912) % 165.28/165.04 [3948]E(f332(f332(f6(x39481,a1),f332(f332(f8(a868,a1,x39481),f103(a1)),x39482)),x39483),f332(f103(a1),f332(f332(f6(x39481,a868),x39482),x39483))) % 165.28/165.04 [3949]E(f332(f332(f9(x39491,a1),f332(f332(f8(a868,a1,x39491),f103(a1)),x39492)),x39493),f332(f103(a1),f332(f332(f9(x39491,a868),x39492),x39493))) % 165.28/165.04 [3998]E(f332(f332(f135(x39981),f179(x39981,x39982,x39983)),f332(f332(f139(x39981),f332(f197(f869(x39981)),f179(x39981,x39982,x39983))),x39983)),x39983) % 165.28/165.04 [4003]E(f332(f80(f875(f874(x40031,x40032),a862)),f332(f332(f269(x40031,x40032),x40033),f332(f16(f875(x40032,a862),x40031),f255(f875(x40032,a862))))),f332(f332(f269(x40031,x40032),f332(f80(f875(x40031,a862)),x40033)),f332(f16(f875(x40032,a862),x40031),f255(f875(x40032,a862))))) % 165.28/165.04 [4004]E(f332(f80(f875(f874(x40041,x40042),a862)),f332(f332(f269(x40041,x40042),f255(f875(x40041,a862))),f332(f16(f875(x40042,a862),x40041),x40043))),f332(f332(f269(x40041,x40042),f255(f875(x40041,a862))),f332(f16(f875(x40042,a862),x40041),f332(f80(f875(x40042,a862)),x40043)))) % 165.28/165.04 [4028]E(f119(f872(x40281),f332(f241(f870(f872(x40281)),f870(f872(x40281)),f129(x40281),f5(f870(f872(x40281)))),x40282),f124(x40281,x40283)),f124(x40281,f128(f872(f870(f872(x40281))),x40282,x40283))) % 165.28/165.04 [4053]E(f332(f332(f42(f875(x40531,a862),f875(x40531,a862)),x40532),f332(f332(f7(f875(x40531,a862),f875(x40531,a862),f875(x40531,a862)),f104(f875(x40531,a862))),x40533)),f332(f332(f104(f875(x40531,a862)),f40(f875(x40531,a862),x40532)),x40533)) % 165.28/165.04 [4060]E(f332(f143(f869(x40601),f869(x40601),f135(x40601),f116(x40601)),f332(f332(f152(f869(x40601)),x40602),x40603)),f332(f332(f135(x40601),x40602),f332(f143(f869(x40601),f869(x40601),f135(x40601),f116(x40601)),x40603))) % 165.28/165.04 [4082]E(f332(f332(f310(f875(x40821,a862)),f332(f286(x40821,x40821,x40822),f332(f332(f310(x40821),x40823),f196(f875(x40821,a862))))),f196(f875(f875(x40821,a862),a862))),f332(f332(f61(x40821),f332(f332(f310(x40821),x40823),f196(f875(x40821,a862)))),x40822)) % 165.28/165.04 [4092]E(f332(f332(f81(a868),f332(f332(f82(a868),x40921),f332(f332(f39(a868),x40922),x40923))),f332(f332(f39(a868),f332(f332(f82(a868),x40921),f45(a868,x40922,x40923))),x40923)),f332(f332(f39(a868),f332(f332(f82(a868),x40921),x40922)),x40923)) % 165.28/165.04 [4093]E(f332(f332(f81(a1),f332(f332(f82(a1),x40931),f332(f332(f39(a1),x40932),x40933))),f332(f332(f39(a1),f332(f332(f82(a1),x40931),f45(a1,x40932,x40933))),x40933)),f332(f332(f39(a1),f332(f332(f82(a1),x40931),x40932)),x40933)) % 165.28/165.04 [4130]E(f332(f332(f22(f875(x41301,a862)),f332(f174(x41301),x41302)),f332(f332(f310(x41301),x41303),f196(f875(x41301,a862)))),f332(f174(x41301),f332(f137(x41301,f332(f332(f8(a862,a862,x41301),a327),f332(a329,x41303))),x41302))) % 165.28/165.04 [4180]E(f332(f332(f135(x41801),f332(f143(f869(x41801),f869(x41801),f135(x41801),f116(x41801)),x41802)),f332(f143(f869(x41801),f869(x41801),f135(x41801),f116(x41801)),x41803)),f332(f143(f869(x41801),f869(x41801),f135(x41801),f116(x41801)),f332(f332(f135(f869(x41801)),x41802),x41803))) % 165.28/165.04 [4185]E(f332(f332(f267(f869(x41851),f869(x41851)),f332(f137(x41851,x41852),x41853)),f332(f137(x41851,f332(f74(a862,a862,x41851,a327),x41852)),x41853)),f168(x41851,x41852,x41853)) % 165.28/165.04 [4188]E(f332(f332(f81(a868),f332(f332(f81(a868),f332(f332(f39(a868),x41881),x41882)),f332(f332(f39(a868),x41883),x41882))),f332(f332(f39(a868),f332(f332(f81(a868),f45(a868,x41881,x41882)),f45(a868,x41883,x41882))),x41882)),f332(f332(f39(a868),f332(f332(f81(a868),x41881),x41883)),x41882)) % 165.28/165.04 [4189]E(f332(f332(f81(a1),f332(f332(f81(a1),f332(f332(f39(a1),x41891),x41892)),f332(f332(f39(a1),x41893),x41892))),f332(f332(f39(a1),f332(f332(f81(a1),f45(a1,x41891,x41892)),f45(a1,x41893,x41892))),x41892)),f332(f332(f39(a1),f332(f332(f81(a1),x41891),x41893)),x41892)) % 165.28/165.04 [4245]E(f332(f332(f104(f875(f869(x42451),a862)),f332(f332(f7(f869(x42451),f875(f869(x42451),a862),a862),f334(f869(x42451))),f162(x42451,x42452))),f332(f332(f7(f869(x42451),f875(f869(x42451),a862),a862),f334(f869(x42451))),f162(x42451,x42453))),f161(x42451,f332(f332(f104(f875(x42451,a862)),f332(f332(f7(x42451,f875(x42451,a862),a862),f334(x42451)),x42452)),f332(f332(f7(x42451,f875(x42451,a862),a862),f334(x42451)),x42453)))) % 165.28/165.04 [4258]E(f332(f252(x42581),f332(f332(f18(x42581,a862,a862),f332(f332(f8(a862,f875(a862,a862),x42581),a331),f332(f332(f7(x42581,x42581,a862),a329),x42582))),f332(f332(f7(x42581,f875(x42581,a862),a862),f334(x42581)),x42583))),f332(f332(f310(x42581),x42582),x42583)) % 165.28/165.04 [4278]E(f332(f332(f87(f869(f869(x42781)),f869(f869(x42781))),f54(x42781,x42782)),f332(f332(f18(f869(f869(x42781)),f869(f869(x42781)),f869(f869(x42781))),f332(f332(f8(f869(f869(x42781)),f875(f869(f869(x42781)),f869(f869(x42781))),f869(f869(x42781))),f135(f869(x42781))),f332(f155(f869(x42781),f869(x42781)),f332(f152(x42781),x42783)))),f5(f869(f869(x42781))))),f54(x42781,f332(f332(f152(x42781),x42783),x42782))) % 165.28/165.04 [4282]E(f332(f252(x42821),f332(f332(f18(x42821,a862,a862),f332(f332(f8(a862,f875(a862,a862),x42821),a331),f332(f332(f7(x42821,f875(x42821,a862),a862),f334(x42821)),x42822))),f332(f332(f7(x42821,f875(x42821,a862),a862),f334(x42821)),x42823))),f332(f332(f113(f875(x42821,a862)),x42822),x42823)) % 165.28/165.04 [4283]E(f332(f252(x42831),f332(f332(f18(x42831,a862,a862),f332(f332(f8(a862,f875(a862,a862),x42831),a330),f332(f332(f7(x42831,f875(x42831,a862),a862),f334(x42831)),x42832))),f332(f332(f7(x42831,f875(x42831,a862),a862),f334(x42831)),x42833))),f332(f332(f104(f875(x42831,a862)),x42832),x42833)) % 165.28/165.04 [4374]E(f332(f332(f42(x43741,f875(f875(x43741,a862),a862)),x43742),f332(f332(f7(x43741,f875(f875(x43741,a862),a862),f875(f875(x43741,a862),a862)),f332(f332(f8(f875(x43741,a862),f875(f875(f875(x43741,a862),a862),f875(f875(x43741,a862),a862)),x43741),f310(f875(x43741,a862))),f332(f332(f8(f875(x43741,a862),f875(x43741,a862),x43741),f286(x43741,x43741,x43743)),f332(f332(f7(x43741,f875(x43741,a862),f875(x43741,a862)),f310(x43741)),f196(f875(x43741,a862)))))),f196(f875(f875(x43741,a862),a862)))),f332(f332(f61(x43741),x43742),x43743)) % 165.28/165.04 [4376]E(f332(f332(f213(x43761),f332(f332(f82(a1),f332(f332(f74(f874(a1,a1),a1,x43761,f266(a1,a1)),f224(x43761)),x43762)),f332(f332(f74(f874(a1,a1),a1,x43761,f266(a1,a1)),f224(x43761)),x43763))),f332(f332(f82(a1),f332(f332(f74(f874(a1,a1),a1,x43761,f270(a1,a1)),f224(x43761)),x43762)),f332(f332(f74(f874(a1,a1),a1,x43761,f270(a1,a1)),f224(x43761)),x43763))),f233(x43761,x43762,x43763)) % 165.28/165.04 [4379]E(f332(f252(f869(x43791)),f332(f332(f18(f869(x43791),a862,a862),f332(f332(f8(a862,f875(a862,a862),f869(x43791)),a330),f332(f332(f7(f869(x43791),a868,a862),f332(f332(f8(a868,f875(a868,a862),f869(x43791)),a329),f197(f869(x43791)))),x43792))),f332(f332(f7(f869(x43791),f875(x43791,a862),a862),f332(f332(f8(f875(x43791,a862),f875(f875(x43791,a862),a862),f869(x43791)),f246(f875(x43791,a862))),f174(x43791))),f332(f174(x43791),x43793)))),f332(f174(f869(x43791)),f55(x43791,x43792,x43793))) % 165.28/165.04 [3758]E(f45(a868,f332(f332(f81(a868),f332(f332(f82(a868),x37581),x37582)),x37583),x37582),f45(a868,x37583,x37582)) % 165.28/165.04 [3804]E(f140(a868,f332(f302(a868,f332(f332(f81(a868),x38041),x38042)),x38043)),f332(f332(f139(a868),x38042),f140(a868,f332(f302(a868,x38041),x38043)))) % 165.28/165.04 [3850]E(f332(f332(f81(a1),f332(f103(a1),x38501)),f332(f332(f81(a1),f332(f103(a1),x38502)),x38503)),f332(f332(f81(a1),f332(f103(a1),f332(f332(f81(a868),x38501),x38502))),x38503)) % 165.28/165.04 [3857]E(f332(f332(f113(f875(x38571,a862)),f332(f332(f22(f875(x38571,a862)),x38572),x38573)),x38573),f332(f332(f113(f875(x38571,a862)),x38572),x38573)) % 165.28/165.04 [3858]E(f332(f332(f22(f875(x38581,a862)),f332(f332(f22(f875(x38581,a862)),x38582),x38583)),x38583),f332(f332(f22(f875(x38581,a862)),x38582),x38583)) % 165.28/165.04 [3881]E(f332(f332(f289(x38811,x38811,x38812),f308(x38811,f196(f875(f874(x38811,x38811),a862)))),x38813),x38813) % 165.28/165.04 [3888]E(f332(f332(f113(f875(x38881,a862)),f332(f285(x38881),x38882)),f332(f285(x38881),x38883)),f332(f285(x38881),f332(f332(f113(f875(f874(x38881,x38881),a862)),x38882),x38883))) % 165.28/165.04 [3899]E(f276(x38991,f332(f332(f152(f874(a102,x38991)),f332(f332(f267(a102,x38991),f2(a102)),x38992)),x38993)),f276(x38991,x38993)) % 165.28/165.04 [3902]E(f332(f332(f113(f875(x39021,a862)),f40(f875(x39021,a862),x39022)),f40(f875(x39021,a862),x39023)),f40(f875(x39021,a862),f332(f332(f113(f875(f875(x39021,a862),a862)),x39022),x39023))) % 165.28/165.04 [3903]E(f332(f332(f104(f875(x39031,a862)),f41(f875(x39031,a862),x39032)),f41(f875(x39031,a862),x39033)),f41(f875(x39031,a862),f332(f332(f113(f875(f875(x39031,a862),a862)),x39032),x39033))) % 165.28/165.04 [3940]E(f332(f332(f289(x39401,x39401,x39401),f332(f332(f191(f874(x39401,x39401),a862),x39402),x39403)),x39403),f332(f332(f191(f874(x39401,x39401),a862),f332(a115,x39402)),x39403)) % 165.28/165.04 [3989]P24(f332(f332(f246(f875(x39891,a862)),f332(f332(f22(f875(x39891,a862)),x39892),x39893)),x39892)) % 165.28/165.04 [3990]P24(f332(f332(f246(f875(x39901,a862)),f332(f332(f104(f875(x39901,a862)),x39902),x39903)),x39903)) % 165.28/165.04 [3991]P24(f332(f332(f246(f875(x39911,a862)),f332(f332(f104(f875(x39911,a862)),x39912),x39913)),x39912)) % 165.28/165.04 [4016]E(f308(x40161,f332(f332(f113(f875(f874(x40161,x40161),a862)),f308(x40161,x40162)),f308(x40161,x40163))),f308(x40161,f332(f332(f113(f875(f874(x40161,x40161),a862)),x40162),x40163))) % 165.28/165.04 [4020]E(f40(f875(x40201,a862),f332(f332(f310(f875(x40201,a862)),x40202),f332(f332(f310(f875(x40201,a862)),x40203),f196(f875(f875(x40201,a862),a862))))),f332(f332(f113(f875(x40201,a862)),x40202),x40203)) % 165.28/165.04 [4021]E(f41(f875(x40211,a862),f332(f332(f310(f875(x40211,a862)),x40212),f332(f332(f310(f875(x40211,a862)),x40213),f196(f875(f875(x40211,a862),a862))))),f332(f332(f104(f875(x40211,a862)),x40212),x40213)) % 165.28/165.04 [4027]E(f332(f332(f289(x40271,x40271,x40271),f332(f332(f191(f874(x40271,x40271),a862),x40272),x40273)),x40273),f332(f332(f289(x40271,x40271,x40271),x40273),f332(f332(f191(f874(x40271,x40271),a862),x40272),x40273))) % 165.28/165.04 [4097]E(f332(f332(f113(f875(x40971,a862)),f332(f252(x40971),f332(f332(f7(x40971,x40971,a862),a329),x40972))),x40973),f332(f332(f310(x40971),x40972),x40973)) % 165.28/165.04 [4099]E(f332(a107,f332(f332(f6(x40991,a1),f332(f332(f8(a868,a1,x40991),f103(a1)),x40992)),x40993)),f332(f332(f6(x40991,a868),x40992),x40993)) % 165.28/165.04 [4100]E(f332(a107,f332(f332(f9(x41001,a1),f332(f332(f8(a868,a1,x41001),f103(a1)),x41002)),x41003)),f332(f332(f9(x41001,a868),x41002),x41003)) % 165.28/165.04 [4177]E(f332(f157(f869(x41771),x41771,f332(f173(x41771),x41772),f332(f16(f875(f869(x41771),f869(x41771)),x41771),f332(f332(f7(f869(x41771),f869(x41771),f869(x41771)),f135(x41771)),x41772))),x41773),f332(f173(x41771),f332(f332(f135(x41771),x41773),x41772))) % 165.28/165.04 [4208]P24(f332(f332(f246(f875(f875(x42081,a862),a862)),f332(f332(f113(f875(f875(x42081,a862),a862)),f332(f309(x42081),x42082)),f332(f309(x42081),x42083))),f332(f309(x42081),f332(f332(f113(f875(x42081,a862)),x42082),x42083)))) % 165.28/165.04 [4301]E(f332(f252(x43011),f332(f332(f18(x43011,a862,a862),f332(f332(f8(a862,f875(a862,a862),x43011),a330),f332(f332(f7(x43011,f875(x43011,a862),a862),f334(x43011)),x43012))),f332(f332(f8(a862,a862,x43011),a327),f332(f332(f7(x43011,f875(x43011,a862),a862),f334(x43011)),x43013)))),f332(f332(f22(f875(x43011,a862)),x43012),x43013)) % 165.28/165.04 [4323]E(f332(f38(a868),f332(f252(a868),f332(f332(f18(a868,a862,a862),f332(f332(f8(a862,f875(a862,a862),a868),a330),f332(f332(f7(a868,a868,a862),f247(a868)),f332(f197(f869(x43231)),x43232)))),f332(f332(f8(x43231,a862,a868),x43233),f332(f166(x43231),x43232))))),f332(f197(f869(x43231)),f332(f137(x43231,x43233),x43232))) % 165.28/165.04 [4325]E(f332(f197(f869(x43251)),f178(x43251,x43252,x43253)),f332(f38(a868),f332(f252(a868),f332(f332(f18(a868,a862,a862),f332(f332(f8(a862,f875(a862,a862),a868),a330),f332(f332(f7(a868,a868,a862),f247(a868)),f332(f197(f869(x43251)),x43252)))),f332(f332(f7(a868,f875(a868,a862),a862),f334(a868)),x43253))))) % 165.28/165.04 [4422]E(f332(f332(f104(f875(f874(f869(x44221),f869(x44221)),a862)),f332(f311(f874(f874(x44221,f869(x44221)),f874(x44221,f869(x44221))),f874(f869(x44221),f869(x44221)),f272(f874(x44221,f869(x44221)),f869(x44221),f874(x44221,f869(x44221)),f869(x44221),f332(f271(x44221,f869(x44221),f869(x44221)),f152(x44221)),f332(f271(x44221,f869(x44221),f869(x44221)),f152(x44221)))),f324(x44221,f869(x44221),x44222,f332(f144(x44221,x44222),x44223)))),f332(f252(f874(f869(x44221),f869(x44221))),f332(f271(f869(x44221),f869(x44221),a862),f332(f332(f7(f869(x44221),f875(f869(x44221),a862),f875(f869(x44221),a862)),f332(f332(f8(f875(a862,a862),f875(f875(f869(x44221),a862),f875(f869(x44221),a862)),f869(x44221)),f8(a862,a862,f869(x44221))),f332(f332(f8(a862,f875(a862,a862),f869(x44221)),a330),f332(f332(f7(f869(x44221),a868,a862),f332(f332(f8(a868,f875(a868,a862),f869(x44221)),a329),f197(f869(x44221)))),f332(a115,x44223))))),f332(f332(f7(f869(x44221),a868,a862),f332(f332(f8(a868,f875(a868,a862),f869(x44221)),a329),f197(f869(x44221)))),f332(a115,x44223)))))),f332(f144(x44221,x44222),f332(a115,x44223))) % 165.28/165.04 [3904]E(f45(a868,f332(a115,f332(f332(f81(a868),f332(f332(f82(a868),x39041),x39042)),x39043)),x39042),f45(a868,f332(a115,x39043),x39042)) % 165.28/165.04 [4165]E(f332(f252(x41651),f332(f332(f18(x41651,a862,a862),f332(f332(f8(a862,f875(a862,a862),x41651),a330),x41652)),x41653)),f332(f332(f104(f875(x41651,a862)),f332(f252(x41651),x41652)),f332(f252(x41651),x41653))) % 165.28/165.04 [4166]E(f332(f252(x41661),f332(f332(f18(x41661,a862,a862),f332(f332(f8(a862,f875(a862,a862),x41661),a331),x41662)),x41663)),f332(f332(f113(f875(x41661,a862)),f332(f252(x41661),x41662)),f332(f252(x41661),x41663))) % 165.28/165.04 [4168]E(f332(f332(f135(x41681),f332(f332(f139(x41681),f45(a868,x41682,f332(f197(f869(x41681)),x41683))),x41683)),f332(f332(f177(x41681),f45(a868,x41682,f332(f197(f869(x41681)),x41683))),x41683)),f332(f332(f332(f191(f869(x41681),f869(x41681)),x41682),f169(x41681)),x41683)) % 165.28/165.04 [4174]E(f332(f252(x41741),f332(f332(f18(x41741,a862,a862),f332(f332(f8(a862,f875(a862,a862),x41741),a335),x41742)),x41743)),f332(f332(f113(f875(x41741,a862)),f332(f80(f875(x41741,a862)),f332(f252(x41741),x41742))),f332(f252(x41741),x41743))) % 165.28/165.04 [4190]E(f332(f332(f81(a868),f332(f197(f869(x41901)),f332(f137(x41901,x41902),x41903))),f332(f197(f869(x41901)),f332(f137(x41901,f332(f332(f8(a862,a862,x41901),a327),x41902)),x41903))),f332(f197(f869(x41901)),x41903)) % 165.28/165.04 [4215]P24(f332(f332(f246(f875(x42151,a862)),f332(f332(f113(f875(x42151,a862)),f41(f875(x42151,a862),x42152)),f41(f875(x42151,a862),x42153))),f41(f875(x42151,a862),f332(f332(f104(f875(f875(x42151,a862),a862)),x42152),x42153)))) % 165.28/165.04 [4229]E(f332(f174(x42291),f332(f137(x42291,f332(f332(f8(a862,a862,x42291),a327),f332(f332(f7(x42291,x42291,a862),a329),x42292))),x42293)),f332(f332(f22(f875(x42291,a862)),f332(f174(x42291),x42293)),f332(f332(f310(x42291),x42292),f196(f875(x42291,a862))))) % 165.28/165.04 [4238]P24(f332(f332(f246(f875(f874(x42381,x42381),a862)),f332(f332(f113(f875(f874(x42381,x42381),a862)),f308(x42381,x42382)),f308(x42381,x42383))),f308(x42381,f332(f332(f113(f875(f874(x42381,x42381),a862)),x42382),x42383)))) % 165.28/165.04 [4263]E(f332(f332(f82(a868),f332(a115,f332(a115,f2(a868)))),f332(f332(f6(a868,a868),f332(f332(f8(a868,a868,a868),f332(f81(a868),x42631)),f332(f332(f7(a868,a868,a868),f82(a868)),x42632))),f332(f253(a868),x42633))),f332(f332(f82(a868),x42633),f332(f332(f81(a868),x42631),f332(f332(f81(a868),x42631),f332(f332(f82(a868),f332(f332(f22(a868),x42633),f79(a868))),x42632))))) % 165.28/165.04 [4273]E(f332(f252(x42731),f332(f332(f18(x42731,a862,a862),f332(f332(f8(a862,f875(a862,a862),x42731),a330),f332(f332(f7(x42731,f875(x42731,a862),a862),f334(x42731)),f332(f174(x42731),x42732)))),x42733)),f332(f174(x42731),f332(f137(x42731,x42733),x42732))) % 165.28/165.04 [4421]E(f332(f252(x44211),f332(f332(f8(f875(a868,a862),a862,x44211),f88(a868)),f332(f332(f7(x44211,f875(a868,a862),f875(a868,a862)),f332(f332(f8(f875(a868,f875(a862,a862)),f875(f875(a868,a862),f875(a868,a862)),x44211),f18(a868,a862,a862)),f332(f332(f8(f875(a868,a862),f875(a868,f875(a862,a862)),x44211),f332(f8(a862,f875(a862,a862),a868),a330)),f332(f332(f7(x44211,f875(a868,x44211),f875(a868,a862)),f332(f332(f8(f875(x44211,a862),f875(f875(a868,x44211),f875(a868,a862)),x44211),f8(x44211,a862,a868)),a329)),f332(f166(x44211),x44212))))),f332(f332(f18(a868,a862,a862),f332(f332(f8(a862,f875(a862,a862),a868),a330),f332(f332(f7(a868,a868,a862),f247(a868)),f332(f197(f869(x44211)),x44212)))),f332(f332(f7(a868,f875(a868,a862),a862),f334(a868)),x44213))))),f332(f174(x44211),f178(x44211,x44212,x44213))) % 165.28/165.04 [4313]E(f332(f252(x43131),f332(f332(f18(x43131,a862,a862),f332(f332(f8(a862,f875(a862,a862),x43131),a335),f332(f332(f8(a862,a862,x43131),a327),f332(f332(f7(x43131,x43131,a862),a329),x43132)))),x43133)),f332(f332(f310(x43131),x43132),f332(f252(x43131),x43133))) % 165.28/165.04 [4345]E(f332(f332(f155(f874(x43451,a868),x43451),f266(x43451,a868)),f332(f137(f874(x43451,a868),f332(f332(f7(f874(x43451,a868),f875(a868,a862),a862),f332(f332(f8(a868,f875(f875(a868,a862),a862),f874(x43451,a868)),f334(a868)),f270(x43451,a868))),x43452)),f332(f332(f184(x43451,a868),x43453),f140(a868,f332(f302(a868,f2(a868)),f332(f197(f869(x43451)),x43453)))))),f178(x43451,x43453,x43452)) % 165.28/165.04 [4375]E(f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(f332(f6(a868,a1),f332(f332(f8(a1,a1,a868),f332(f81(a1),x43751)),f332(f332(f7(a868,a1,a1),f332(f332(f8(a1,f875(a1,a1),a868),f82(a1)),f103(a1))),x43752))),f332(f253(a868),x43753))),f332(f332(f82(a1),f332(f103(a1),x43753)),f332(f332(f81(a1),x43751),f332(f332(f81(a1),x43751),f332(f332(f82(a1),f332(f103(a1),f332(f332(f22(a868),x43753),f79(a868)))),x43752))))) % 165.28/165.04 [4415]E(f332(f252(f874(x44151,x44152)),f332(f271(x44151,x44152,a862),f332(f332(f7(x44151,f875(f874(x44152,x44151),a862),f875(x44152,a862)),f332(f332(f8(f875(x44152,f875(f875(f874(x44152,x44151),a862),a862)),f875(f875(f874(x44152,x44151),a862),f875(x44152,a862)),x44151),f7(x44152,f875(f874(x44152,x44151),a862),a862)),f332(f332(f8(f875(x44152,f874(x44152,x44151)),f875(x44152,f875(f875(f874(x44152,x44151),a862),a862)),x44151),f332(f8(f874(x44152,x44151),f875(f875(f874(x44152,x44151),a862),a862),x44152),f334(f874(x44152,x44151)))),f332(f7(x44152,x44151,f874(x44152,x44151)),f267(x44152,x44151))))),x44153))),f332(f287(x44152,x44151),x44153)) % 165.28/165.04 [4437]E(f332(f252(f869(x44371)),f332(f332(f8(f875(x44371,a862),a862,f869(x44371)),f88(x44371)),f332(f332(f8(f875(x44371,f875(f869(x44371),a862)),f875(x44371,a862),f869(x44371)),f332(f8(f875(f869(x44371),a862),a862,x44371),f88(f869(x44371)))),f332(f332(f7(f869(x44371),f875(x44371,f875(f869(x44371),a862)),f875(x44371,f875(f869(x44371),a862))),f332(f332(f8(f875(x44371,f875(f875(f869(x44371),a862),f875(f869(x44371),a862))),f875(f875(x44371,f875(f869(x44371),a862)),f875(x44371,f875(f869(x44371),a862))),f869(x44371)),f18(x44371,f875(f869(x44371),a862),f875(f869(x44371),a862))),f332(f332(f8(f875(x44371,f875(f869(x44371),f875(a862,a862))),f875(x44371,f875(f875(f869(x44371),a862),f875(f869(x44371),a862))),f869(x44371)),f332(f8(f875(f869(x44371),f875(a862,a862)),f875(f875(f869(x44371),a862),f875(f869(x44371),a862)),x44371),f18(f869(x44371),a862,a862))),f332(f332(f8(f875(x44371,f875(f869(x44371),a862)),f875(x44371,f875(f869(x44371),f875(a862,a862))),f869(x44371)),f332(f8(f875(f869(x44371),a862),f875(f869(x44371),f875(a862,a862)),x44371),f332(f8(a862,f875(a862,a862),f869(x44371)),a330))),f332(f332(f7(f869(x44371),f875(x44371,f875(f869(x44371),f869(x44371))),f875(x44371,f875(f869(x44371),a862))),f332(f332(f8(f875(f875(f869(x44371),f869(x44371)),f875(f869(x44371),a862)),f875(f875(x44371,f875(f869(x44371),f869(x44371))),f875(x44371,f875(f869(x44371),a862))),f869(x44371)),f8(f875(f869(x44371),f869(x44371)),f875(f869(x44371),a862),x44371)),f332(f332(f8(f875(f869(x44371),a862),f875(f875(f869(x44371),f869(x44371)),f875(f869(x44371),a862)),f869(x44371)),f8(f869(x44371),a862,f869(x44371))),a329))),f152(x44371)))))),f332(f332(f7(x44371,f875(f869(x44371),a862),f875(f869(x44371),a862)),f332(f332(f8(f875(a862,a862),f875(f875(f869(x44371),a862),f875(f869(x44371),a862)),x44371),f8(a862,a862,f869(x44371))),f332(f332(f8(a862,f875(a862,a862),x44371),a330),f332(f332(f7(x44371,f875(x44371,a862),a862),f334(x44371)),x44372)))),f332(f332(f7(f869(x44371),f875(f869(x44371),a862),a862),f334(f869(x44371))),x44373)))))),f176(x44371,x44372,x44373)) % 165.28/165.04 [4434]E(f332(f332(f87(a1,f874(a1,a1)),f332(f332(f22(a1),x44341),x44342)),f332(f332(f7(a1,f874(a1,a1),f874(a1,a1)),f332(f332(f18(a1,f874(a1,a1),f875(f874(a1,a1),f874(a1,a1))),f332(f332(f8(a862,f875(f874(a1,a1),f875(f874(a1,a1),f874(a1,a1))),a1),f99(f874(a1,a1))),f332(f246(a1),f2(a1)))),f332(f267(a1,a1),f332(f332(f81(a1),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x44343)),f79(a1))))),f332(f332(f267(a1,a1),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x44343)),x44341))),f332(f44(x44342),f332(f332(f267(a1,a1),x44343),x44341))) % 165.28/165.04 [4465]~E(f33(x44651,x44652),f34(x44653,x44654)) % 165.28/165.04 [4484]~E(f332(a28,x44841),f29(x44842,x44843,x44844)) % 165.28/165.04 [4485]~E(f332(a28,x44851),f31(x44852,x44853,x44854)) % 165.28/165.04 [4486]~E(f332(a28,x44861),f30(x44862,x44863,x44864)) % 165.28/165.04 [4487]~E(f29(x44871,x44872,x44873),f332(a28,x44874)) % 165.28/165.04 [4488]~E(f31(x44881,x44882,x44883),f332(a28,x44884)) % 165.28/165.04 [4489]~E(f30(x44891,x44892,x44893),f332(a28,x44894)) % 165.28/165.04 [3445]E(f332(f332(f332(f73(x34451,x34452),x34453),x34454),f332(x34453,x34454)),x34453) % 165.28/165.04 [3453]E(f119(x34531,f332(x34532,x34533),f332(x34534,x34533)),f332(f215(x34531,x34532,x34534),x34533)) % 165.28/165.04 [3464]E(f119(f872(x34641),f332(x34642,x34643),f332(x34644,x34643)),f332(f205(x34641,x34642,x34644),x34643)) % 165.28/165.04 [3507]E(f332(f332(f258(x35071,x35072,x35073),x35074),f2(a868)),x35072) % 165.28/165.04 [3548]E(f193(x35481,x35482,x35483,f332(a115,x35484)),f332(x35483,x35484)) % 165.28/165.04 [3589]E(f172(x35891,x35892,f172(x35891,x35893,x35894)),f172(x35891,x35893,f172(x35891,x35892,x35894))) % 165.28/165.04 [3590]E(f119(x35901,f128(x35901,x35902,x35903),x35904),f128(x35901,x35902,f119(x35901,x35903,x35904))) % 165.28/165.04 [3724]E(f332(f241(x37241,x37242,x37243,x37244),f209(x37242)),x37243) % 165.28/165.04 [3726]E(f332(f157(x37261,x37262,x37263,x37264),f116(x37262)),x37263) % 165.28/165.04 [3727]E(f332(f143(x37271,x37272,x37273,x37274),f116(x37272)),x37274) % 165.28/165.04 [3834]E(f332(f332(f135(x38341),f171(x38341,x38342,x38343)),f171(x38341,x38344,x38343)),f332(f332(f135(x38341),f171(x38341,x38344,x38343)),f171(x38341,x38342,x38343))) % 165.28/165.04 [3847]E(f332(f241(f872(x38471),x38472,f209(x38471),f332(f16(f872(x38471),x38472),f209(x38471))),f332(x38473,x38474)),f209(x38471)) % 165.28/165.04 [3892]E(f332(f332(f113(f875(x38921,a862)),f186(x38921,x38922,x38923)),f186(x38921,x38922,x38924)),f186(x38921,x38922,f187(x38921,x38922,x38924,x38923))) % 165.28/165.04 [3925]E(f332(f332(f273(x39251,x39252,x39253,f874(x39252,x39253)),x39254),f267(x39252,x39253)),x39254) % 165.28/165.04 [3934]E(f242(x39341,x39342,x39343,x39344,f209(x39342)),x39343) % 165.28/165.04 [3935]E(f189(x39351,x39352,x39353,x39354,f116(x39352)),x39353) % 165.28/165.04 [3936]E(f189(x39361,x39362,x39363,f116(x39361),x39364),x39363) % 165.28/165.04 [4222]P46(x42221,x42222,x42223,x42224,f196(f875(x42221,a862)),x42224) % 165.28/165.04 [3246]E(f332(f332(f16(x32461,x32462),x32463),x32464),x32463) % 165.28/165.04 [3362]E(f332(f332(f210(x33621,x33622),x33623),f332(f208(x33621),x33624)),f332(f208(x33622),f332(x33623,x33624))) % 165.28/165.04 [3538]E(f172(x35381,x35382,f332(f137(x35381,x35383),x35384)),f332(f137(x35381,x35383),f172(x35381,x35382,x35384))) % 165.28/165.04 [3573]E(f332(f332(f65(x35731,x35732,x35733),x35734),f196(f875(x35731,a862))),x35734) % 165.28/165.04 [3596]E(f332(f332(f166(x35961),f332(f332(f152(x35961),x35962),x35963)),f332(a115,x35964)),f332(f332(f166(x35961),x35963),x35964)) % 165.28/165.04 [3639]P33(x36391,f2(a868),f332(f332(f332(f93(x36391),x36392),f332(a28,x36393)),x36394)) % 165.28/165.04 [3664]E(f332(f332(x36641,x36642),f332(f192(x36643,x36644,x36641),x36642)),f332(f192(x36643,x36644,x36641),f332(a115,x36642))) % 165.28/165.04 [3763]E(f332(f332(f160(x37631,f332(f332(f152(x37631),x37632),x37633)),f2(a868)),x37634),f332(f332(f152(x37631),x37634),x37633)) % 165.28/165.04 [3774]E(f332(f332(f42(f875(x37741,a862),f875(x37742,a862)),x37743),f311(x37741,x37742,x37744)),f332(f311(x37741,x37742,x37744),f40(f875(x37741,a862),x37743))) % 165.28/165.04 [3775]E(f332(f332(f42(f875(x37751,a862),f875(x37752,a862)),x37753),f312(x37752,x37751,x37754)),f332(f312(x37752,x37751,x37754),f40(f875(x37751,a862),x37753))) % 165.28/165.04 [3874]E(f186(x38741,x38742,f190(x38741,x38742,x38743,x38744)),f332(f332(f104(f875(x38741,a862)),f186(x38741,x38742,x38743)),x38744)) % 165.28/165.04 [3878]E(f332(f130(x38781,x38782),f128(x38781,x38783,x38784)),f332(f332(f81(a868),f332(f332(f81(a868),f332(x38782,x38783)),f332(f130(x38781,x38782),x38784))),f332(a115,f2(a868)))) % 165.28/165.04 [3898]E(f332(f143(x38981,x38982,f332(f7(x38982,x38981,x38981),x38983),x38984),f332(f170(x38982),f116(x38982))),x38984) % 165.28/165.04 [3947]E(f77(x39471,x39472,x39473,x39474,f196(f875(x39471,a862))),x39473) % 165.28/165.04 [3992]E(f332(f332(f332(f332(f73(x39921,f872(x39922)),f332(f16(f872(x39922),x39921),f209(x39922))),x39923),f209(x39922)),x39924),f209(x39922)) % 165.28/165.04 [4148]E(f332(f271(x41481,x41482,x41483),f332(f332(f8(f875(x41482,f874(x41481,x41482)),f875(x41482,x41483),x41481),f332(f8(f874(x41481,x41482),x41483,x41482),x41484)),f267(x41481,x41482))),x41484) % 165.28/165.04 [3443]E(f332(f270(x34431,x34432),f332(f332(f267(x34431,x34432),x34433),x34434)),x34434) % 165.28/165.04 [3444]E(f332(f266(x34441,x34442),f332(f332(f267(x34441,x34442),x34443),x34444)),x34443) % 165.28/165.04 [3480]E(f332(f197(f869(x34801)),f332(f332(f155(x34802,x34801),x34803),x34804)),f332(f197(f869(x34802)),x34804)) % 165.28/165.04 [3481]E(f332(f197(f869(x34811)),f332(f332(f160(x34811,x34812),x34813),x34814)),f332(f197(f869(x34811)),x34812)) % 165.28/165.04 [3501]E(f332(f332(f139(x35011),f332(a115,x35012)),f332(f332(f152(x35011),x35013),x35014)),f332(f332(f139(x35011),x35012),x35014)) % 165.28/165.04 [3568]E(f332(f332(f177(x35681),x35682),f171(x35681,x35683,x35684)),f171(x35681,f332(f332(f244(a868),x35682),x35683),x35684)) % 165.28/165.04 [3569]E(f332(f332(f139(x35691),x35692),f171(x35691,x35693,x35694)),f171(x35691,f332(f332(f22(a868),x35693),x35692),x35694)) % 165.28/165.04 [3575]E(f332(f332(f310(x35751),x35752),f332(f332(f310(x35751),x35753),x35754)),f332(f332(f310(x35751),x35753),f332(f332(f310(x35751),x35752),x35754))) % 165.28/165.04 [3578]E(f332(f332(f155(x35781,x35782),x35783),f117(x35781,x35784)),f117(x35782,f332(f332(f155(x35781,x35782),x35783),x35784))) % 165.28/165.04 [3594]E(f332(f170(x35941),f332(f332(f155(x35942,x35941),x35943),x35944)),f332(f332(f155(x35942,x35941),x35943),f332(f170(x35942),x35944))) % 165.28/165.04 [3595]E(f332(f332(f155(x35951,x35952),x35953),f332(f173(x35951),x35954)),f332(f173(x35952),f332(f332(f155(x35951,x35952),x35953),x35954))) % 165.28/165.04 [3606]E(f332(f332(f177(x36061),f332(a115,x36062)),f332(f332(f152(x36061),x36063),x36064)),f332(f332(f152(x36061),x36063),f332(f332(f177(x36061),x36062),x36064))) % 165.28/165.04 [3610]E(f332(f174(x36101),f332(f332(f155(x36102,x36101),x36103),x36104)),f332(f311(x36102,x36101,x36103),f332(f174(x36102),x36104))) % 165.28/165.04 [3625]E(f332(f332(f155(x36251,x36252),f332(f16(x36252,x36251),x36253)),x36254),f171(x36252,f332(f197(f869(x36251)),x36254),x36253)) % 165.28/165.04 [3663]E(f17(x36631,x36632,x36633,f332(a3,f332(a115,f332(a19,x36634)))),f332(x36633,x36634)) % 165.28/165.04 [3666]E(f332(f332(f135(x36661),f332(f137(x36661,x36662),x36663)),f332(f137(x36661,x36662),x36664)),f332(f137(x36661,x36662),f332(f332(f135(x36661),x36663),x36664))) % 165.28/165.04 [3679]E(f153(x36791,f332(f332(f155(x36792,x36791),x36793),f153(x36792,x36794))),f153(x36791,f332(f332(f155(x36792,x36791),x36793),x36794))) % 165.28/165.04 [3695]E(f332(f287(x36951,x36951),f332(f332(f288(x36952,x36951),x36953),x36954)),f332(f332(f288(x36952,x36951),f332(f287(x36952,x36952),x36953)),x36954)) % 165.28/165.04 [3706]E(f332(f332(f289(x37061,x37062,x37063),x37064),f196(f875(f874(x37062,x37063),a862))),f196(f875(f874(x37061,x37063),a862))) % 165.28/165.04 [3707]E(f332(f332(f177(x37071),f332(f332(f22(a868),x37072),x37073)),f332(f332(f139(x37071),x37073),x37074)),f332(f332(f139(x37071),x37073),f332(f332(f177(x37071),x37072),x37074))) % 165.28/165.04 [3728]E(f332(f332(f135(x37281),f171(x37281,x37282,x37283)),f171(x37281,x37284,x37283)),f171(x37281,f332(f332(f81(a868),x37282),x37284),x37283)) % 165.28/165.04 [3755]E(f40(f875(x37551,a862),f332(f311(x37552,f875(x37551,a862),x37553),x37554)),f332(f332(f42(x37552,f875(x37551,a862)),x37554),x37553)) % 165.28/165.04 [3756]E(f41(f875(x37561,a862),f332(f311(x37562,f875(x37561,a862),x37563),x37564)),f332(f332(f43(x37562,f875(x37561,a862)),x37564),x37563)) % 165.28/165.04 [3757]E(f332(f197(f869(f874(x37571,x37572))),f332(f332(f184(x37571,x37572),x37573),x37574)),f332(f332(f244(a868),f332(f197(f869(x37571)),x37573)),f332(f197(f869(x37572)),x37574))) % 165.28/165.04 [3759]E(f332(f312(x37591,x37592,x37593),f332(f80(f875(x37592,a862)),x37594)),f332(f80(f875(x37591,a862)),f332(f312(x37591,x37592,x37593),x37594))) % 165.28/165.04 [3789]E(f332(f190(x37891,x37892,x37893,f196(f875(x37891,a862))),x37894),f209(x37892)) % 165.28/165.04 [3810]E(f332(f312(x38101,x38102,x38103),f332(f252(x38102),x38104)),f332(f252(x38101),f332(f332(f8(x38102,a862,x38101),x38104),x38103))) % 165.28/165.04 [3828]E(f332(f332(f166(x38281),f332(f332(f135(x38281),x38282),f332(f332(f152(x38281),x38283),x38284))),f332(f197(f869(x38281)),x38282)),x38283) % 165.28/165.04 [3833]E(f332(f190(x38331,x38332,f332(f16(f872(x38332),x38331),f209(x38332)),x38333),x38334),f209(x38332)) % 165.28/165.04 [3855]E(f332(f311(x38551,x38552,x38553),f332(f312(x38551,x38552,x38553),x38554)),f332(f332(f104(f875(x38552,a862)),x38554),f332(f311(x38551,x38552,x38553),f255(f875(x38551,a862))))) % 165.28/165.04 [3873]P24(f332(f332(f334(x38731),f332(x38732,x38733)),f332(f311(x38734,x38731,x38732),f255(f875(x38734,a862))))) % 165.28/165.04 [3885]E(f332(f332(f135(x38851),f171(x38851,x38852,x38853)),f332(f332(f152(x38851),x38853),x38854)),f332(f332(f152(x38851),x38853),f332(f332(f135(x38851),f171(x38851,x38852,x38853)),x38854))) % 165.28/165.04 [3887]E(f332(f332(f269(x38871,x38872),f332(f174(x38871),x38873)),f332(f16(f875(x38872,a862),x38871),f332(f174(x38872),x38874))),f332(f174(f874(x38871,x38872)),f60(x38871,x38872,x38873,x38874))) % 165.28/165.04 [3901]E(f156(x39011,x39012,f332(f332(f152(x39011),x39013),x39014)),f332(f332(f81(a868),f332(f332(f81(a868),f332(x39012,x39013)),f156(x39011,x39012,x39014))),f332(a115,f2(a868)))) % 165.28/165.04 [3916]E(f193(f869(x39161),f332(f332(f152(x39161),x39162),x39163),f332(f332(f7(a868,f869(x39161),f869(x39161)),f139(x39161)),x39163),x39164),f332(f332(f139(x39161),x39164),f332(f332(f152(x39161),x39162),x39163))) % 165.28/165.04 [3917]P21(x39171,f874(x39172,x39171),f336(x39173,x39174,x39172,x39171),f332(f332(f42(x39172,f875(x39171,a862)),x39174),x39173)) % 165.28/165.04 [3926]E(f332(f332(f22(f875(x39261,a862)),f332(f332(f22(f875(x39261,a862)),x39262),x39263)),f332(f332(f310(x39261),x39264),f196(f875(x39261,a862)))),f332(f332(f22(f875(x39261,a862)),x39262),f332(f332(f310(x39261),x39264),x39263))) % 165.28/165.04 [3938]E(f332(f332(f191(f875(x39381,x39382),f875(x39381,x39382)),x39383),f74(x39382,x39382,x39381,x39384)),f74(x39382,x39382,x39381,f332(f332(f191(x39382,x39382),x39383),x39384))) % 165.28/165.04 [4015]E(f332(f332(f332(f191(f869(x40151),f869(x40151)),x40152),f169(x40151)),f332(f332(f332(f191(f869(x40151),f869(x40151)),x40153),f169(x40151)),x40154)),f332(f332(f332(f191(f869(x40151),f869(x40151)),f332(f332(f81(a868),x40152),x40153)),f169(x40151)),x40154)) % 165.28/165.04 [4102]P24(f332(f332(f246(f875(x41021,a862)),f332(f174(x41021),f332(f332(f160(x41021,x41022),x41023),x41024))),f332(f332(f310(x41021),x41024),f332(f174(x41021),x41022)))) % 165.28/165.04 [4138]E(f332(f332(f42(f875(x41381,a862),f875(f874(x41381,x41382),a862)),x41383),f332(f332(f7(f875(x41381,a862),f875(x41381,f875(x41382,a862)),f875(f874(x41381,x41382),a862)),f269(x41381,x41382)),x41384)),f332(f332(f269(x41381,x41382),f40(f875(x41381,a862),x41383)),x41384)) % 165.28/165.04 [4176]E(f221(x41761,x41762,x41763,f332(f74(x41762,f875(a102,f875(a102,f875(f874(a102,a102),f875(a102,f870(x41762))))),x41761,f216(x41762)),x41764)),f222(x41761,x41762,x41764,x41763)) % 165.28/165.04 [4193]E(f218(x41931,x41932,x41933,f332(f74(x41932,f875(a102,f875(a102,f875(f874(a102,a102),f875(a102,f870(f872(x41932)))))),x41931,f217(x41932)),x41934)),f219(x41931,x41932,x41934,x41933)) % 165.28/165.04 [4198]P24(f332(f67(x41981,x41982,x41983,x41984,f196(f875(x41981,a862))),x41984)) % 165.28/165.04 [4240]E(f332(f332(f42(x42401,f875(x42402,a862)),x42403),f332(f332(f7(x42401,f875(x42402,a862),f875(x42402,a862)),f332(f332(f8(x42402,f875(f875(x42402,a862),f875(x42402,a862)),x42401),f310(x42402)),x42404)),f196(f875(x42402,a862)))),f332(f311(x42401,x42402,x42404),x42403)) % 165.28/165.04 [4247]P24(f332(f332(f246(f875(x42471,a862)),f332(f263(x42472,x42471),f332(f332(f104(f875(f874(x42472,x42471),a862)),x42473),x42474))),f332(f332(f104(f875(x42471,a862)),f332(f263(x42472,x42471),x42473)),f332(f263(x42472,x42471),x42474)))) % 165.28/165.04 [4248]P24(f332(f332(f246(f875(x42481,a862)),f332(f265(x42481,x42482),f332(f332(f104(f875(f874(x42481,x42482),a862)),x42483),x42484))),f332(f332(f104(f875(x42481,a862)),f332(f265(x42481,x42482),x42483)),f332(f265(x42481,x42482),x42484)))) % 165.28/165.04 [4310]P24(f332(f332(f246(f875(f874(x43101,x43102),a862)),f332(f311(x43102,f874(x43101,x43102),f336(x43103,x43104,x43101,x43102)),f332(f332(f42(x43101,f875(x43102,a862)),x43104),x43103))),f332(f332(f269(x43101,x43102),x43104),x43103))) % 165.28/165.04 [4311]E(f332(f121(x43111,f874(x43111,x43112),x43113),f332(f332(f8(f875(x43112,f870(f874(x43111,x43112))),f870(f874(x43111,x43112)),x43111),f121(x43112,f874(x43111,x43112),x43114)),f332(f332(f8(f875(x43112,f874(x43111,x43112)),f875(x43112,f870(f874(x43111,x43112))),x43111),f332(f8(f874(x43111,x43112),f870(f874(x43111,x43112)),x43112),f127(f874(x43111,x43112)))),f267(x43111,x43112)))),f132(x43111,x43112,x43113,x43114)) % 165.28/165.04 [4351]E(f86(f874(x43511,x43512),f332(f271(x43511,x43512,a862),f332(f332(f7(x43511,f875(x43512,a862),f875(x43512,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x43512,a862),f875(x43512,a862)),x43511),f8(a862,a862,x43512)),f332(f332(f8(a862,f875(a862,a862),x43511),a330),f332(a329,x43513)))),f332(a329,x43514)))),f332(f332(f267(x43511,x43512),x43513),x43514)) % 165.28/165.04 [4352]E(f91(f874(x43521,x43522),f332(f271(x43521,x43522,a862),f332(f332(f7(x43521,f875(x43522,a862),f875(x43522,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x43522,a862),f875(x43522,a862)),x43521),f8(a862,a862,x43522)),f332(f332(f8(a862,f875(a862,a862),x43521),a330),f332(a329,x43523)))),f332(a329,x43524)))),f332(f332(f267(x43521,x43522),x43523),x43524)) % 165.28/165.04 [4423]E(f332(f332(f271(f869(x44231),f869(x44231),f874(f869(x44231),f869(x44231))),f332(f332(f18(f869(x44231),f875(f869(x44231),f874(f869(x44231),f869(x44231))),f875(f869(x44231),f874(f869(x44231),f869(x44231)))),f332(f332(f8(f875(f869(x44231),f875(f874(f869(x44231),f869(x44231)),f874(f869(x44231),f869(x44231)))),f875(f875(f869(x44231),f874(f869(x44231),f869(x44231))),f875(f869(x44231),f874(f869(x44231),f869(x44231)))),f869(x44231)),f18(f869(x44231),f874(f869(x44231),f869(x44231)),f874(f869(x44231),f869(x44231)))),f332(f332(f8(f875(f869(x44231),f874(f869(x44231),f869(x44231))),f875(f869(x44231),f875(f874(f869(x44231),f869(x44231)),f874(f869(x44231),f869(x44231)))),f869(x44231)),f332(f8(f874(f869(x44231),f869(x44231)),f875(f874(f869(x44231),f869(x44231)),f874(f869(x44231),f869(x44231))),f869(x44231)),f332(f99(f874(f869(x44231),f869(x44231))),f332(x44232,x44233)))),f332(f332(f8(f869(x44231),f875(f869(x44231),f874(f869(x44231),f869(x44231))),f869(x44231)),f267(f869(x44231),f869(x44231))),f332(f152(x44231),x44233))))),f332(f332(f7(f869(x44231),f875(f869(x44231),f869(x44231)),f875(f869(x44231),f874(f869(x44231),f869(x44231)))),f332(f332(f8(f875(f869(x44231),f874(f869(x44231),f869(x44231))),f875(f875(f869(x44231),f869(x44231)),f875(f869(x44231),f874(f869(x44231),f869(x44231)))),f869(x44231)),f8(f869(x44231),f874(f869(x44231),f869(x44231)),f869(x44231))),f267(f869(x44231),f869(x44231)))),f332(f152(x44231),x44233)))),f168(x44231,x44232,x44234)),f168(x44231,x44232,f332(f332(f152(x44231),x44233),x44234))) % 165.28/165.04 [4429]E(f332(f143(f875(x44291,f872(x44292)),f874(x44291,x44292),f332(f7(f874(x44291,x44292),f875(x44291,f872(x44292)),f875(x44291,f872(x44292))),f332(f271(x44291,x44292,f875(f875(x44291,f872(x44292)),f875(x44291,f872(x44292)))),f332(f332(f7(x44291,f875(x44292,f872(x44292)),f875(x44292,f875(f875(x44291,f872(x44292)),f875(x44291,f872(x44292))))),f332(f332(f8(f875(f872(x44292),f875(f875(x44291,f872(x44292)),f875(x44291,f872(x44292)))),f875(f875(x44292,f872(x44292)),f875(x44292,f875(f875(x44291,f872(x44292)),f875(x44291,f872(x44292))))),x44291),f8(f872(x44292),f875(f875(x44291,f872(x44292)),f875(x44291,f872(x44292))),x44292)),f332(f332(f8(f875(f875(x44291,f872(x44292)),f875(f872(x44292),f875(x44291,f872(x44292)))),f875(f872(x44292),f875(f875(x44291,f872(x44292)),f875(x44291,f872(x44292)))),x44291),f7(f875(x44291,f872(x44292)),f872(x44292),f875(x44291,f872(x44292)))),f332(f7(f875(x44291,f872(x44292)),x44291,f875(f872(x44292),f875(x44291,f872(x44292)))),f73(x44291,f872(x44292)))))),f208(x44292)))),x44293),f332(f170(f874(x44291,x44292)),x44294)),f187(x44291,x44292,x44293,f332(f180(x44291,x44292),x44294))) % 165.28/165.04 [3520]E(f332(f197(f867(x35201)),f332(f332(f332(f93(x35201),x35202),x35203),x35204)),f2(a868)) % 165.28/165.04 [3642]E(f332(f332(f177(x36421),x36422),f332(f332(f177(x36421),x36423),x36424)),f332(f332(f177(x36421),f332(f332(f244(a868),x36422),x36423)),x36424)) % 165.28/165.04 [3643]E(f332(f332(f139(x36431),x36432),f332(f332(f139(x36431),x36433),x36434)),f332(f332(f139(x36431),f332(f332(f81(a868),x36432),x36433)),x36434)) % 165.28/165.04 [3655]E(f332(f332(f135(x36551),f332(f332(f152(x36551),x36552),x36553)),x36554),f332(f332(f152(x36551),x36552),f332(f332(f135(x36551),x36553),x36554))) % 165.28/165.04 [3656]E(f332(f332(f135(x36561),f332(f332(f135(x36561),x36562),x36563)),x36564),f332(f332(f135(x36561),x36562),f332(f332(f135(x36561),x36563),x36564))) % 165.28/165.04 [3739]E(f332(f332(f166(x37391),f332(f332(f152(x37391),x37392),x37393)),x37394),f193(x37391,x37392,f332(f166(x37391),x37393),x37394)) % 165.28/165.04 [3748]E(f332(f332(f191(x37481,x37481),x37482),f332(f332(f191(x37481,x37481),x37483),x37484)),f332(f332(f191(x37481,x37481),f332(f332(f82(a868),x37483),x37482)),x37484)) % 165.28/165.04 [3777]E(f332(f332(f113(f875(x37771,a862)),x37772),f332(f332(f310(x37771),x37773),x37774)),f332(f332(f310(x37771),x37773),f332(f332(f113(f875(x37771,a862)),x37772),x37774))) % 165.28/165.04 [3792]E(f332(f332(f332(f191(x37921,x37921),x37922),x37923),f332(x37923,x37924)),f332(x37923,f332(f332(f332(f191(x37921,x37921),x37922),x37923),x37924))) % 165.28/165.04 [3800]E(f332(f332(f289(x38001,x38002,x38003),f196(f875(f874(x38001,x38002),a862))),x38004),f196(f875(f874(x38001,x38003),a862))) % 165.28/165.04 [3816]E(f332(f332(f113(f875(x38161,a862)),f332(f332(f310(x38161),x38162),x38163)),x38164),f332(f332(f310(x38161),x38162),f332(f332(f113(f875(x38161,a862)),x38163),x38164))) % 165.28/165.04 [3836]E(f187(x38361,x38362,f332(f180(x38361,x38362),x38363),f332(f180(x38361,x38362),x38364)),f332(f180(x38361,x38362),f332(f332(f135(f874(x38361,x38362)),x38364),x38363))) % 165.28/165.04 [3837]E(f332(f38(f874(x38371,x38372)),f332(f332(f269(x38371,x38372),x38373),f332(f16(f875(x38372,a862),x38371),x38374))),f332(f332(f82(a868),f332(f38(x38371),x38373)),f332(f38(x38372),x38374))) % 165.28/165.04 [3844]E(f332(f332(f104(f875(x38441,a862)),f332(f332(f310(x38441),x38442),x38443)),f332(f332(f310(x38441),x38442),x38444)),f332(f332(f310(x38441),x38442),f332(f332(f104(f875(x38441,a862)),x38443),x38444))) % 165.28/165.04 [3859]E(f332(f332(f113(f875(x38591,a862)),x38592),f332(f332(f113(f875(x38591,a862)),x38593),x38594)),f332(f332(f113(f875(x38591,a862)),x38593),f332(f332(f113(f875(x38591,a862)),x38592),x38594))) % 165.28/165.04 [3860]E(f332(f332(f104(f875(x38601,a862)),x38602),f332(f332(f104(f875(x38601,a862)),x38603),x38604)),f332(f332(f104(f875(x38601,a862)),x38603),f332(f332(f104(f875(x38601,a862)),x38602),x38604))) % 165.28/165.04 [3869]E(f65(x38691,x38692,f332(f332(f8(x38692,f875(x38692,x38692),x38691),x38693),x38694)),f332(f66(x38692,x38691,x38693),x38694)) % 165.28/165.04 [3879]E(f182(x38791,f332(f332(f155(f869(x38792),f869(x38791)),f332(f155(x38792,x38791),x38793)),x38794)),f332(f332(f155(f869(x38792),f869(x38791)),f332(f155(x38792,x38791),x38793)),f182(x38792,x38794))) % 165.28/165.04 [3897]E(f332(f143(f869(x38971),f869(x38971),f135(x38971),f116(x38971)),f332(f332(f155(x38972,f869(x38971)),x38973),x38974)),f165(x38972,x38971,x38973,x38974)) % 165.28/165.04 [3900]E(f190(x39001,x39002,x39003,f332(f80(f875(x39001,a862)),f332(f332(f310(x39001),x39004),f196(f875(x39001,a862))))),f332(f332(f332(f73(x39001,f872(x39002)),x39003),x39004),f209(x39002))) % 165.28/165.04 [3943]E(f332(f332(f332(f73(x39431,f872(x39432)),f332(f180(x39431,x39432),x39433)),f332(f266(x39431,x39432),x39434)),f332(f208(x39432),f332(f270(x39431,x39432),x39434))),f332(f180(x39431,x39432),f332(f332(f152(f874(x39431,x39432)),x39434),x39433))) % 165.28/165.04 [3960]E(f332(f74(x39601,x39601,x39601,f332(f332(f191(x39601,x39601),x39602),x39603)),f332(f332(f191(x39601,x39601),x39604),x39603)),f332(f332(f191(x39601,x39601),f332(f332(f81(a868),x39602),x39604)),x39603)) % 165.28/165.04 [3984]E(f332(f332(f104(f875(x39841,a862)),f332(f332(f113(f875(x39841,a862)),x39842),x39843)),f332(f332(f113(f875(x39841,a862)),x39842),x39844)),f332(f332(f113(f875(x39841,a862)),x39842),f332(f332(f104(f875(x39841,a862)),x39843),x39844))) % 165.28/165.04 [3985]E(f332(f332(f104(f875(x39851,a862)),f332(f332(f22(f875(x39851,a862)),x39852),x39853)),f332(f332(f22(f875(x39851,a862)),x39852),x39854)),f332(f332(f22(f875(x39851,a862)),x39852),f332(f332(f113(f875(x39851,a862)),x39853),x39854))) % 165.28/165.04 [3986]E(f332(f332(f113(f875(x39861,a862)),f332(f332(f22(f875(x39861,a862)),x39862),x39863)),f332(f332(f22(f875(x39861,a862)),x39862),x39864)),f332(f332(f22(f875(x39861,a862)),x39862),f332(f332(f104(f875(x39861,a862)),x39863),x39864))) % 165.28/165.04 [3987]E(f332(f332(f113(f875(x39871,a862)),f332(f332(f104(f875(x39871,a862)),x39872),x39873)),f332(f332(f104(f875(x39871,a862)),x39872),x39874)),f332(f332(f104(f875(x39871,a862)),x39872),f332(f332(f113(f875(x39871,a862)),x39873),x39874))) % 165.28/165.04 [3988]E(f332(f332(f22(f875(x39881,a862)),f332(f332(f104(f875(x39881,a862)),x39882),x39883)),f332(f332(f104(f875(x39881,a862)),x39882),x39884)),f332(f332(f104(f875(x39881,a862)),x39882),f332(f332(f22(f875(x39881,a862)),x39883),x39884))) % 165.28/165.04 [3994]E(f332(f38(f874(x39941,x39942)),f332(f332(f269(x39941,x39942),f332(f332(f310(x39941),x39943),f196(f875(x39941,a862)))),f332(f16(f875(x39942,a862),x39941),x39944))),f332(f38(x39942),x39944)) % 165.28/165.04 [4031]E(f332(f332(f43(x40311,f875(x40312,a862)),x40313),f332(f332(f8(f875(x40312,a862),f875(x40312,a862),x40311),f80(f875(x40312,a862))),x40314)),f332(f80(f875(x40312,a862)),f332(f332(f42(x40311,f875(x40312,a862)),x40313),x40314))) % 165.28/165.04 [4032]E(f332(f332(f42(x40321,f875(x40322,a862)),x40323),f332(f332(f8(f875(x40322,a862),f875(x40322,a862),x40321),f80(f875(x40322,a862))),x40324)),f332(f80(f875(x40322,a862)),f332(f332(f43(x40321,f875(x40322,a862)),x40323),x40324))) % 165.28/165.04 [4046]E(f332(f332(f289(x40461,x40461,x40461),f332(f332(f191(f874(x40461,x40461),a862),x40462),x40463)),f332(f332(f191(f874(x40461,x40461),a862),x40464),x40463)),f332(f332(f191(f874(x40461,x40461),a862),f332(f332(f81(a868),x40462),x40464)),x40463)) % 165.28/165.04 [4077]E(f332(f332(f43(x40771,f875(f875(x40772,a862),a862)),x40773),f332(f332(f8(f875(x40772,a862),f875(f875(x40772,a862),a862),x40771),f309(x40772)),x40774)),f332(f309(x40772),f332(f332(f43(x40771,f875(x40772,a862)),x40773),x40774))) % 165.28/165.04 [4106]E(f332(f332(f42(f875(x41061,a862),f875(x41062,a862)),x41063),f332(f332(f7(f875(x41061,a862),f875(x41061,f875(x41062,a862)),f875(x41062,a862)),f42(x41061,f875(x41062,a862))),x41064)),f332(f332(f42(x41061,f875(x41062,a862)),f40(f875(x41061,a862),x41063)),x41064)) % 165.28/165.04 [4107]E(f332(f332(f43(f875(x41071,a862),f875(x41072,a862)),x41073),f332(f332(f7(f875(x41071,a862),f875(x41071,f875(x41072,a862)),f875(x41072,a862)),f43(x41071,f875(x41072,a862))),x41074)),f332(f332(f43(x41071,f875(x41072,a862)),f40(f875(x41071,a862),x41073)),x41074)) % 165.28/165.04 [4112]E(f332(f332(f155(x41121,x41122),x41123),f332(f143(f869(x41121),f869(x41121),f135(x41121),f116(x41121)),x41124)),f332(f143(f869(x41122),f869(x41122),f135(x41122),f116(x41122)),f332(f332(f155(f869(x41121),f869(x41122)),f332(f155(x41121,x41122),x41123)),x41124))) % 165.28/165.04 [4116]E(f193(f869(x41161),f116(x41161),f332(f332(f8(f869(x41161),f869(x41161),a868),f332(f152(x41161),x41162)),f332(f332(f7(a868,f869(x41161),f869(x41161)),f177(x41161)),x41163)),x41164),f332(f332(f177(x41161),x41164),f332(f332(f152(x41161),x41162),x41163))) % 165.28/165.04 [4158]P24(f332(f332(f246(f875(x41581,a862)),f332(f311(x41582,x41581,x41583),f332(f312(x41582,x41581,x41583),x41584))),x41584)) % 165.28/165.04 [4161]E(f332(f311(f874(x41611,x41612),f874(x41612,x41611),f332(f271(x41611,x41612,f874(x41612,x41611)),f332(f7(x41612,x41611,f874(x41612,x41611)),f267(x41612,x41611)))),f332(f332(f269(x41611,x41612),x41613),f332(f16(f875(x41612,a862),x41611),x41614))),f332(f332(f269(x41612,x41611),x41614),f332(f16(f875(x41611,a862),x41612),x41613))) % 165.28/165.04 [4170]E(f332(f332(f42(x41701,f875(x41702,a862)),x41703),f332(f332(f8(f875(x41701,a862),f875(x41702,a862),x41701),f312(x41702,x41701,x41704)),f332(f332(f7(x41701,f875(x41701,a862),f875(x41701,a862)),f310(x41701)),f196(f875(x41701,a862))))),f332(f312(x41702,x41701,x41704),x41703)) % 165.28/165.04 [4171]E(f332(f332(f42(x41711,f875(x41712,a862)),x41713),f332(f332(f8(f875(x41711,a862),f875(x41712,a862),x41711),f286(x41711,x41712,x41714)),f332(f332(f7(x41711,f875(x41711,a862),f875(x41711,a862)),f310(x41711)),f196(f875(x41711,a862))))),f332(f286(x41711,x41712,x41714),x41713)) % 165.28/165.04 [4262]E(f332(f332(f113(f875(x42621,a862)),f332(f332(f113(f875(x42621,a862)),f332(f332(f104(f875(x42621,a862)),x42622),x42623)),f332(f332(f104(f875(x42621,a862)),x42623),x42624))),f332(f332(f104(f875(x42621,a862)),x42624),x42622)),f332(f332(f104(f875(x42621,a862)),f332(f332(f104(f875(x42621,a862)),f332(f332(f113(f875(x42621,a862)),x42622),x42623)),f332(f332(f113(f875(x42621,a862)),x42623),x42624))),f332(f332(f113(f875(x42621,a862)),x42624),x42622))) % 165.28/165.04 [4324]E(f332(f143(f869(x43241),f869(x43241),f135(x43241),f116(x43241)),f332(f332(f155(x43242,f869(x43241)),f332(f332(f7(x43242,f869(x43241),f869(x43241)),f332(f332(f8(x43241,f875(f869(x43241),f869(x43241)),x43242),f152(x43241)),x43243)),f116(x43241))),x43244)),f332(f332(f155(x43242,x43241),x43243),x43244)) % 165.28/165.04 [4335]E(f332(f332(f87(a1,x43351),f332(f106(a1),f332(f332(f81(a1),x43352),a100))),f332(f332(f18(a1,x43351,x43351),f332(f332(f7(a1,x43351,f875(x43351,x43351)),f332(f332(f8(a862,f875(x43351,f875(x43351,x43351)),a1),f99(x43351)),a201)),x43353)),f332(f332(f8(a868,x43351,a1),x43354),a107))),f193(x43351,x43353,x43354,f332(f106(a868),x43352))) % 165.28/165.04 [4549]~P24(f332(f332(f196(f875(x45491,f875(x45492,a862))),x45493),x45494)) % 165.28/165.04 [3803]E(f332(f332(f166(x38031),f332(f332(f135(x38031),x38032),x38033)),f332(f332(f81(a868),f332(f197(f869(x38031)),x38032)),x38034)),f332(f332(f166(x38031),x38033),x38034)) % 165.28/165.04 [3809]E(f332(f332(f139(x38091),x38092),f332(f332(f177(x38091),f332(f332(f81(a868),x38093),x38092)),x38094)),f332(f332(f177(x38091),x38093),f332(f332(f139(x38091),x38092),x38094))) % 165.28/165.04 [3914]E(f332(f332(f113(f875(x39141,a862)),f332(f263(x39142,x39141),x39143)),f332(f263(x39142,x39141),x39144)),f332(f263(x39142,x39141),f332(f332(f113(f875(f874(x39142,x39141),a862)),x39143),x39144))) % 165.28/165.04 [3915]E(f332(f332(f113(f875(x39151,a862)),f332(f265(x39151,x39152),x39153)),f332(f265(x39151,x39152),x39154)),f332(f265(x39151,x39152),f332(f332(f113(f875(f874(x39151,x39152),a862)),x39153),x39154))) % 165.28/165.04 [3920]E(f332(f332(f113(f875(x39201,a862)),f332(f332(f113(f875(x39201,a862)),x39202),x39203)),x39204),f332(f332(f113(f875(x39201,a862)),x39202),f332(f332(f113(f875(x39201,a862)),x39203),x39204))) % 165.28/165.04 [3921]E(f332(f332(f22(f875(x39211,a862)),f332(f332(f104(f875(x39211,a862)),x39212),x39213)),x39214),f332(f332(f104(f875(x39211,a862)),x39212),f332(f332(f22(f875(x39211,a862)),x39213),x39214))) % 165.28/165.04 [3922]E(f332(f332(f104(f875(x39221,a862)),f332(f332(f104(f875(x39221,a862)),x39222),x39223)),x39224),f332(f332(f104(f875(x39221,a862)),x39222),f332(f332(f104(f875(x39221,a862)),x39223),x39224))) % 165.28/165.04 [3962]E(f332(f332(f113(f875(f874(x39621,x39622),a862)),f332(f287(x39622,x39621),x39623)),f332(f287(x39622,x39621),x39624)),f332(f287(x39622,x39621),f332(f332(f113(f875(f874(x39622,x39621),a862)),x39623),x39624))) % 165.28/165.04 [3963]E(f332(f332(f104(f875(f874(x39631,x39632),a862)),f332(f287(x39632,x39631),x39633)),f332(f287(x39632,x39631),x39634)),f332(f287(x39632,x39631),f332(f332(f104(f875(f874(x39632,x39631),a862)),x39633),x39634))) % 165.28/165.04 [3977]E(f332(f332(f113(f875(x39771,f875(x39772,a862))),f256(x39772,x39771,x39773)),f256(x39772,x39771,x39774)),f256(x39772,x39771,f332(f332(f113(f875(x39772,f875(x39771,a862))),x39773),x39774))) % 165.28/165.04 [3978]E(f332(f332(f104(f875(x39781,f875(x39782,a862))),f256(x39782,x39781,x39783)),f256(x39782,x39781,x39784)),f256(x39782,x39781,f332(f332(f104(f875(x39782,f875(x39781,a862))),x39783),x39784))) % 165.28/165.04 [4035]E(f332(f332(f104(f875(x40351,a862)),f332(f332(f113(f875(x40351,a862)),x40352),x40353)),f332(f332(f113(f875(x40351,a862)),x40354),x40353)),f332(f332(f113(f875(x40351,a862)),f332(f332(f104(f875(x40351,a862)),x40352),x40354)),x40353)) % 165.28/165.04 [4036]E(f332(f332(f113(f875(x40361,a862)),f332(f332(f22(f875(x40361,a862)),x40362),x40363)),f332(f332(f22(f875(x40361,a862)),x40364),x40363)),f332(f332(f22(f875(x40361,a862)),f332(f332(f113(f875(x40361,a862)),x40362),x40364)),x40363)) % 165.28/165.04 [4037]E(f332(f332(f113(f875(x40371,a862)),f332(f332(f104(f875(x40371,a862)),x40372),x40373)),f332(f332(f104(f875(x40371,a862)),x40374),x40373)),f332(f332(f104(f875(x40371,a862)),f332(f332(f113(f875(x40371,a862)),x40372),x40374)),x40373)) % 165.28/165.04 [4038]E(f332(f332(f22(f875(x40381,a862)),f332(f332(f104(f875(x40381,a862)),x40382),x40383)),f332(f332(f104(f875(x40381,a862)),x40384),x40383)),f332(f332(f104(f875(x40381,a862)),f332(f332(f22(f875(x40381,a862)),x40382),x40384)),x40383)) % 165.28/165.04 [4039]E(f332(f332(f22(f875(x40391,a862)),f332(f332(f104(f875(x40391,a862)),x40392),x40393)),f332(f332(f104(f875(x40391,a862)),x40394),x40393)),f332(f332(f22(f875(x40391,a862)),f332(f332(f104(f875(x40391,a862)),x40392),x40393)),x40394)) % 165.28/165.04 [4049]E(f332(f332(f22(f875(x40491,a862)),f332(f332(f22(f875(x40491,a862)),x40492),f332(f332(f310(x40491),x40493),f196(f875(x40491,a862))))),x40494),f332(f332(f22(f875(x40491,a862)),x40492),f332(f332(f310(x40491),x40493),x40494))) % 165.28/165.04 [4103]E(f332(f332(f113(f875(x41031,a862)),f332(f332(f310(x41031),x41032),f332(f332(f310(x41031),x41033),f196(f875(x41031,a862))))),f332(f285(x41031),x41034)),f332(f285(x41031),f332(f332(f310(f874(x41031,x41031)),f332(f332(f267(x41031,x41031),x41032),x41033)),x41034))) % 165.28/165.04 [4133]E(f332(f332(f42(a868,f875(x41331,a862)),f332(f301(a868),x41332)),f332(f332(f8(a868,f875(x41331,a862),a868),x41333),f332(f332(f7(a868,a868,a868),f81(a868)),x41334))),f332(f332(f42(a868,f875(x41331,a862)),f303(a868,x41334,f332(f332(f81(a868),x41332),x41334))),x41333)) % 165.28/165.04 [4134]E(f176(x41341,f332(f286(x41341,x41341,x41342),f332(f332(f310(x41341),x41343),f196(f875(x41341,a862)))),f332(f286(f869(x41341),f869(x41341),f159(x41341,x41342)),f332(f332(f310(f869(x41341)),x41344),f196(f875(f869(x41341),a862))))),f332(f286(f869(x41341),f869(x41341),f159(x41341,x41342)),f332(f332(f310(f869(x41341)),f332(f332(f152(x41341),x41343),x41344)),f196(f875(f869(x41341),a862))))) % 165.28/165.04 [4196]E(f332(f180(x41961,x41962),f332(f332(f155(x41961,f874(x41961,x41962)),f332(f332(f18(x41961,x41962,f874(x41961,x41962)),f267(x41961,x41962)),x41963)),x41964)),f190(x41961,x41962,f332(f74(x41962,f872(x41962),x41961,f208(x41962)),x41963),f332(f174(x41961),x41964))) % 165.28/165.04 [4201]E(f332(f252(x42011),f332(f332(f7(x42011,f875(x42012,a862),a862),f332(f332(f8(x42012,f875(f875(x42012,a862),a862),x42011),f334(x42012)),x42013)),x42014)),f332(f312(x42011,x42012,x42013),x42014)) % 165.28/165.04 [4295]E(f332(f252(x42951),f332(f332(f7(x42951,f875(f874(x42952,x42951),a862),a862),f332(f332(f8(f874(x42952,x42951),f875(f875(f874(x42952,x42951),a862),a862),x42951),f334(f874(x42952,x42951))),f332(f267(x42952,x42951),x42953))),x42954)),f332(f286(x42952,x42951,x42954),f332(f332(f310(x42952),x42953),f196(f875(x42952,a862))))) % 165.28/165.04 [4309]E(f332(f332(f155(f874(x43091,a868),x43091),f266(x43091,a868)),f332(f137(f874(x43091,a868),f332(f332(f8(a868,a862,f874(x43091,a868)),x43092),f332(f332(f8(a868,a868,f874(x43091,a868)),a115),f270(x43091,a868)))),f332(f332(f184(x43091,a868),x43093),x43094))),f332(f332(f155(f874(x43091,a868),x43091),f266(x43091,a868)),f332(f137(f874(x43091,a868),f332(f332(f8(a868,a862,f874(x43091,a868)),x43092),f270(x43091,a868))),f332(f332(f184(x43091,a868),x43093),f332(f332(f155(a868,a868),a115),x43094))))) % 165.28/165.04 [4317]P24(f332(f332(f246(f875(f875(x43171,a862),a862)),f332(f332(f42(x43172,f875(f875(x43171,a862),a862)),x43173),f332(f332(f8(f875(x43171,a862),f875(f875(x43171,a862),a862),x43172),f309(x43171)),x43174))),f332(f309(x43171),f332(f332(f42(x43172,f875(x43171,a862)),x43173),x43174)))) % 165.28/165.04 [4359]E(f332(f332(f87(a1,x43591),f332(f106(a1),f332(f332(f81(a1),x43592),a100))),f332(f332(f18(a1,x43591,x43591),f332(f332(f7(a1,x43591,f875(x43591,x43591)),f332(f332(f8(a862,f875(x43591,f875(x43591,x43591)),a1),f99(x43591)),a201)),x43593)),f332(f332(f18(a1,x43591,x43591),f332(f332(f8(a868,f875(x43591,x43591),a1),x43594),a107)),f332(f332(f8(a868,x43591,a1),f192(x43591,x43593,x43594)),a107)))),f332(f192(x43591,x43593,x43594),f332(f106(a868),x43592))) % 165.28/165.04 [4362]E(f332(f332(f155(x43621,x43622),f332(f74(f872(x43622),x43622,x43621,f243(x43622)),x43623)),f332(f137(x43621,f332(f332(f8(a862,a862,x43621),a327),f332(f332(f7(x43621,f872(x43622),a862),f332(f332(f8(f872(x43622),f875(f872(x43622),a862),x43621),a329),x43623)),f209(x43622)))),x43624)),f164(x43621,x43622,x43623,x43624)) % 165.28/165.04 [4385]E(f332(f252(f874(x43851,x43852)),f332(f271(x43851,x43852,a862),f332(f332(f7(x43851,f875(x43852,a862),f875(x43852,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x43852,a862),f875(x43852,a862)),x43851),f8(a862,a862,x43852)),f332(f332(f8(a862,f875(a862,a862),x43851),a330),f332(f332(f7(x43851,f875(x43851,a862),a862),f334(x43851)),x43853)))),f332(f332(f7(x43852,f875(x43852,a862),a862),f334(x43852)),x43854)))),f234(x43851,x43852,x43853,x43854)) % 165.28/165.04 [4418]E(f332(f332(f42(x44181,f875(f874(x44181,x44182),a862)),x44183),f332(f332(f18(x44181,f875(x44182,f875(f874(x44181,x44182),a862)),f875(f874(x44181,x44182),a862)),f332(f332(f8(f875(x44182,a862),f875(f875(x44182,f875(f874(x44181,x44182),a862)),f875(f874(x44181,x44182),a862)),x44181),f42(x44182,f875(f874(x44181,x44182),a862))),x44184)),f332(f332(f7(x44181,f875(f874(x44181,x44182),a862),f875(x44182,f875(f874(x44181,x44182),a862))),f332(f332(f8(f875(x44182,f875(f875(f874(x44181,x44182),a862),f875(f874(x44181,x44182),a862))),f875(f875(f874(x44181,x44182),a862),f875(x44182,f875(f874(x44181,x44182),a862))),x44181),f7(x44182,f875(f874(x44181,x44182),a862),f875(f874(x44181,x44182),a862))),f332(f332(f8(f875(x44182,f874(x44181,x44182)),f875(x44182,f875(f875(f874(x44181,x44182),a862),f875(f874(x44181,x44182),a862))),x44181),f332(f8(f874(x44181,x44182),f875(f875(f874(x44181,x44182),a862),f875(f874(x44181,x44182),a862)),x44182),f310(f874(x44181,x44182)))),f267(x44181,x44182)))),f196(f875(f874(x44181,x44182),a862))))),f332(f332(f269(x44181,x44182),x44183),x44184)) % 165.28/165.04 [3972]E(f332(f332(f135(x39721),f332(f332(f177(x39721),x39722),x39723)),f332(f332(f177(x39721),f332(f332(f22(a868),x39722),f332(f197(f869(x39721)),x39723))),x39724)),f332(f332(f177(x39721),x39722),f332(f332(f135(x39721),x39723),x39724))) % 165.28/165.04 [3973]E(f332(f332(f135(x39731),f332(f332(f139(x39731),x39732),x39733)),f332(f332(f139(x39731),f332(f332(f22(a868),x39732),f332(f197(f869(x39731)),x39733))),x39734)),f332(f332(f139(x39731),x39732),f332(f332(f135(x39731),x39733),x39734))) % 165.28/165.04 [4024]E(f332(f332(f81(a868),f332(f332(f82(a868),x40241),x40242)),f332(f332(f81(a868),f332(f332(f82(a868),x40243),x40242)),x40244)),f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f81(a868),x40241),x40243)),x40242)),x40244)) % 165.28/165.04 [4226]P24(f332(f332(f246(f875(x42261,a862)),f332(f332(f22(f875(x42261,a862)),f332(f263(x42262,x42261),x42263)),f332(f263(x42262,x42261),x42264))),f332(f263(x42262,x42261),f332(f332(f22(f875(f874(x42262,x42261),a862)),x42263),x42264)))) % 165.28/165.04 [4227]P24(f332(f332(f246(f875(x42271,a862)),f332(f332(f22(f875(x42271,a862)),f332(f265(x42271,x42272),x42273)),f332(f265(x42271,x42272),x42274))),f332(f265(x42271,x42272),f332(f332(f22(f875(f874(x42271,x42272),a862)),x42273),x42274)))) % 165.28/165.04 [4337]E(f332(f332(f81(a1),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x43371),x43372)),f196(f875(f874(a868,a868),a862)))))),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x43373),x43374)),f196(f875(f874(a868,a868),a862)))))),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),f332(f332(f81(a868),x43371),x43373)),f332(f332(f81(a868),x43372),x43374))),f196(f875(f874(a868,a868),a862)))))) % 165.28/165.04 [4380]E(f332(f332(f82(a1),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x43801),x43802)),f196(f875(f874(a868,a868),a862)))))),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x43803),x43804)),f196(f875(f874(a868,a868),a862)))))),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),f332(f332(f81(a868),f332(f332(f82(a868),x43801),x43803)),f332(f332(f82(a868),x43802),x43804))),f332(f332(f81(a868),f332(f332(f82(a868),x43801),x43804)),f332(f332(f82(a868),x43802),x43803)))),f196(f875(f874(a868,a868),a862)))))) % 165.28/165.04 [4400]E(f332(f252(x44001),f332(f332(f8(f875(x44002,a862),a862,x44001),f89(x44002)),f332(f332(f8(f875(x44002,a862),f875(x44002,a862),x44001),f332(f18(x44002,a862,a862),f332(f332(f8(a862,f875(a862,a862),x44002),a335),f332(f332(f7(x44002,f875(x44002,a862),a862),f334(x44002)),x44003)))),f332(f332(f7(x44001,f875(x44002,f875(x44001,a862)),f875(x44002,a862)),f332(f332(f8(f875(f875(x44001,a862),a862),f875(f875(x44002,f875(x44001,a862)),f875(x44002,a862)),x44001),f8(f875(x44001,a862),a862,x44002)),f334(x44001))),x44004)))),f332(f332(f43(x44002,f875(x44001,a862)),x44003),x44004)) % 165.28/165.04 [4433]E(f332(f332(f289(x44331,x44331,x44331),f332(f332(f310(f874(x44331,x44331)),f332(f332(f267(x44331,x44331),x44332),x44333)),x44334)),f308(x44331,f332(f332(f310(f874(x44331,x44331)),f332(f332(f267(x44331,x44331),x44332),x44333)),x44334))),f332(f332(f113(f875(f874(x44331,x44331),a862)),f332(f332(f289(x44331,x44331,x44331),x44334),f308(x44331,x44334))),f332(f252(f874(x44331,x44331)),f332(f271(x44331,x44331,a862),f332(f332(f7(x44331,f875(x44331,a862),f875(x44331,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x44331,a862),f875(x44331,a862)),x44331),f8(a862,a862,x44331)),f332(f332(f8(a862,f875(a862,a862),x44331),a330),f332(f332(f7(x44331,f875(f874(x44331,x44331),a862),a862),f332(f332(f8(f874(x44331,x44331),f875(f875(f874(x44331,x44331),a862),a862),x44331),f334(f874(x44331,x44331))),f332(f332(f7(x44331,x44331,f874(x44331,x44331)),f267(x44331,x44331)),x44332))),f308(x44331,x44334))))),f332(f332(f7(x44331,f875(f874(x44331,x44331),a862),a862),f332(f332(f8(f874(x44331,x44331),f875(f875(f874(x44331,x44331),a862),a862),x44331),f334(f874(x44331,x44331))),f332(f267(x44331,x44331),x44333))),f308(x44331,x44334))))))) % 165.28/165.04 [4228]E(f332(f137(x42281,f332(f332(f18(x42281,a862,a862),f332(f332(f8(a862,f875(a862,a862),x42281),a330),x42282)),x42283)),x42284),f332(f137(x42281,x42283),f332(f137(x42281,x42282),x42284))) % 165.28/165.04 [4331]E(f332(f332(f135(x43311),f332(f332(f332(f99(f869(x43311)),f332(f332(f334(a868),f2(a868)),x43312)),f332(f332(f152(x43311),x43313),f116(x43311))),f116(x43311))),f178(x43311,x43314,f332(f252(a868),f332(f332(f7(a868,f875(a868,a862),a862),f332(f332(f8(a868,f875(f875(a868,a862),a862),a868),f334(a868)),a115)),x43312)))),f178(x43311,f332(f332(f152(x43311),x43313),x43314),x43312)) % 165.28/165.04 [4427]E(f332(f252(f874(x44271,x44272)),f332(f332(f8(f875(a868,a862),a862,f874(x44271,x44272)),f88(a868)),f332(f332(f7(f874(x44271,x44272),f875(a868,a862),f875(a868,a862)),f332(f332(f8(f875(a868,f875(a862,a862)),f875(f875(a868,a862),f875(a868,a862)),f874(x44271,x44272)),f18(a868,a862,a862)),f332(f332(f8(f875(a868,a862),f875(a868,f875(a862,a862)),f874(x44271,x44272)),f332(f8(a862,f875(a862,a862),a868),a330)),f332(f332(f7(f874(x44271,x44272),f875(a868,f874(x44271,x44272)),f875(a868,a862)),f332(f332(f8(f875(f874(x44271,x44272),a862),f875(f875(a868,f874(x44271,x44272)),f875(a868,a862)),f874(x44271,x44272)),f8(f874(x44271,x44272),a862,a868)),a329)),f332(f332(f18(a868,x44272,f874(x44271,x44272)),f332(f332(f8(x44271,f875(x44272,f874(x44271,x44272)),a868),f267(x44271,x44272)),f332(f166(x44271),x44273))),f332(f166(x44272),x44274)))))),f332(f332(f7(a868,a868,a862),f247(a868)),f332(f332(f244(a868),f332(f197(f869(x44271)),x44273)),f332(f197(f869(x44272)),x44274)))))),f332(f174(f874(x44271,x44272)),f332(f332(f184(x44271,x44272),x44273),x44274))) % 165.28/165.04 [4350]E(f332(f252(f874(x43501,x43502)),f332(f271(x43501,x43502,a862),f332(f332(f7(x43501,f875(x43502,a862),f875(x43502,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x43502,a862),f875(x43502,a862)),x43501),f8(a862,a862,x43502)),f332(f332(f8(a862,f875(a862,a862),x43501),a330),x43503))),x43504))),f332(f332(f269(x43501,x43502),f332(f252(x43501),x43503)),f332(f16(f875(x43502,a862),x43501),f332(f252(x43502),x43504)))) % 165.28/165.04 [4353]E(f332(f252(f874(x43531,x43532)),f332(f271(x43531,x43532,a862),f332(f332(f18(x43531,f875(x43532,a862),f875(x43532,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x43532,a862),f875(x43532,a862)),x43531),f8(a862,a862,x43532)),f332(f332(f8(a862,f875(a862,a862),x43531),a330),x43533))),x43534))),f332(f332(f269(x43531,x43532),f332(f252(x43531),x43533)),f332(f332(f8(f875(x43532,a862),f875(x43532,a862),x43531),f252(x43532)),x43534))) % 165.28/165.04 [4369]E(f332(f252(x43691),f332(f332(f8(f875(x43692,a862),a862,x43691),f89(x43692)),f332(f332(f8(f875(x43692,a862),f875(x43692,a862),x43691),f332(f18(x43692,a862,a862),f332(f332(f8(a862,f875(a862,a862),x43692),a335),f332(f332(f7(x43692,f875(x43692,a862),a862),f334(x43692)),x43693)))),x43694))),f332(f332(f43(x43692,f875(x43691,a862)),x43693),f332(f332(f8(f875(x43691,a862),f875(x43691,a862),x43692),f252(x43691)),f332(f7(x43691,x43692,a862),x43694)))) % 165.28/165.04 [4413]E(f332(f332(f155(f874(x44131,a868),x44131),f266(x44131,a868)),f332(f137(f874(x44131,a868),f332(f332(f7(f874(x44131,a868),f875(a868,a862),a862),f332(f332(f8(a868,f875(f875(a868,a862),a862),f874(x44131,a868)),f334(a868)),f270(x44131,a868))),x44132)),f332(f332(f184(x44131,a868),x44133),f140(a868,f332(f302(a868,x44134),f332(f332(f81(a868),x44134),f332(f197(f869(x44131)),x44133))))))),f332(f332(f155(f874(x44131,a868),x44131),f266(x44131,a868)),f332(f137(f874(x44131,a868),f332(f332(f7(f874(x44131,a868),f875(a868,a862),a862),f332(f332(f8(a868,f875(f875(a868,a862),a862),f874(x44131,a868)),f334(a868)),f332(f332(f7(f874(x44131,a868),a868,a868),f332(f332(f8(a868,f875(a868,a868),f874(x44131,a868)),f81(a868)),f270(x44131,a868))),x44134))),x44132)),f332(f332(f184(x44131,a868),x44133),f140(a868,f332(f302(a868,f2(a868)),f332(f197(f869(x44131)),x44133))))))) % 165.28/165.04 [4414]E(f332(a115,f332(f332(f245(a868),f332(f197(f869(x44141)),x44142)),f332(f143(a868,f869(x44143),f332(f7(f869(x44143),a868,a868),f332(f332(f8(a868,f875(a868,a868),f869(x44143)),f245(a868)),f332(f332(f7(f869(x44143),a868,a868),f332(f332(f8(a868,f875(a868,a868),f869(x44143)),f22(a868)),f197(f869(x44143)))),f332(a115,f2(a868))))),f2(a868)),f332(f170(f869(x44143)),f332(f137(f869(x44143),f332(f332(f8(a862,a862,f869(x44143)),a327),f332(f332(f7(f869(x44143),f869(x44143),a862),a329),f116(x44143)))),x44144))))),f332(f332(f245(a868),f332(a115,f332(f197(f869(x44141)),x44142))),f332(f143(a868,f869(x44143),f332(f7(f869(x44143),a868,a868),f332(f332(f8(a868,f875(a868,a868),f869(x44143)),f245(a868)),f197(f869(x44143)))),f2(a868)),f332(f170(f869(x44143)),x44144)))) % 165.28/165.04 [4368]E(f332(f332(f135(x43681),f178(x43681,x43682,x43683)),f178(x43681,x43684,f332(f252(a868),f332(f332(f7(a868,f875(a868,a862),a862),f332(f332(f8(a868,f875(f875(a868,a862),a862),a868),f334(a868)),f332(f332(f7(a868,a868,a868),f81(a868)),f332(f197(f869(x43681)),x43682)))),x43683)))),f178(x43681,f332(f332(f135(x43681),x43682),x43684),x43683)) % 165.28/165.04 [4420]E(f332(f332(f152(f869(x44201)),f332(f332(f152(x44201),x44202),f332(f143(f869(x44201),f869(x44201),f135(x44201),f116(x44201)),f332(f332(f155(f869(x44201),f869(x44201)),f157(f869(x44201),x44201,f116(x44201),f332(f332(f8(f869(x44201),f875(f869(x44201),f869(x44201)),x44201),f16(f869(x44201),f869(x44201))),f332(f332(f7(x44201,f869(x44201),f869(x44201)),f152(x44201)),f116(x44201))))),x44203)))),f182(x44201,f332(f332(f152(f869(x44201)),x44204),f332(f143(f869(f869(x44201)),f869(f869(x44201)),f135(f869(x44201)),f116(f869(x44201))),f332(f332(f155(f869(x44201),f869(f869(x44201))),f157(f869(f869(x44201)),x44201,f116(f869(x44201)),f332(f16(f875(f869(x44201),f869(f869(x44201))),x44201),f332(f332(f7(f869(x44201),f869(f869(x44201)),f869(f869(x44201))),f152(f869(x44201))),f116(f869(x44201)))))),x44203))))),f182(x44201,f332(f332(f152(f869(x44201)),f332(f332(f152(x44201),x44202),x44204)),x44203))) % 165.28/165.04 [4428]E(f332(f252(f874(x44281,x44281)),f332(f271(x44281,x44281,a862),f332(f332(f7(x44281,f875(f874(x44282,x44282),a862),f875(x44281,a862)),f332(f332(f8(f875(x44281,f875(f875(f874(x44282,x44282),a862),a862)),f875(f875(f874(x44282,x44282),a862),f875(x44281,a862)),x44281),f7(x44281,f875(f874(x44282,x44282),a862),a862)),f332(f332(f8(f875(x44281,f874(x44282,x44282)),f875(x44281,f875(f875(f874(x44282,x44282),a862),a862)),x44281),f332(f8(f874(x44282,x44282),f875(f875(f874(x44282,x44282),a862),a862),x44281),f334(f874(x44282,x44282)))),f332(f332(f7(x44281,f875(x44281,x44282),f875(x44281,f874(x44282,x44282))),f332(f332(f8(f875(x44282,f874(x44282,x44282)),f875(f875(x44281,x44282),f875(x44281,f874(x44282,x44282))),x44281),f8(x44282,f874(x44282,x44282),x44281)),f332(f332(f8(x44282,f875(x44282,f874(x44282,x44282)),x44281),f267(x44282,x44282)),x44283))),x44283)))),x44284))),f332(f332(f288(x44282,x44281),x44284),x44283)) % 165.28/165.04 [4490]~E(f34(x44901,x44902),f29(x44903,x44904,x44905)) % 165.28/165.04 [4491]~E(f34(x44911,x44912),f31(x44913,x44914,x44915)) % 165.28/165.04 [4492]~E(f34(x44921,x44922),f30(x44923,x44924,x44925)) % 165.28/165.04 [4493]~E(f33(x44931,x44932),f29(x44933,x44934,x44935)) % 165.28/165.04 [4494]~E(f33(x44941,x44942),f31(x44943,x44944,x44945)) % 165.28/165.04 [4495]~E(f33(x44951,x44952),f30(x44953,x44954,x44955)) % 165.28/165.04 [4496]~E(f29(x44961,x44962,x44963),f34(x44964,x44965)) % 165.28/165.04 [4497]~E(f29(x44971,x44972,x44973),f33(x44974,x44975)) % 165.28/165.04 [4498]~E(f31(x44981,x44982,x44983),f34(x44984,x44985)) % 165.28/165.04 [4499]~E(f31(x44991,x44992,x44993),f33(x44994,x44995)) % 165.28/165.04 [4500]~E(f30(x45001,x45002,x45003),f34(x45004,x45005)) % 165.28/165.04 [4501]~E(f30(x45011,x45012,x45013),f33(x45014,x45015)) % 165.28/165.04 [3539]E(f332(f332(f155(x35391,x35392),x35393),f171(x35391,x35394,x35395)),f171(x35392,x35394,f332(x35393,x35395))) % 165.28/165.04 [3912]E(f332(f187(x39121,x39122,x39123,x39124),x39125),f332(f241(f872(x39122),x39122,f332(x39123,x39125),f208(x39122)),f332(x39124,x39125))) % 165.28/165.04 [3999]E(f187(x39991,x39992,f187(x39991,x39992,x39993,x39994),x39995),f187(x39991,x39992,x39993,f187(x39991,x39992,x39994,x39995))) % 165.28/165.04 [4175]E(f268(x41751,x41752,x41753,f256(x41752,x41751,x41754),f256(x41753,x41752,x41755)),f256(x41753,x41751,f268(x41753,x41752,x41751,x41755,x41754))) % 165.28/165.04 [4182]E(f332(f332(f113(f875(x41821,a862)),f332(f174(x41821),f332(f332(f177(x41821),f332(f197(f869(x41822)),x41823)),x41824))),f186(x41821,x41822,x41825)),f186(x41821,x41822,f189(x41821,x41822,x41825,x41824,x41823))) % 165.28/165.04 [3733]E(f332(f332(f271(x37331,x37332,x37333),x37334),x37335),f332(f332(x37334,f332(f266(x37331,x37332),x37335)),f332(f270(x37331,x37332),x37335))) % 165.28/165.04 [3760]E(f332(f241(x37601,x37602,x37603,x37604),f332(f208(x37602),x37605)),f332(x37604,x37605)) % 165.28/165.04 [3769]E(f332(f332(f332(f66(x37691,x37692,x37693),x37694),x37695),f196(f875(x37692,a862))),x37695) % 165.28/165.04 [3911]E(f128(f872(x39111),f332(f332(f210(x39112,x39111),x39113),x39114),f123(x39112,x39111,x39113,x39115)),f123(x39112,x39111,x39113,f128(f872(x39112),x39114,x39115))) % 165.28/165.04 [3944]E(f242(x39441,x39442,x39443,x39444,f332(f208(x39442),x39445)),f332(x39444,x39445)) % 165.28/165.04 [4055]E(f332(f74(f872(x40551),f872(x40552),f872(x40553),f332(f210(x40551,x40552),x40554)),f332(f210(x40553,x40551),x40555)),f332(f210(x40553,x40552),f332(f74(x40551,x40552,x40553,x40554),x40555))) % 165.28/165.04 [4057]E(f332(f74(f869(x40571),f869(x40572),f869(x40573),f332(f155(x40571,x40572),x40574)),f332(f155(x40573,x40571),x40575)),f332(f155(x40573,x40572),f332(f74(x40571,x40572,x40573,x40574),x40575))) % 165.28/165.04 [4113]E(f332(f241(x41131,f874(x41132,f870(x41132)),x41133,f332(f271(x41132,f870(x41132),x41131),x41134)),f332(f136(x41132),x41135)),f131(x41131,x41132,x41133,x41134,x41135)) % 165.28/165.04 [4114]E(f124(x41141,f123(x41142,f870(f872(x41141)),f332(f332(f7(x41142,a102,f870(f872(x41141))),x41143),x41144),f332(x41145,x41144))),f332(f203(x41142,x41141,x41145,x41143),x41144)) % 165.28/165.04 [4137]E(f86(x41371,f67(x41372,x41371,x41373,x41374,x41375)),f332(f332(f65(x41372,x41371,x41373),x41374),x41375)) % 165.28/165.04 [4173]E(f332(f332(f81(a868),f332(f332(f81(a868),f332(x41731,f332(f266(x41732,x41733),x41734))),f332(x41735,f332(f270(x41732,x41733),x41734)))),f332(a115,f2(a868))),f275(x41732,x41733,x41731,x41735,x41734)) % 165.28/165.04 [4364]E(f164(x43641,x43642,f332(f332(f7(x43641,f872(x43642),f872(x43642)),f332(f332(f18(x43641,f872(x43642),f875(f872(x43642),f872(x43642))),f332(f332(f8(a862,f875(f872(x43642),f875(f872(x43642),f872(x43642))),x43641),f99(f872(x43642))),x43643)),f332(f332(f8(x43642,f872(x43642),x43641),f208(x43642)),x43644))),f209(x43642)),x43645),f332(f332(f155(x43641,x43642),x43644),f332(f137(x43641,x43643),x43645))) % 165.28/165.04 [4541]~E(f332(f332(f332(f73(x45411,f872(x45412)),x45413),x45414),f332(f208(x45412),x45415)),f332(f16(f872(x45412),x45411),f209(x45412))) % 165.28/165.04 [3667]E(f332(f332(f177(x36671),x36672),f332(f332(f155(x36673,x36671),x36674),x36675)),f332(f332(f155(x36673,x36671),x36674),f332(f332(f177(x36673),x36672),x36675))) % 165.28/165.04 [3668]E(f332(f332(f139(x36681),x36682),f332(f332(f155(x36683,x36681),x36684),x36685)),f332(f332(f155(x36683,x36681),x36684),f332(f332(f139(x36683),x36682),x36685))) % 165.28/165.04 [3701]E(f332(f332(f155(x37011,x37012),x37013),f332(f332(f152(x37011),x37014),x37015)),f332(f332(f152(x37012),f332(x37013,x37014)),f332(f332(f155(x37011,x37012),x37013),x37015))) % 165.28/165.04 [3764]E(f332(f311(x37641,x37642,x37643),f332(f332(f310(x37641),x37644),x37645)),f332(f332(f310(x37642),f332(x37643,x37644)),f332(f311(x37641,x37642,x37643),x37645))) % 165.28/165.04 [3793]E(f175(x37931,f332(f332(f152(x37931),x37932),x37933),f332(f332(f152(x37931),x37934),x37935)),f332(f332(f152(x37931),x37932),f332(f332(f152(x37931),x37934),f175(x37931,x37933,x37935)))) % 165.28/165.04 [3830]E(f332(f332(f184(x38301,x38302),f332(f332(f177(x38301),x38303),x38304)),f332(f332(f177(x38302),x38303),x38305)),f332(f332(f177(f874(x38301,x38302)),x38303),f332(f332(f184(x38301,x38302),x38304),x38305))) % 165.28/165.04 [3831]E(f332(f332(f184(x38311,x38312),f332(f332(f139(x38311),x38313),x38314)),f332(f332(f139(x38312),x38313),x38315)),f332(f332(f139(f874(x38311,x38312)),x38313),f332(f332(f184(x38311,x38312),x38314),x38315))) % 165.28/165.04 [3843]E(f332(f332(f160(x38431,f332(f332(f152(x38431),x38432),x38433)),f332(a115,x38434)),x38435),f332(f332(f152(x38431),x38432),f332(f332(f160(x38431,x38433),x38434),x38435))) % 165.28/165.04 [3846]E(f332(f241(f872(x38461),x38462,f209(x38461),x38463),f332(f332(f16(f872(x38462),x38464),f209(x38462)),x38465)),f209(x38461)) % 165.28/165.04 [3848]E(f332(f332(f135(x38481),f332(f332(f155(x38482,x38481),x38483),x38484)),f332(f332(f155(x38482,x38481),x38483),x38485)),f332(f332(f155(x38482,x38481),x38483),f332(f332(f135(x38482),x38484),x38485))) % 165.28/165.04 [3852]E(f332(f332(x38521,x38522),f332(f332(f258(x38523,x38524,x38521),x38522),x38525)),f332(f332(f258(x38523,x38524,x38521),x38522),f332(a115,x38525))) % 165.28/165.04 [3882]E(f165(x38821,x38822,x38823,f332(f332(f152(x38821),x38824),x38825)),f332(f332(f135(x38822),f332(x38823,x38824)),f165(x38821,x38822,x38823,x38825))) % 165.28/165.04 [3895]E(f332(f332(f289(x38951,x38952,x38953),f332(f287(x38952,x38951),x38954)),f332(f287(x38953,x38952),x38955)),f332(f287(x38953,x38951),f332(f332(f289(x38953,x38952,x38951),x38955),x38954))) % 165.28/165.04 [3930]E(f332(f332(f332(f191(f869(x39301),f869(x39301)),x39302),f169(x39301)),f332(f332(f155(x39303,x39301),x39304),x39305)),f332(f332(f155(x39303,x39301),x39304),f332(f332(f332(f191(f869(x39303),f869(x39303)),x39302),f169(x39303)),x39305))) % 165.28/165.04 [3931]E(f332(f332(f273(x39311,x39312,x39311,x39313),f332(f267(x39312,x39311),x39314)),x39315),f332(x39315,x39314)) % 165.28/165.04 [3958]E(f156(x39581,x39582,f332(f332(f155(x39583,x39581),x39584),x39585)),f156(x39583,f332(f74(x39581,a868,x39583,x39582),x39584),x39585)) % 165.28/165.04 [4022]E(f332(f332(f74(f872(x40221),f872(x40222),x40223,f332(f210(x40221,x40222),x40224)),f332(f16(f872(x40221),x40223),f209(x40221))),x40225),f209(x40222)) % 165.28/165.04 [4023]E(f179(f874(x40231,x40232),f332(f74(x40232,a862,f874(x40231,x40232),x40233),f270(x40231,x40232)),f332(f332(f184(x40231,x40232),x40234),x40235)),f332(f332(f184(x40231,x40232),x40234),f179(x40232,x40233,x40235))) % 165.28/165.04 [4029]E(f332(f311(x40291,x40292,f332(f332(f8(x40293,x40292,x40291),x40294),x40295)),f255(f875(x40291,a862))),f332(f311(x40293,x40292,x40294),f332(f311(x40291,x40293,x40295),f255(f875(x40291,a862))))) % 165.28/165.04 [4042]E(f179(f874(x40421,x40422),f332(f74(x40421,a862,f874(x40421,x40422),x40423),f266(x40421,x40422)),f332(f332(f184(x40421,x40422),x40424),x40425)),f332(f332(f184(x40421,x40422),f179(x40421,x40423,x40424)),x40425)) % 165.28/165.04 [4061]E(f332(f332(f113(f875(x40611,a862)),f332(f312(x40611,x40612,x40613),f332(f332(f310(x40612),x40614),f196(f875(x40612,a862))))),f332(f312(x40611,x40612,x40613),x40615)),f332(f312(x40611,x40612,x40613),f332(f332(f310(x40612),x40614),x40615))) % 165.28/165.04 [4121]E(f332(f332(f135(f874(x41211,x41212)),f332(f332(f155(x41212,f874(x41211,x41212)),f332(f267(x41211,x41212),x41213)),x41214)),f60(x41211,x41212,x41215,x41214)),f60(x41211,x41212,f332(f332(f152(x41211),x41213),x41215),x41214)) % 165.28/165.04 [4122]E(f332(f332(f155(x41221,x41222),x41223),f179(x41221,f332(f74(x41222,a862,x41221,x41224),x41223),x41225)),f179(x41222,x41224,f332(f332(f155(x41221,x41222),x41223),x41225))) % 165.28/165.04 [4128]E(f332(f143(x41281,x41282,f332(f7(x41282,x41281,x41281),f332(f7(x41281,x41282,x41281),x41283)),x41284),f332(f170(x41282),f332(f170(x41282),x41285))),f332(f143(x41281,x41282,x41283,x41284),x41285)) % 165.28/165.04 [4129]E(f332(f332(f332(f73(x41291,f872(x41292)),f190(x41291,x41292,x41293,x41294)),x41295),f332(x41293,x41295)),f190(x41291,x41292,x41293,f332(f332(f310(x41291),x41295),x41294))) % 165.28/165.04 [4199]E(f332(f241(f869(x41991),x41991,f164(x41992,x41991,x41993,x41994),f332(f332(f7(x41991,f869(x41991),f869(x41991)),f152(x41991)),f164(x41992,x41991,x41993,x41994))),f332(x41993,x41995)),f164(x41992,x41991,x41993,f332(f332(f152(x41992),x41995),x41994))) % 165.28/165.04 [4236]P24(f332(f332(f246(f875(x42361,a862)),f332(f311(x42362,x42361,x42363),f332(f332(f104(f875(x42362,a862)),x42364),x42365))),f332(f332(f104(f875(x42361,a862)),f332(f311(x42362,x42361,x42363),x42364)),f332(f311(x42362,x42361,x42363),x42365)))) % 165.28/165.04 [4237]P24(f332(f332(f246(f875(x42371,a862)),f332(f286(x42372,x42371,x42373),f332(f332(f104(f875(x42372,a862)),x42374),x42375))),f332(f332(f104(f875(x42371,a862)),f332(f286(x42372,x42371,x42373),x42374)),f332(f286(x42372,x42371,x42373),x42375)))) % 165.28/165.04 [4338]E(f332(f270(x43381,x43382),f332(f272(x43383,x43381,x43382,x43382,x43384,f35(x43382)),x43385)),f332(f270(x43383,x43382),x43385)) % 165.28/165.04 [4339]E(f332(f266(x43391,x43392),f332(f272(x43391,x43391,x43393,x43392,f35(x43391),x43394),x43395)),f332(f266(x43391,x43393),x43395)) % 165.28/165.04 [4424]E(f332(f143(f875(x44241,f872(x44242)),f874(x44241,x44242),f332(f332(f8(f875(x44241,f875(x44242,f875(x44241,f872(x44242)))),f875(f874(x44241,x44242),f875(x44241,f872(x44242))),f875(x44241,f872(x44242))),f271(x44241,x44242,f875(x44241,f872(x44242)))),f332(f332(f7(f875(x44241,f872(x44242)),f875(x44242,f872(x44242)),f875(x44241,f875(x44242,f875(x44241,f872(x44242))))),f332(f332(f8(f875(x44241,f875(f875(x44242,f872(x44242)),f875(x44242,f875(x44241,f872(x44242))))),f875(f875(x44242,f872(x44242)),f875(x44241,f875(x44242,f875(x44241,f872(x44242))))),f875(x44241,f872(x44242))),f7(x44241,f875(x44242,f872(x44242)),f875(x44242,f875(x44241,f872(x44242))))),f332(f332(f8(f875(x44241,f875(f872(x44242),f875(x44241,f872(x44242)))),f875(x44241,f875(f875(x44242,f872(x44242)),f875(x44242,f875(x44241,f872(x44242))))),f875(x44241,f872(x44242))),f332(f8(f875(f872(x44242),f875(x44241,f872(x44242))),f875(f875(x44242,f872(x44242)),f875(x44242,f875(x44241,f872(x44242)))),x44241),f8(f872(x44242),f875(x44241,f872(x44242)),x44242))),f73(x44241,f872(x44242))))),f208(x44242))),x44243),f332(f332(f184(x44241,x44242),x44244),x44245)),f189(x44241,x44242,x44243,x44244,x44245)) % 165.28/165.04 [4426]P20(x44261,x44262,f332(f332(f310(f867(x44261)),f332(f332(f332(f93(x44261),f332(f332(f7(x44261,f875(a864,a862),f875(a864,a862)),f332(f332(f8(f875(a864,f875(a862,a862)),f875(f875(a864,a862),f875(a864,a862)),x44261),f18(a864,a862,a862)),f332(f332(f8(f875(a864,a862),f875(a864,f875(a862,a862)),x44261),f332(f8(a862,f875(a862,a862),a864),a330)),x44263))),f332(f332(f8(a862,a862,a864),a327),x44264))),f33(x44264,x44265)),x44263)),f196(f875(f867(x44261),a862)))) % 165.28/165.04 [3508]E(f332(f332(f332(f332(f216(x35081),x35082),x35083),x35084),x35085),f211(x35081,x35082)) % 165.28/165.04 [3509]E(f332(f332(f332(f332(f217(x35091),x35092),x35093),x35094),x35095),f200(x35091,x35092)) % 165.28/165.04 [3555]E(f96(x35551,x35552,f332(f332(f332(f93(x35551),x35553),x35554),x35555)),f2(a868)) % 165.28/165.04 [3651]E(f332(f332(f332(f332(f73(x36511,x36512),x36513),x36514),x36515),x36514),x36515) % 165.28/165.04 [3883]E(f332(f332(f42(x38831,f875(x38832,a862)),f332(f332(f310(x38831),x38833),x38834)),x38835),f332(f332(f113(f875(x38832,a862)),f332(x38835,x38833)),f332(f332(f42(x38831,f875(x38832,a862)),x38834),x38835))) % 165.28/165.04 [3884]E(f332(f332(f43(x38841,f875(x38842,a862)),f332(f332(f310(x38841),x38843),x38844)),x38845),f332(f332(f104(f875(x38842,a862)),f332(x38845,x38843)),f332(f332(f43(x38841,f875(x38842,a862)),x38844),x38845))) % 165.28/165.04 [3937]E(f332(f121(x39371,x39372,f332(x39373,x39374)),f332(f332(f7(x39371,a102,f870(x39372)),x39375),x39374)),f332(f206(x39371,x39372,x39373,x39375),x39374)) % 165.28/165.04 [3951]E(f332(f332(f113(f875(x39511,a862)),f332(f311(x39512,x39511,x39513),x39514)),f332(f311(x39512,x39511,x39513),x39515)),f332(f311(x39512,x39511,x39513),f332(f332(f113(f875(x39512,a862)),x39514),x39515))) % 165.28/165.04 [3952]E(f332(f332(f113(f875(x39521,a862)),f332(f312(x39521,x39522,x39523),x39524)),f332(f312(x39521,x39522,x39523),x39525)),f332(f312(x39521,x39522,x39523),f332(f332(f113(f875(x39522,a862)),x39524),x39525))) % 165.28/165.04 [3953]E(f332(f332(f22(f875(x39531,a862)),f332(f312(x39531,x39532,x39533),x39534)),f332(f312(x39531,x39532,x39533),x39535)),f332(f312(x39531,x39532,x39533),f332(f332(f22(f875(x39532,a862)),x39534),x39535))) % 165.28/165.04 [3954]E(f332(f332(f104(f875(x39541,a862)),f332(f312(x39541,x39542,x39543),x39544)),f332(f312(x39541,x39542,x39543),x39545)),f332(f312(x39541,x39542,x39543),f332(f332(f104(f875(x39542,a862)),x39544),x39545))) % 165.28/165.04 [3955]E(f332(f332(f113(f875(x39551,a862)),f332(f286(x39552,x39551,x39553),x39554)),f332(f286(x39552,x39551,x39553),x39555)),f332(f286(x39552,x39551,x39553),f332(f332(f113(f875(x39552,a862)),x39554),x39555))) % 165.28/165.04 [3957]E(f190(x39571,x39572,f190(x39571,x39572,x39573,x39574),x39575),f190(x39571,x39572,x39573,f332(f332(f104(f875(x39571,a862)),x39574),x39575))) % 165.28/165.04 [4018]E(f332(f332(f160(x40181,f332(f332(f135(x40181),x40182),f332(f332(f152(x40181),x40183),x40184))),f332(f197(f869(x40181)),x40182)),x40185),f332(f332(f135(x40181),x40182),f332(f332(f152(x40181),x40185),x40184))) % 165.28/165.04 [4026]E(f332(f332(f43(x40261,f875(x40262,a862)),x40263),f332(f332(f8(f875(x40262,a862),f875(x40262,a862),x40261),f332(f310(x40262),x40264)),x40265)),f332(f332(f310(x40262),x40264),f332(f332(f43(x40261,f875(x40262,a862)),x40263),x40265))) % 165.28/165.04 [4095]E(f190(x40951,x40952,f332(f332(f332(f73(x40951,f872(x40952)),x40953),x40954),f332(f208(x40952),x40955)),f332(f80(f875(x40951,a862)),f332(f332(f310(x40951),x40954),f196(f875(x40951,a862))))),f190(x40951,x40952,x40953,f332(f80(f875(x40951,a862)),f332(f332(f310(x40951),x40954),f196(f875(x40951,a862)))))) % 165.28/165.04 [4186]E(f332(f332(f155(x41861,x41862),x41863),f332(f137(x41861,f332(f74(x41862,a862,x41861,x41864),x41863)),x41865)),f332(f137(x41862,x41864),f332(f332(f155(x41861,x41862),x41863),x41865))) % 165.28/165.04 [4192]E(f332(f197(f869(x41921)),f332(f137(x41921,x41922),f332(f332(f155(x41923,x41921),x41924),x41925))),f332(f197(f869(x41923)),f332(f137(x41923,f332(f74(x41921,a862,x41923,x41922),x41924)),x41925))) % 165.28/165.04 [4330]E(f332(f332(f113(f875(x43301,a862)),f332(f332(f22(f875(x43301,a862)),f186(x43301,x43302,x43303)),f332(f252(x43301),f332(f332(f7(x43301,f875(x43301,a862),a862),f334(x43301)),f332(f332(f22(f875(x43301,a862)),x43304),f186(x43301,x43302,x43305)))))),f332(f252(x43301),f332(f332(f7(x43301,f875(x43301,a862),a862),f334(x43301)),f332(f332(f104(f875(x43301,a862)),x43304),f186(x43301,x43302,x43305))))),f186(x43301,x43302,f77(x43301,f872(x43302),x43303,x43305,x43304))) % 165.28/165.04 [4405]E(f332(f157(f869(f874(x44051,x44052)),x44052,f116(f874(x44051,x44052)),f332(f332(f7(x44052,f875(f869(x44052),f869(f874(x44051,x44052))),f875(f869(x44052),f869(f874(x44051,x44052)))),f332(f332(f8(f875(f869(f874(x44051,x44052)),f869(f874(x44051,x44052))),f875(f875(f869(x44052),f869(f874(x44051,x44052))),f875(f869(x44052),f869(f874(x44051,x44052)))),x44052),f8(f869(f874(x44051,x44052)),f869(f874(x44051,x44052)),f869(x44052))),f332(f332(f8(f874(x44051,x44052),f875(f869(f874(x44051,x44052)),f869(f874(x44051,x44052))),x44052),f152(f874(x44051,x44052))),f332(f267(x44051,x44052),x44053)))),f332(f184(x44051,x44052),x44054))),x44055),f332(f332(f184(x44051,x44052),f332(f332(f152(x44051),x44053),x44054)),x44055)) % 165.28/165.04 [3877]E(f332(f332(f160(x38771,f332(f332(f160(x38771,x38772),x38773),x38774)),x38773),x38775),f332(f332(f160(x38771,x38772),x38773),x38775)) % 165.28/165.04 [3932]E(f332(f263(x39321,x39322),f332(f332(f310(f874(x39321,x39322)),f332(f332(f267(x39321,x39322),x39323),x39324)),x39325)),f332(f332(f310(x39322),x39324),f332(f263(x39321,x39322),x39325))) % 165.28/165.04 [3933]E(f332(f265(x39331,x39332),f332(f332(f310(f874(x39331,x39332)),f332(f332(f267(x39331,x39332),x39333),x39334)),x39335)),f332(f332(f310(x39331),x39333),f332(f265(x39331,x39332),x39335))) % 165.28/165.04 [4011]E(f332(f332(f113(f875(f874(x40111,x40112),a862)),f332(f332(f269(x40111,x40112),x40113),x40114)),f332(f332(f269(x40111,x40112),x40115),x40114)),f332(f332(f269(x40111,x40112),f332(f332(f113(f875(x40111,a862)),x40113),x40115)),x40114)) % 165.28/165.04 [4012]E(f332(f332(f22(f875(f874(x40121,x40122),a862)),f332(f332(f269(x40121,x40122),x40123),x40124)),f332(f332(f269(x40121,x40122),x40125),x40124)),f332(f332(f269(x40121,x40122),f332(f332(f22(f875(x40121,a862)),x40123),x40125)),x40124)) % 165.28/165.04 [4013]E(f332(f332(f104(f875(f874(x40131,x40132),a862)),f332(f332(f269(x40131,x40132),x40133),x40134)),f332(f332(f269(x40131,x40132),x40135),x40134)),f332(f332(f269(x40131,x40132),f332(f332(f104(f875(x40131,a862)),x40133),x40135)),x40134)) % 165.28/165.04 [4073]E(f332(f332(f113(f875(x40731,a862)),f332(f332(f42(x40732,f875(x40731,a862)),x40733),x40734)),f332(f332(f42(x40732,f875(x40731,a862)),x40735),x40734)),f332(f332(f42(x40732,f875(x40731,a862)),f332(f332(f113(f875(x40732,a862)),x40733),x40735)),x40734)) % 165.28/165.04 [4074]E(f332(f332(f104(f875(x40741,a862)),f332(f332(f43(x40742,f875(x40741,a862)),x40743),x40744)),f332(f332(f43(x40742,f875(x40741,a862)),x40745),x40744)),f332(f332(f43(x40742,f875(x40741,a862)),f332(f332(f113(f875(x40742,a862)),x40743),x40745)),x40744)) % 165.28/165.04 [4088]E(f332(f332(f42(x40881,f875(x40882,a862)),x40883),f332(f332(f8(f875(x40882,a862),f875(x40882,a862),x40881),f332(f22(f875(x40882,a862)),x40884)),x40885)),f332(f332(f22(f875(x40882,a862)),x40884),f332(f332(f43(x40881,f875(x40882,a862)),x40883),x40885))) % 165.28/165.04 [4089]E(f332(f332(f42(x40891,f875(x40892,a862)),x40893),f332(f332(f8(f875(x40892,a862),f875(x40892,a862),x40891),f332(f104(f875(x40892,a862)),x40894)),x40895)),f332(f332(f104(f875(x40892,a862)),x40894),f332(f332(f42(x40891,f875(x40892,a862)),x40893),x40895))) % 165.28/165.04 [4090]E(f332(f332(f43(x40901,f875(x40902,a862)),x40903),f332(f332(f8(f875(x40902,a862),f875(x40902,a862),x40901),f332(f113(f875(x40902,a862)),x40904)),x40905)),f332(f332(f113(f875(x40902,a862)),x40904),f332(f332(f43(x40901,f875(x40902,a862)),x40903),x40905))) % 165.28/165.04 [4127]E(f187(x41271,x41272,x41273,f332(f180(x41271,x41272),f332(f170(f874(x41271,x41272)),f332(f332(f184(x41271,x41272),x41274),x41275)))),f189(x41271,x41272,x41273,x41274,x41275)) % 165.28/165.04 [4149]E(f193(f869(x41491),f332(f332(f152(x41491),x41492),x41493),f332(f332(f8(f869(x41491),f869(x41491),a868),f332(f152(x41491),x41494)),f332(f332(f7(a868,x41491,f869(x41491)),f160(x41491,x41493)),x41492)),x41495),f332(f332(f160(x41491,f332(f332(f152(x41491),x41494),x41493)),x41495),x41492)) % 165.28/165.04 [4153]E(f332(f332(f42(x41531,f875(f874(x41532,x41533),a862)),x41534),f332(f332(f8(f875(f874(x41533,x41532),a862),f875(f874(x41532,x41533),a862),x41531),f287(x41533,x41532)),x41535)),f332(f287(x41533,x41532),f332(f332(f42(x41531,f875(f874(x41533,x41532),a862)),x41534),x41535))) % 165.28/165.04 [4154]E(f332(f332(f43(x41541,f875(f874(x41542,x41543),a862)),x41544),f332(f332(f8(f875(f874(x41543,x41542),a862),f875(f874(x41542,x41543),a862),x41541),f287(x41543,x41542)),x41545)),f332(f287(x41543,x41542),f332(f332(f43(x41541,f875(f874(x41543,x41542),a862)),x41544),x41545))) % 165.28/165.04 [4210]E(f186(x42101,x42102,f332(f332(f18(x42101,f872(x42103),f872(x42102)),f332(f332(f8(f875(x42103,x42102),f875(f872(x42103),f872(x42102)),x42101),f210(x42103,x42102)),x42104)),x42105)),f186(x42101,x42103,x42105)) % 165.28/165.04 [4261]P24(f332(f332(f246(f875(x42611,a862)),f332(f332(f22(f875(x42611,a862)),f332(f311(x42612,x42611,x42613),x42614)),f332(f311(x42612,x42611,x42613),x42615))),f332(f311(x42612,x42611,x42613),f332(f332(f22(f875(x42612,a862)),x42614),x42615)))) % 165.28/165.04 [4409]E(f332(f157(f869(f874(x44091,x44092)),x44091,f116(f874(x44091,x44092)),f332(f332(f7(x44091,f875(f869(x44091),f869(f874(x44091,x44092))),f875(f869(x44091),f869(f874(x44091,x44092)))),f332(f332(f8(f875(f869(f874(x44091,x44092)),f869(f874(x44091,x44092))),f875(f875(f869(x44091),f869(f874(x44091,x44092))),f875(f869(x44091),f869(f874(x44091,x44092)))),x44091),f8(f869(f874(x44091,x44092)),f869(f874(x44091,x44092)),f869(x44091))),f332(f332(f8(f874(x44091,x44092),f875(f869(f874(x44091,x44092)),f869(f874(x44091,x44092))),x44091),f152(f874(x44091,x44092))),f332(f332(f7(x44091,x44092,f874(x44091,x44092)),f267(x44091,x44092)),x44093)))),f332(f332(f7(f869(x44091),f869(x44092),f869(f874(x44091,x44092))),f184(x44091,x44092)),x44094))),x44095),f332(f332(f184(x44091,x44092),x44095),f332(f332(f152(x44092),x44093),x44094))) % 165.28/165.04 [4115]E(f332(f332(f113(f875(x41151,a862)),f332(f286(x41152,x41151,x41153),x41154)),f332(f286(x41152,x41151,x41155),x41154)),f332(f286(x41152,x41151,f332(f332(f113(f875(f874(x41152,x41151),a862)),x41153),x41155)),x41154)) % 165.28/165.04 [4156]E(f332(f332(f135(f874(x41561,x41562)),f332(f332(f184(x41561,x41562),x41563),f332(f332(f177(x41562),f332(f197(f869(x41561)),x41563)),x41564))),f332(f332(f184(x41561,x41562),x41565),f332(f332(f139(x41562),f332(f197(f869(x41561)),x41563)),x41564))),f332(f332(f184(x41561,x41562),f332(f332(f135(x41561),x41563),x41565)),x41564)) % 165.28/165.04 [4264]E(f332(f332(f269(x42641,x42642),x42643),f332(f332(f18(x42641,f875(x42642,a862),f875(x42642,a862)),f332(f332(f8(f875(x42642,a862),f875(f875(x42642,a862),f875(x42642,a862)),x42641),f113(f875(x42642,a862))),x42644)),x42645)),f332(f332(f113(f875(f874(x42641,x42642),a862)),f332(f332(f269(x42641,x42642),x42643),x42644)),f332(f332(f269(x42641,x42642),x42643),x42645))) % 165.28/165.04 [4265]E(f332(f332(f269(x42651,x42652),x42653),f332(f332(f18(x42651,f875(x42652,a862),f875(x42652,a862)),f332(f332(f8(f875(x42652,a862),f875(f875(x42652,a862),f875(x42652,a862)),x42651),f22(f875(x42652,a862))),x42654)),x42655)),f332(f332(f22(f875(f874(x42651,x42652),a862)),f332(f332(f269(x42651,x42652),x42653),x42654)),f332(f332(f269(x42651,x42652),x42653),x42655))) % 165.28/165.04 [4266]E(f332(f332(f269(x42661,x42662),x42663),f332(f332(f18(x42661,f875(x42662,a862),f875(x42662,a862)),f332(f332(f8(f875(x42662,a862),f875(f875(x42662,a862),f875(x42662,a862)),x42661),f104(f875(x42662,a862))),x42664)),x42665)),f332(f332(f104(f875(f874(x42661,x42662),a862)),f332(f332(f269(x42661,x42662),x42663),x42664)),f332(f332(f269(x42661,x42662),x42663),x42665))) % 165.28/165.04 [4270]E(f332(f332(f42(x42701,f875(x42702,a862)),x42703),f332(f332(f7(x42701,f875(x42702,a862),f875(x42702,a862)),f332(f332(f8(f875(x42702,a862),f875(f875(x42702,a862),f875(x42702,a862)),x42701),f22(f875(x42702,a862))),x42704)),x42705)),f332(f332(f22(f875(x42702,a862)),f332(f332(f42(x42701,f875(x42702,a862)),x42703),x42704)),x42705)) % 165.28/165.04 [4271]E(f332(f332(f42(x42711,f875(x42712,a862)),x42713),f332(f332(f7(x42711,f875(x42712,a862),f875(x42712,a862)),f332(f332(f8(f875(x42712,a862),f875(f875(x42712,a862),f875(x42712,a862)),x42711),f104(f875(x42712,a862))),x42714)),x42715)),f332(f332(f104(f875(x42712,a862)),f332(f332(f42(x42711,f875(x42712,a862)),x42713),x42714)),x42715)) % 165.28/165.04 [4272]E(f332(f332(f43(x42721,f875(x42722,a862)),x42723),f332(f332(f7(x42721,f875(x42722,a862),f875(x42722,a862)),f332(f332(f8(f875(x42722,a862),f875(f875(x42722,a862),f875(x42722,a862)),x42721),f113(f875(x42722,a862))),x42724)),x42725)),f332(f332(f113(f875(x42722,a862)),f332(f332(f43(x42721,f875(x42722,a862)),x42723),x42724)),x42725)) % 165.28/165.04 [4276]E(f332(f332(f42(x42761,f875(x42762,a862)),x42763),f332(f332(f18(x42761,f875(x42762,a862),f875(x42762,a862)),f332(f332(f8(f875(x42762,a862),f875(f875(x42762,a862),f875(x42762,a862)),x42761),f113(f875(x42762,a862))),x42764)),x42765)),f332(f332(f113(f875(x42762,a862)),f332(f332(f42(x42761,f875(x42762,a862)),x42763),x42764)),f332(f332(f42(x42761,f875(x42762,a862)),x42763),x42765))) % 165.28/165.04 [4277]E(f332(f332(f43(x42771,f875(x42772,a862)),x42773),f332(f332(f18(x42771,f875(x42772,a862),f875(x42772,a862)),f332(f332(f8(f875(x42772,a862),f875(f875(x42772,a862),f875(x42772,a862)),x42771),f104(f875(x42772,a862))),x42774)),x42775)),f332(f332(f104(f875(x42772,a862)),f332(f332(f43(x42771,f875(x42772,a862)),x42773),x42774)),f332(f332(f43(x42771,f875(x42772,a862)),x42773),x42775))) % 165.28/165.04 [4291]E(f332(f332(f42(x42911,f875(x42912,a862)),x42913),f332(f332(f18(x42911,f875(x42912,a862),f875(x42912,a862)),f332(f332(f8(f875(x42912,a862),f875(f875(x42912,a862),f875(x42912,a862)),x42911),f113(f875(x42912,a862))),x42914)),x42915)),f332(f332(f113(f875(x42912,a862)),f40(f875(x42912,a862),f332(f311(x42911,f875(x42912,a862),x42914),x42913))),f40(f875(x42912,a862),f332(f311(x42911,f875(x42912,a862),x42915),x42913)))) % 165.28/165.04 [4292]E(f332(f332(f43(x42921,f875(x42922,a862)),x42923),f332(f332(f18(x42921,f875(x42922,a862),f875(x42922,a862)),f332(f332(f8(f875(x42922,a862),f875(f875(x42922,a862),f875(x42922,a862)),x42921),f104(f875(x42922,a862))),x42924)),x42925)),f332(f332(f104(f875(x42922,a862)),f41(f875(x42922,a862),f332(f311(x42921,f875(x42922,a862),x42924),x42923))),f41(f875(x42922,a862),f332(f311(x42921,f875(x42922,a862),x42925),x42923)))) % 165.28/165.04 [4326]E(f332(f332(f139(x43261),f332(f197(f869(x43261)),f179(x43261,x43262,f332(f332(f155(x43263,x43261),x43264),x43265)))),f332(f332(f155(x43263,x43261),x43264),x43265)),f332(f332(f155(x43263,x43261),x43264),f332(f332(f139(x43263),f332(f197(f869(x43263)),f179(x43263,f332(f74(x43261,a862,x43263,x43262),x43264),x43265))),x43265))) % 165.28/165.04 [4200]E(f332(f332(f135(f874(x42001,x42002)),f332(f332(f184(x42001,x42002),f332(f332(f177(x42001),f332(f197(f869(x42002)),x42003)),x42004)),x42003)),f332(f332(f184(x42001,x42002),f332(f332(f139(x42001),f332(f197(f869(x42002)),x42003)),x42004)),x42005)),f332(f332(f184(x42001,x42002),x42004),f332(f332(f135(x42002),x42003),x42005))) % 165.28/165.04 [4318]E(f86(x43181,f332(f332(f18(x43181,a862,a862),f332(f332(f8(a862,f875(a862,a862),x43181),a330),f332(f332(f7(x43181,f875(x43181,a862),a862),f334(x43181)),x43182))),f332(f332(f7(x43181,x43183,a862),f332(f332(f8(x43183,f875(x43183,a862),x43181),a329),x43184)),x43185))),f332(f78(x43181,x43183,x43182,x43184),x43185)) % 165.28/165.04 [4370]E(f332(f332(f87(a1,x43701),f332(f106(a1),f332(f332(f81(a1),x43702),a100))),f332(f332(f18(a1,x43701,x43701),f332(f332(f7(a1,x43701,f875(x43701,x43701)),f332(f332(f8(a862,f875(x43701,f875(x43701,x43701)),a1),f99(x43701)),a201)),f193(x43701,x43703,x43704,x43705))),f332(f332(f8(a868,x43701,a1),x43704),f332(f332(f7(a1,a868,a868),f332(f332(f8(a868,f875(a868,a868),a1),f81(a868)),a107)),x43705)))),f193(x43701,x43703,x43704,f332(f332(f81(a868),f332(f106(a868),x43702)),x43705))) % 165.28/165.04 [4406]E(f332(f180(x44061,x44062),f332(f332(f155(f874(x44061,x44063),f874(x44061,x44062)),f332(f271(x44061,x44063,f874(x44061,x44062)),f332(f332(f7(x44061,f875(x44063,x44062),f875(x44063,f874(x44061,x44062))),f332(f332(f8(f875(x44062,f874(x44061,x44062)),f875(f875(x44063,x44062),f875(x44063,f874(x44061,x44062))),x44061),f8(x44062,f874(x44061,x44062),x44063)),f267(x44061,x44062))),x44064))),x44065)),f332(f74(f872(x44063),f872(x44062),x44061,f332(f210(x44063,x44062),x44064)),f332(f180(x44061,x44063),x44065))) % 165.28/165.04 [4363]E(f186(x43631,x43632,f332(f332(f18(x43631,f872(x43632),f872(x43632)),f332(f332(f18(x43631,f872(x43632),f875(f872(x43632),f872(x43632))),f332(f332(f8(a862,f875(f872(x43632),f875(f872(x43632),f872(x43632))),x43631),f99(f872(x43632))),x43633)),x43634)),x43635)),f332(f332(f113(f875(x43631,a862)),f332(f332(f104(f875(x43631,a862)),f186(x43631,x43632,x43634)),f332(f252(x43631),x43633))),f332(f332(f104(f875(x43631,a862)),f186(x43631,x43632,x43635)),f332(f252(x43631),f332(f332(f8(a862,a862,x43631),a327),x43633))))) % 165.28/165.04 [4404]E(f332(f332(f87(a1,x44041),f332(f106(a1),f332(f332(f81(a1),x44042),a100))),f332(f332(f18(a1,x44041,x44041),f332(f332(f7(a1,x44041,f875(x44041,x44041)),f332(f332(f8(a862,f875(x44041,f875(x44041,x44041)),a1),f99(x44041)),a201)),f332(f192(x44041,x44043,x44044),x44045))),f332(f332(f18(a1,x44041,x44041),f332(f332(f8(a868,f875(x44041,x44041),a1),x44044),f332(f332(f7(a1,a868,a868),f332(f332(f8(a868,f875(a868,a868),a1),f81(a868)),a107)),x44045))),f332(f332(f8(a868,x44041,a1),f192(x44041,x44043,x44044)),f332(f332(f7(a1,a868,a868),f332(f332(f8(a868,f875(a868,a868),a1),f81(a868)),a107)),x44045))))),f332(f192(x44041,x44043,x44044),f332(f332(f81(a868),f332(f106(a868),x44042)),x44045))) % 165.28/165.04 [4438]E(f332(f252(f874(x44381,x44382)),f332(f271(x44381,x44382,a862),f332(f332(f8(f875(x44382,f875(x44383,a862)),f875(x44382,a862),x44381),f332(f8(f875(x44383,a862),a862,x44382),f88(x44383))),f332(f332(f7(x44381,f875(x44382,f875(x44383,a862)),f875(x44382,f875(x44383,a862))),f332(f332(f8(f875(f875(x44383,a862),f875(x44383,a862)),f875(f875(x44382,f875(x44383,a862)),f875(x44382,f875(x44383,a862))),x44381),f8(f875(x44383,a862),f875(x44383,a862),x44382)),f332(f332(f8(f875(x44383,f875(a862,a862)),f875(f875(x44383,a862),f875(x44383,a862)),x44381),f18(x44383,a862,a862)),f332(f332(f8(f875(x44383,a862),f875(x44383,f875(a862,a862)),x44381),f332(f8(a862,f875(a862,a862),x44383),a330)),f332(f332(f7(x44381,f875(f874(x44381,x44383),a862),f875(x44383,a862)),f332(f332(f8(f875(x44383,f875(f875(f874(x44381,x44383),a862),a862)),f875(f875(f874(x44381,x44383),a862),f875(x44383,a862)),x44381),f7(x44383,f875(f874(x44381,x44383),a862),a862)),f332(f332(f8(f875(x44383,f874(x44381,x44383)),f875(x44383,f875(f875(f874(x44381,x44383),a862),a862)),x44381),f332(f8(f874(x44381,x44383),f875(f875(f874(x44381,x44383),a862),a862),x44383),f334(f874(x44381,x44383)))),f267(x44381,x44383)))),x44384))))),f332(f332(f7(x44382,f875(f874(x44383,x44382),a862),f875(x44383,a862)),f332(f332(f8(f875(x44383,f875(f875(f874(x44383,x44382),a862),a862)),f875(f875(f874(x44383,x44382),a862),f875(x44383,a862)),x44382),f7(x44383,f875(f874(x44383,x44382),a862),a862)),f332(f332(f8(f875(x44383,f874(x44383,x44382)),f875(x44383,f875(f875(f874(x44383,x44382),a862),a862)),x44382),f332(f8(f874(x44383,x44382),f875(f875(f874(x44383,x44382),a862),a862),x44383),f334(f874(x44383,x44382)))),f332(f7(x44383,x44382,f874(x44383,x44382)),f267(x44383,x44382))))),x44385))))),f332(f332(f289(x44381,x44383,x44382),x44384),x44385)) % 165.28/165.04 [4522]~E(f31(x45221,x45222,x45223),f29(x45224,x45225,x45226)) % 165.28/165.04 [4525]~E(f30(x45251,x45252,x45253),f29(x45254,x45255,x45256)) % 165.28/165.04 [4526]~E(f30(x45261,x45262,x45263),f31(x45264,x45265,x45266)) % 165.28/165.04 [3967]E(f131(x39671,x39672,x39673,x39674,f128(x39672,x39675,x39676)),f332(f332(x39674,x39675),x39676)) % 165.28/165.04 [4184]E(f189(x41841,x41842,f187(x41841,x41842,x41843,x41844),x41845,x41846),f187(x41841,x41842,x41843,f189(x41841,x41842,x41844,x41845,x41846))) % 165.28/165.04 [4307]E(f332(f74(f874(x43071,x43072),x43072,f874(x43073,x43074),f270(x43071,x43072)),f272(x43073,x43071,x43074,x43072,x43075,x43076)),f332(f74(x43074,x43072,f874(x43073,x43074),x43076),f270(x43073,x43074))) % 165.28/165.04 [4308]E(f332(f74(f874(x43081,x43082),x43081,f874(x43083,x43084),f266(x43081,x43082)),f272(x43083,x43081,x43084,x43082,x43085,x43086)),f332(f74(x43083,x43081,f874(x43083,x43084),x43085),f266(x43083,x43084))) % 165.28/165.04 [3906]E(f332(f332(f74(x39061,x39062,x39063,x39064),x39065),x39066),f332(x39064,f332(x39065,x39066))) % 165.28/165.04 [3699]E(f332(f332(f271(x36991,x36992,x36993),x36994),f332(f332(f267(x36991,x36992),x36995),x36996)),f332(f332(x36994,x36995),x36996)) % 165.28/165.04 [3761]E(f332(f332(f332(f8(x37611,x37612,x37613),x37614),x37615),x37616),f332(x37614,f332(x37615,x37616))) % 165.28/165.04 [3762]E(f332(f332(f332(f7(x37621,x37622,x37623),x37624),x37625),x37626),f332(f332(x37624,x37626),x37625)) % 165.28/165.04 [3779]E(f332(f332(f332(f18(x37791,x37792,x37793),x37794),x37795),x37796),f332(f332(x37794,x37796),f332(x37795,x37796))) % 165.28/165.04 [3801]E(f332(f157(x38011,x38012,x38013,x38014),f332(f332(f152(x38012),x38015),x38016)),f332(f332(x38014,x38015),x38016)) % 165.28/165.04 [3842]E(f171(f874(x38421,x38422),f332(f332(f244(a868),x38423),x38424),f332(f332(f267(x38421,x38422),x38425),x38426)),f332(f332(f184(x38421,x38422),f171(x38421,x38423,x38425)),f171(x38422,x38424,x38426))) % 165.28/165.04 [3910]E(f332(f332(f152(f874(x39101,x39102)),f332(f332(f267(x39101,x39102),x39103),x39104)),f332(f332(f184(x39101,x39102),x39105),x39106)),f332(f332(f184(x39101,x39102),f332(f332(f152(x39101),x39103),x39105)),f332(f332(f152(x39102),x39104),x39106))) % 165.28/165.04 [3913]E(f332(f332(f155(x39131,x39132),x39133),f332(f332(f160(x39131,x39134),x39135),x39136)),f332(f332(f160(x39132,f332(f332(f155(x39131,x39132),x39133),x39134)),x39135),f332(x39133,x39136))) % 165.28/165.04 [3956]E(f332(f143(x39561,x39562,x39563,x39564),f332(f332(f152(x39562),x39565),x39566)),f332(f143(x39561,x39562,x39563,f332(f332(x39563,x39564),x39565)),x39566)) % 165.28/165.04 [3982]E(f274(x39821,x39822,x39823,x39824,f332(f332(f267(x39821,x39822),x39825),x39826)),f332(f332(x39824,x39825),x39826)) % 165.28/165.04 [4066]E(f332(f332(f42(x40661,f875(x40662,a862)),x40663),f332(f74(x40664,f875(x40662,a862),x40661,x40665),x40666)),f332(f332(f42(x40664,f875(x40662,a862)),f332(f311(x40661,x40664,x40666),x40663)),x40665)) % 165.28/165.04 [4118]E(f332(f332(f210(x41181,x41182),x41183),f332(f332(f210(x41184,x41181),x41185),x41186)),f332(f332(f210(x41184,x41182),f332(f74(x41181,x41182,x41184,x41183),x41185)),x41186)) % 165.28/165.04 [4120]E(f332(f332(f155(x41201,x41202),x41203),f332(f332(f155(x41204,x41201),x41205),x41206)),f332(f332(f155(x41204,x41202),f332(f74(x41201,x41202,x41204,x41203),x41205)),x41206)) % 165.28/165.04 [4125]E(f332(f311(x41251,x41252,f332(f74(x41253,x41252,x41251,x41254),x41255)),x41256),f332(f311(x41253,x41252,x41254),f332(f311(x41251,x41253,x41255),x41256))) % 165.28/165.04 [4126]E(f332(f312(x41261,x41262,f332(f74(x41263,x41262,x41261,x41264),x41265)),x41266),f332(f312(x41261,x41263,x41265),f332(f312(x41263,x41262,x41264),x41266))) % 165.28/165.04 [4155]E(f187(x41551,x41552,x41553,f332(f332(f332(f73(x41551,f872(x41552)),x41554),x41555),f332(f208(x41552),x41556))),f332(f332(f332(f73(x41551,f872(x41552)),f187(x41551,x41552,x41553,x41554)),x41555),f332(f208(x41552),x41556))) % 165.28/165.04 [4157]E(f332(f143(x41571,x41572,x41573,f332(f143(x41571,x41572,x41573,x41574),x41575)),x41576),f332(f143(x41571,x41572,x41573,x41574),f332(f332(f135(x41572),x41575),x41576))) % 165.28/165.04 [4297]E(f332(f272(x42971,x42971,x42972,x42973,f35(x42971),x42974),f332(f332(f267(x42971,x42972),x42975),x42976)),f332(f332(f267(x42971,x42973),x42975),f332(x42974,x42976))) % 165.28/165.04 [4298]E(f332(f272(x42981,x42982,x42983,x42983,x42984,f35(x42983)),f332(f332(f267(x42981,x42983),x42985),x42986)),f332(f332(f267(x42982,x42983),f332(x42984,x42985)),x42986)) % 165.28/165.04 [4388]E(f332(f332(f155(f874(x43881,x43882),f874(x43881,x43883)),f332(f271(x43881,x43882,f874(x43881,x43883)),f332(f332(f7(x43881,f875(x43882,x43883),f875(x43882,f874(x43881,x43883))),f332(f332(f8(f875(x43883,f874(x43881,x43883)),f875(f875(x43882,x43883),f875(x43882,f874(x43881,x43883))),x43881),f8(x43883,f874(x43881,x43883),x43882)),f267(x43881,x43883))),x43884))),f332(f332(f184(x43881,x43882),x43885),x43886)),f332(f332(f184(x43881,x43883),x43885),f332(f332(f155(x43882,x43883),x43884),x43886))) % 165.28/165.04 [3766]E(f97(x37661,x37662,x37663,f332(f332(f332(f93(x37661),x37664),x37665),x37666)),f332(f332(f332(x37663,x37664),x37665),x37666)) % 165.28/165.04 [3767]E(f98(x37671,x37672,x37673,f332(f332(f332(f93(x37671),x37674),x37675),x37676)),f332(f332(f332(x37673,x37674),x37675),x37676)) % 165.28/165.04 [3966]E(f332(f332(f74(x39661,x39662,x39663,f332(f16(x39662,x39661),x39664)),x39665),x39666),x39664) % 165.28/165.04 [4001]E(f332(f311(x40011,x40012,x40013),f332(f311(x40014,x40011,x40015),x40016)),f332(f311(x40014,x40012,f332(f332(f8(x40011,x40012,x40014),x40013),x40015)),x40016)) % 165.28/165.04 [4007]E(f332(f332(f42(x40071,f875(x40072,a862)),f332(f311(x40073,x40071,x40074),x40075)),x40076),f332(f332(f42(x40073,f875(x40072,a862)),x40075),f332(f332(f8(x40071,f875(x40072,a862),x40073),x40076),x40074))) % 165.28/165.04 [4008]E(f332(f332(f43(x40081,f875(x40082,a862)),f332(f311(x40083,x40081,x40084),x40085)),x40086),f332(f332(f43(x40083,f875(x40082,a862)),x40085),f332(f332(f8(x40081,f875(x40082,a862),x40083),x40086),x40084))) % 165.28/165.04 [4009]E(f332(f332(f42(x40091,f875(x40092,a862)),x40093),f332(f332(f8(x40094,f875(x40092,a862),x40091),x40095),x40096)),f332(f332(f42(x40094,f875(x40092,a862)),f332(f311(x40091,x40094,x40096),x40093)),x40095)) % 165.28/165.04 [4010]E(f332(f332(f43(x40101,f875(x40102,a862)),x40103),f332(f332(f8(x40104,f875(x40102,a862),x40101),x40105),x40106)),f332(f332(f43(x40104,f875(x40102,a862)),f332(f311(x40101,x40104,x40106),x40103)),x40105)) % 165.28/165.04 [4068]E(f332(f332(f42(x40681,f875(x40682,a862)),x40683),f332(f332(f8(f875(x40684,a862),f875(x40682,a862),x40681),f311(x40684,x40682,x40685)),x40686)),f332(f311(x40684,x40682,x40685),f332(f332(f42(x40681,f875(x40684,a862)),x40683),x40686))) % 165.28/165.04 [4069]E(f332(f332(f42(x40691,f875(x40692,a862)),x40693),f332(f332(f8(f875(x40694,a862),f875(x40692,a862),x40691),f312(x40692,x40694,x40695)),x40696)),f332(f312(x40692,x40694,x40695),f332(f332(f42(x40691,f875(x40694,a862)),x40693),x40696))) % 165.28/165.04 [4070]E(f332(f332(f43(x40701,f875(x40702,a862)),x40703),f332(f332(f8(f875(x40704,a862),f875(x40702,a862),x40701),f312(x40702,x40704,x40705)),x40706)),f332(f312(x40702,x40704,x40705),f332(f332(f43(x40701,f875(x40704,a862)),x40703),x40706))) % 165.28/165.04 [4071]E(f332(f332(f42(x40711,f875(x40712,a862)),x40713),f332(f332(f8(f875(x40714,a862),f875(x40712,a862),x40711),f286(x40714,x40712,x40715)),x40716)),f332(f286(x40714,x40712,x40715),f332(f332(f42(x40711,f875(x40714,a862)),x40713),x40716))) % 165.28/165.04 [4163]E(f332(f143(x41631,x41632,f332(f7(x41632,x41631,x41631),x41633),x41634),f332(f170(x41632),f332(f332(f152(x41632),x41635),x41636))),f332(f332(x41633,x41635),f332(f143(x41631,x41632,f332(f7(x41632,x41631,x41631),x41633),x41634),f332(f170(x41632),x41636)))) % 165.28/165.04 [4223]E(f332(f332(f18(f874(x42231,x42232),x42232,x42233),f332(f332(f8(x42234,f875(x42232,x42233),f874(x42231,x42232)),x42235),f332(f332(f8(x42231,x42234,f874(x42231,x42232)),x42236),f266(x42231,x42232)))),f270(x42231,x42232)),f332(f271(x42231,x42232,x42233),f332(f332(f8(x42234,f875(x42232,x42233),x42231),x42235),x42236))) % 165.28/165.04 [4230]E(f332(f143(x42301,x42302,f332(f7(x42302,x42301,x42301),x42303),f332(f143(x42301,x42302,f332(f7(x42302,x42301,x42301),x42303),x42304),f332(f170(x42302),x42305))),f332(f170(x42302),x42306)),f332(f143(x42301,x42302,f332(f7(x42302,x42301,x42301),x42303),x42304),f332(f170(x42302),f332(f332(f135(x42302),x42306),x42305)))) % 165.28/165.04 [4232]E(f332(f332(f155(f874(x42321,x42322),f874(x42323,x42322)),f332(f271(x42321,x42322,f874(x42323,x42322)),f332(f332(f8(x42323,f875(x42322,f874(x42323,x42322)),x42321),f267(x42323,x42322)),x42324))),f332(f332(f184(x42321,x42322),x42325),x42326)),f332(f332(f184(x42323,x42322),f332(f332(f155(x42321,x42323),x42324),x42325)),x42326)) % 165.28/165.04 [4280]P24(f332(f332(f246(f875(x42801,a862)),f332(f286(x42802,x42801,x42803),f332(f332(f43(x42804,f875(x42802,a862)),x42805),x42806))),f332(f332(f43(x42804,f875(x42801,a862)),x42805),f332(f332(f8(f875(x42802,a862),f875(x42801,a862),x42804),f286(x42802,x42801,x42803)),x42806)))) % 165.28/165.04 [4081]E(f332(f332(f184(x40811,x40812),f332(f332(f160(x40811,x40813),x40814),f332(f266(x40811,x40812),x40815))),f332(f332(f160(x40812,x40816),x40814),f332(f270(x40811,x40812),x40815))),f332(f332(f160(f874(x40811,x40812),f332(f332(f184(x40811,x40812),x40813),x40816)),x40814),x40815)) % 165.28/165.04 [4144]E(f332(f332(f113(f875(f874(x41441,x41442),a862)),f332(f332(f289(x41441,x41443,x41442),x41444),x41445)),f332(f332(f289(x41441,x41443,x41442),x41444),x41446)),f332(f332(f289(x41441,x41443,x41442),x41444),f332(f332(f113(f875(f874(x41443,x41442),a862)),x41445),x41446))) % 165.28/165.04 [4243]E(f332(f332(f310(f874(x42431,x42432)),f332(f332(f267(x42431,x42432),x42433),x42434)),f332(f332(f113(f875(f874(x42431,x42432),a862)),f332(f332(f269(x42431,x42432),x42435),f332(f16(f875(x42432,a862),x42431),f332(f332(f310(x42432),x42434),x42436)))),f332(f332(f269(x42431,x42432),f332(f332(f310(x42431),x42433),x42435)),f332(f16(f875(x42432,a862),x42431),x42436)))),f332(f332(f269(x42431,x42432),f332(f332(f310(x42431),x42433),x42435)),f332(f16(f875(x42432,a862),x42431),f332(f332(f310(x42432),x42434),x42436)))) % 165.28/165.04 [4321]E(f332(f332(f104(f875(x43211,a862)),f332(f312(x43211,x43212,f332(f74(f874(x43212,x43213),x43212,x43211,f266(x43212,x43213)),x43214)),x43215)),f332(f312(x43211,x43213,f332(f74(f874(x43212,x43213),x43213,x43211,f270(x43212,x43213)),x43214)),x43216)),f332(f312(x43211,f874(x43212,x43213),x43214),f332(f332(f269(x43212,x43213),x43215),f332(f16(f875(x43213,a862),x43212),x43216)))) % 165.28/165.04 [4065]E(f332(f332(f332(f73(x40651,x40652),f332(f332(f332(f73(x40651,x40652),x40653),x40654),x40655)),x40654),x40656),f332(f332(f332(f73(x40651,x40652),x40653),x40654),x40656)) % 165.28/165.04 [4169]E(f332(f332(f113(f875(f874(x41691,x41692),a862)),f332(f332(f289(x41691,x41693,x41692),x41694),x41695)),f332(f332(f289(x41691,x41693,x41692),x41696),x41695)),f332(f332(f289(x41691,x41693,x41692),f332(f332(f113(f875(f874(x41691,x41693),a862)),x41694),x41696)),x41695)) % 165.28/165.04 [4305]E(f332(f332(f42(x43051,f875(x43052,a862)),x43053),f332(f332(f7(x43051,f875(x43054,f875(x43052,a862)),f875(x43052,a862)),f332(f332(f8(f875(x43054,a862),f875(f875(x43054,f875(x43052,a862)),f875(x43052,a862)),x43051),f42(x43054,f875(x43052,a862))),x43055)),x43056)),f332(f332(f42(x43054,f875(x43052,a862)),f332(f332(f42(x43051,f875(x43054,a862)),x43053),x43055)),x43056)) % 165.28/165.04 [4306]E(f332(f332(f43(x43061,f875(x43062,a862)),x43063),f332(f332(f7(x43061,f875(x43064,f875(x43062,a862)),f875(x43062,a862)),f332(f332(f8(f875(x43064,a862),f875(f875(x43064,f875(x43062,a862)),f875(x43062,a862)),x43061),f43(x43064,f875(x43062,a862))),x43065)),x43066)),f332(f332(f43(x43064,f875(x43062,a862)),f332(f332(f42(x43061,f875(x43064,a862)),x43063),x43065)),x43066)) % 165.28/165.04 [4358]E(f332(f271(x43581,x43582,f874(x43583,x43584)),f332(f332(f7(x43581,f875(x43582,x43584),f875(x43582,f874(x43583,x43584))),f332(f332(f8(f875(x43584,f874(x43583,x43584)),f875(f875(x43582,x43584),f875(x43582,f874(x43583,x43584))),x43581),f8(x43584,f874(x43583,x43584),x43582)),f332(f332(f8(x43583,f875(x43584,f874(x43583,x43584)),x43581),f267(x43583,x43584)),x43585))),x43586)),f272(x43581,x43583,x43582,x43584,x43585,x43586)) % 165.28/165.04 [4279]E(f332(f332(f332(f73(x42791,f872(x42792)),f190(x42791,x42792,x42793,f332(f332(f22(f875(x42791,a862)),x42794),f332(f332(f310(x42791),x42795),f196(f875(x42791,a862)))))),x42795),x42796),f332(f332(f332(f73(x42791,f872(x42792)),f190(x42791,x42792,x42793,x42794)),x42795),x42796)) % 165.28/165.04 [4383]E(f332(f311(x43831,x43832,f332(f332(f18(x43831,x43832,x43832),f332(f332(f18(x43831,x43832,f875(x43832,x43832)),f332(f332(f8(a862,f875(x43832,f875(x43832,x43832)),x43831),f99(x43832)),x43833)),x43834)),x43835)),x43836),f332(f332(f113(f875(x43832,a862)),f332(f311(x43831,x43832,x43834),f332(f332(f104(f875(x43831,a862)),x43836),f332(f252(x43831),x43833)))),f332(f311(x43831,x43832,x43835),f332(f332(f104(f875(x43831,a862)),x43836),f332(f252(x43831),f332(f332(f8(a862,a862,x43831),a327),x43833)))))) % 165.28/165.04 [4394]E(f332(f311(x43941,f874(x43942,x43943),f332(f332(f18(x43941,x43943,f874(x43942,x43943)),f332(f332(f8(x43942,f875(x43943,f874(x43942,x43943)),x43941),f267(x43942,x43943)),x43944)),x43945)),x43946),f332(f332(f269(x43942,x43943),f332(f311(x43941,x43942,x43944),x43946)),f332(f332(f8(f875(x43941,a862),f875(x43943,a862),x43942),f311(x43941,x43943,x43945)),f332(f332(f7(x43942,f875(x43941,a862),f875(x43941,a862)),f332(f332(f8(f875(x43941,a862),f875(f875(x43941,a862),f875(x43941,a862)),x43942),f104(f875(x43941,a862))),f332(f332(f8(f875(x43942,a862),f875(x43941,a862),x43942),f312(x43941,x43942,x43944)),f332(f332(f7(x43942,f875(x43942,a862),f875(x43942,a862)),f310(x43942)),f196(f875(x43942,a862)))))),x43946)))) % 165.28/165.04 [4340]E(f332(f270(x43401,x43402),f332(f272(x43403,x43401,x43404,x43402,x43405,x43406),x43407)),f332(x43406,f332(f270(x43403,x43404),x43407))) % 165.28/165.04 [4341]E(f332(f266(x43411,x43412),f332(f272(x43413,x43411,x43414,x43412,x43415,x43416),x43417)),f332(x43415,f332(f266(x43413,x43414),x43417))) % 165.28/165.04 [4043]E(f332(f332(f184(x40431,x40432),f332(f332(f160(x40431,x40433),x40434),x40435)),f332(f332(f160(x40432,x40436),x40434),x40437)),f332(f332(f160(f874(x40431,x40432),f332(f332(f184(x40431,x40432),x40433),x40436)),x40434),f332(f332(f267(x40431,x40432),x40435),x40437))) % 165.28/165.04 [4111]E(f332(f332(f332(f273(x41111,x41112,x41113,x41114),x41115),x41116),x41117),f332(f332(f271(x41112,x41113,x41114),x41116),f332(x41115,x41117))) % 165.28/165.04 [4124]E(f332(f332(f332(f273(x41241,x41242,x41243,x41244),x41245),x41246),x41247),f332(f332(x41246,f332(f266(x41242,x41243),f332(x41245,x41247))),f332(f270(x41242,x41243),f332(x41245,x41247)))) % 165.28/165.04 [4159]E(f189(x41591,x41592,f332(f332(f332(f73(x41591,f872(x41592)),x41593),x41594),f332(f208(x41592),x41595)),x41596,x41597),f189(x41591,x41592,x41593,f332(f332(f152(x41591),x41594),x41596),f332(f332(f152(x41592),x41595),x41597))) % 165.28/165.04 [4178]E(f332(f74(x41781,x41782,x41783,x41784),f332(f74(x41785,x41781,x41783,x41786),x41787)),f332(f74(x41785,x41782,x41783,f332(f74(x41781,x41782,x41785,x41784),x41786)),x41787)) % 165.28/165.04 [4239]E(f332(f74(f872(x42391),f872(x42392),x42393,f332(f210(x42391,x42392),x42394)),f332(f332(f332(f73(x42393,f872(x42391)),x42395),x42396),f332(f208(x42391),x42397))),f332(f332(f332(f73(x42393,f872(x42392)),f332(f74(f872(x42391),f872(x42392),x42393,f332(f210(x42391,x42392),x42394)),x42395)),x42396),f332(f208(x42392),f332(x42394,x42397)))) % 165.28/165.04 [4365]E(f332(f272(x43651,x43652,x43653,x43653,x43654,f35(x43653)),f332(f272(x43651,x43651,x43655,x43653,f35(x43651),x43656),x43657)),f332(f332(f267(x43652,x43653),f332(x43654,f332(f266(x43651,x43655),x43657))),f332(x43656,f332(f270(x43651,x43655),x43657)))) % 165.28/165.04 [4366]E(f332(f272(x43661,x43661,x43662,x43663,f35(x43661),x43664),f332(f272(x43665,x43661,x43662,x43662,x43666,f35(x43662)),x43667)),f332(f332(f267(x43661,x43663),f332(x43666,f332(f266(x43665,x43662),x43667))),f332(x43664,f332(f270(x43665,x43662),x43667)))) % 165.28/165.04 [4381]E(f332(f272(x43811,x43812,x43813,x43813,x43814,f35(x43813)),f332(f272(x43815,x43811,x43813,x43813,x43816,f35(x43813)),x43817)),f332(f272(x43815,x43812,x43813,x43813,f332(f74(x43811,x43812,x43815,x43814),x43816),f35(x43813)),x43817)) % 165.28/165.04 [4382]E(f332(f272(x43821,x43821,x43822,x43823,f35(x43821),x43824),f332(f272(x43821,x43821,x43825,x43822,f35(x43821),x43826),x43827)),f332(f272(x43821,x43821,x43825,x43823,f35(x43821),f332(f74(x43822,x43823,x43825,x43824),x43826)),x43827)) % 165.28/165.04 [4391]E(f332(f272(x43911,x43912,x43913,x43913,x43914,f35(x43913)),f332(f272(x43911,x43911,x43915,x43913,f35(x43911),x43916),x43917)),f332(f272(x43912,x43912,x43915,x43913,f35(x43912),x43916),f332(f272(x43911,x43912,x43915,x43915,x43914,f35(x43915)),x43917))) % 165.28/165.04 [4078]E(f332(f332(f289(x40781,x40782,x40783),f332(f332(f289(x40781,x40784,x40782),x40785),x40786)),x40787),f332(f332(f289(x40781,x40784,x40783),x40785),f332(f332(f289(x40784,x40782,x40783),x40786),x40787))) % 165.28/165.04 [4150]E(f332(f332(f271(x41501,x41502,x41503),f332(f74(x41504,f875(x41502,x41503),x41501,x41505),x41506)),x41507),f332(f332(x41505,f332(x41506,f332(f266(x41501,x41502),x41507))),f332(f270(x41501,x41502),x41507))) % 165.28/165.04 [4203]E(f332(f74(x42031,x42032,x42033,x42034),f332(f332(f332(f73(x42033,x42031),x42035),x42036),x42037)),f332(f332(f332(f73(x42033,x42032),f332(f74(x42031,x42032,x42033,x42034),x42035)),x42036),f332(x42034,x42037))) % 165.28/165.04 [4235]E(f332(f143(x42351,x42352,f332(f7(x42352,x42351,x42351),x42353),x42354),f332(f170(x42352),f332(f332(f155(x42355,x42352),x42356),x42357))),f332(f143(x42351,x42355,f332(f7(x42355,x42351,x42351),f332(f74(x42352,f875(x42351,x42351),x42355,x42353),x42356)),x42354),f332(f170(x42355),x42357))) % 165.28/165.04 [4179]E(f332(f332(f42(x41791,f875(f874(x41792,x41793),a862)),x41794),f332(f332(f8(f875(f874(x41795,x41793),a862),f875(f874(x41792,x41793),a862),x41791),f332(f289(x41792,x41795,x41793),x41796)),x41797)),f332(f332(f289(x41792,x41795,x41793),x41796),f332(f332(f42(x41791,f875(f874(x41795,x41793),a862)),x41794),x41797))) % 165.28/165.04 [4327]E(f332(f332(f42(x43271,f875(f874(x43272,x43273),a862)),x43274),f332(f332(f7(x43271,f875(f874(x43275,x43273),a862),f875(f874(x43272,x43273),a862)),f332(f332(f8(f875(f874(x43272,x43275),a862),f875(f875(f874(x43275,x43273),a862),f875(f874(x43272,x43273),a862)),x43271),f289(x43272,x43275,x43273)),x43276)),x43277)),f332(f332(f289(x43272,x43275,x43273),f332(f332(f42(x43271,f875(f874(x43272,x43275),a862)),x43274),x43276)),x43277)) % 165.28/165.04 [4328]E(f332(f143(x43281,x43282,f332(f332(f7(x43281,f875(x43282,x43283),f875(x43282,x43281)),f332(f332(f8(f875(x43283,x43281),f875(f875(x43282,x43283),f875(x43282,x43281)),x43281),f8(x43283,x43281,x43282)),x43284)),x43285),x43286),x43287),f332(f143(x43281,x43283,x43284,x43286),f332(f332(f155(x43282,x43283),x43285),x43287))) % 165.28/165.04 [4392]E(f332(f332(f43(x43921,f875(x43922,a862)),x43923),f332(f332(f8(f875(x43924,f875(x43922,a862)),f875(x43922,a862),x43921),f332(f43(x43924,f875(x43922,a862)),x43925)),f332(f332(f7(x43921,f875(x43924,f875(x43922,a862)),f875(x43924,f875(x43922,a862))),f332(f332(f8(f875(f875(x43922,a862),f875(x43922,a862)),f875(f875(x43924,f875(x43922,a862)),f875(x43924,f875(x43922,a862))),x43921),f8(f875(x43922,a862),f875(x43922,a862),x43924)),f332(f332(f8(f875(x43922,a862),f875(f875(x43922,a862),f875(x43922,a862)),x43921),f113(f875(x43922,a862))),x43926))),x43927))),f332(f332(f113(f875(x43922,a862)),f332(f332(f43(x43921,f875(x43922,a862)),x43923),x43926)),f332(f332(f43(x43924,f875(x43922,a862)),x43925),x43927))) % 165.28/165.04 [4393]E(f332(f332(f42(x43931,f875(x43932,a862)),x43933),f332(f332(f8(f875(x43934,f875(x43932,a862)),f875(x43932,a862),x43931),f332(f42(x43934,f875(x43932,a862)),x43935)),f332(f332(f7(x43931,f875(x43934,f875(x43932,a862)),f875(x43934,f875(x43932,a862))),f332(f332(f8(f875(f875(x43932,a862),f875(x43932,a862)),f875(f875(x43934,f875(x43932,a862)),f875(x43934,f875(x43932,a862))),x43931),f8(f875(x43932,a862),f875(x43932,a862),x43934)),f332(f332(f8(f875(x43932,a862),f875(f875(x43932,a862),f875(x43932,a862)),x43931),f104(f875(x43932,a862))),x43936))),x43937))),f332(f332(f104(f875(x43932,a862)),f332(f332(f42(x43931,f875(x43932,a862)),x43933),x43936)),f332(f332(f42(x43934,f875(x43932,a862)),x43935),x43937))) % 165.28/165.04 [4386]E(f206(x43861,x43862,f332(f332(f332(x43863,x43864),x43865),x43866),f332(f332(f7(x43861,f874(a102,a102),f875(a102,f870(x43862))),f332(f332(f7(x43861,a102,f875(f874(a102,a102),f875(a102,f870(x43862)))),f332(f332(f7(x43861,a102,f875(a102,f875(f874(a102,a102),f875(a102,f870(x43862))))),x43867),x43864)),x43865)),x43866)),f332(f332(f332(f221(x43861,x43862,x43863,x43867),x43864),x43865),x43866)) % 165.28/165.04 [4399]E(f207(x43991,x43992,f332(f332(f332(x43993,x43994),x43995),x43996),f332(f332(f7(x43991,f874(a102,a102),f875(a102,f870(x43992))),f332(f332(f7(x43991,a102,f875(f874(a102,a102),f875(a102,f870(x43992)))),f332(f332(f7(x43991,a102,f875(a102,f875(f874(a102,a102),f875(a102,f870(x43992))))),x43997),x43994)),x43995)),x43996)),f223(x43991,x43992,x43993,x43997,x43994,x43995,x43996)) % 165.28/165.04 [4390]E(f203(x43901,x43902,f332(f332(f332(x43903,x43904),x43905),x43906),f332(f332(f7(x43901,f874(a102,a102),f875(a102,f870(f872(x43902)))),f332(f332(f7(x43901,a102,f875(f874(a102,a102),f875(a102,f870(f872(x43902))))),f332(f332(f7(x43901,a102,f875(a102,f875(f874(a102,a102),f875(a102,f870(f872(x43902)))))),x43907),x43904)),x43905)),x43906)),f332(f332(f332(f218(x43901,x43902,x43903,x43907),x43904),x43905),x43906)) % 165.28/165.04 [4401]E(f204(x44011,x44012,f332(f332(f332(x44013,x44014),x44015),x44016),f332(f332(f7(x44011,f874(a102,a102),f875(a102,f870(f872(x44012)))),f332(f332(f7(x44011,a102,f875(f874(a102,a102),f875(a102,f870(f872(x44012))))),f332(f332(f7(x44011,a102,f875(a102,f875(f874(a102,a102),f875(a102,f870(f872(x44012)))))),x44017),x44014)),x44015)),x44016)),f220(x44011,x44012,x44013,x44017,x44014,x44015,x44016)) % 165.28/165.04 [4299]E(f332(f272(x42991,x42992,x42993,x42994,x42995,x42996),f332(f332(f267(x42991,x42993),x42997),x42998)),f332(f332(f267(x42992,x42994),f332(x42995,x42997)),f332(x42996,x42998))) % 165.28/165.04 [4403]E(f332(f332(f155(f874(x44031,x44032),f874(x44033,x44034)),f332(f271(x44031,x44032,f874(x44033,x44034)),f332(f332(f7(x44031,f875(x44032,x44034),f875(x44032,f874(x44033,x44034))),f332(f332(f8(f875(x44034,f874(x44033,x44034)),f875(f875(x44032,x44034),f875(x44032,f874(x44033,x44034))),x44031),f8(x44034,f874(x44033,x44034),x44032)),f332(f332(f8(x44033,f875(x44034,f874(x44033,x44034)),x44031),f267(x44033,x44034)),x44035))),x44036))),f332(f332(f184(x44031,x44032),x44037),x44038)),f332(f332(f184(x44033,x44034),f332(f332(f155(x44031,x44033),x44035),x44037)),f332(f332(f155(x44032,x44034),x44036),x44038))) % 165.28/165.04 [4407]E(f332(f332(f155(f874(x44071,x44072),x44073),f332(f271(x44071,x44072,x44073),f332(f332(f8(f875(x44072,f874(x44071,x44074)),f875(x44072,x44073),x44071),f332(f8(f874(x44071,x44074),x44073,x44072),x44075)),f332(f332(f7(x44071,f875(x44072,x44074),f875(x44072,f874(x44071,x44074))),f332(f332(f8(f875(x44074,f874(x44071,x44074)),f875(f875(x44072,x44074),f875(x44072,f874(x44071,x44074))),x44071),f8(x44074,f874(x44071,x44074),x44072)),f267(x44071,x44074))),x44076)))),f332(f332(f184(x44071,x44072),x44077),x44078)),f332(f332(f155(f874(x44071,x44074),x44073),x44075),f332(f332(f184(x44071,x44074),x44077),f332(f332(f155(x44072,x44074),x44076),x44078)))) % 165.28/165.04 [4332]E(f332(f332(f155(f874(x43321,x43322),x43323),f332(f271(x43321,x43322,x43323),f332(f332(f8(f875(x43322,f874(x43324,x43322)),f875(x43322,x43323),x43321),f332(f8(f874(x43324,x43322),x43323,x43322),x43325)),f332(f332(f8(x43324,f875(x43322,f874(x43324,x43322)),x43321),f267(x43324,x43322)),x43326)))),f332(f332(f184(x43321,x43322),x43327),x43328)),f332(f332(f155(f874(x43324,x43322),x43323),x43325),f332(f332(f184(x43324,x43322),f332(f332(f155(x43321,x43324),x43326),x43327)),x43328))) % 165.28/165.04 [4290]E(f332(f332(f271(x42901,x42902,x42903),f332(f332(f8(f875(x42902,f874(x42904,x42905)),f875(x42902,x42903),x42901),f332(f8(f874(x42904,x42905),x42903,x42902),f332(f271(x42904,x42905,x42903),x42906))),x42907)),x42908),f332(f332(f271(x42904,x42905,x42903),x42906),f332(f332(f271(x42901,x42902,f874(x42904,x42905)),x42907),x42908))) % 165.28/165.04 [4408]E(f332(f332(f42(f874(x44081,x44082),f875(f874(x44083,x44084),a862)),f332(f332(f269(x44081,x44082),x44085),f332(f16(f875(x44082,a862),x44081),x44086))),f332(f271(x44081,x44082,f875(f874(x44083,x44084),a862)),f332(f332(f7(x44081,f875(x44082,f875(x44083,f875(x44084,a862))),f875(x44082,f875(f874(x44083,x44084),a862))),f332(f332(f8(f875(f875(x44083,f875(x44084,a862)),f875(f874(x44083,x44084),a862)),f875(f875(x44082,f875(x44083,f875(x44084,a862))),f875(x44082,f875(f874(x44083,x44084),a862))),x44081),f8(f875(x44083,f875(x44084,a862)),f875(f874(x44083,x44084),a862),x44082)),f332(f332(f8(f875(x44083,a862),f875(f875(x44083,f875(x44084,a862)),f875(f874(x44083,x44084),a862)),x44081),f269(x44083,x44084)),x44087))),f332(f332(f8(f875(x44084,a862),f875(x44083,f875(x44084,a862)),x44082),f16(f875(x44084,a862),x44083)),x44088)))),f332(f332(f269(x44083,x44084),f332(f332(f42(x44081,f875(x44083,a862)),x44085),x44087)),f332(f16(f875(x44084,a862),x44083),f332(f332(f42(x44082,f875(x44084,a862)),x44086),x44088)))) % 165.28/165.04 [4346]E(f332(f332(f273(x43461,x43462,x43463,x43464),f332(f332(f273(x43461,x43465,x43466,f874(x43462,x43463)),x43467),x43468)),x43469),f332(f332(f273(x43461,x43465,x43466,x43464),x43467),f332(f332(f7(x43465,f875(x43462,f875(x43463,x43464)),f875(x43466,x43464)),f332(f332(f8(f875(x43466,f874(x43462,x43463)),f875(f875(x43462,f875(x43463,x43464)),f875(x43466,x43464)),x43465),f273(x43466,x43462,x43463,x43464)),x43468)),x43469))) % 165.28/165.04 [4378]E(f332(f74(f874(x43781,x43782),f874(x43783,x43784),f874(x43785,x43786),f272(x43781,x43783,x43782,x43784,x43787,x43788)),f272(x43785,x43781,x43786,x43782,x43789,x437810)),f272(x43785,x43783,x43786,x43784,f332(f74(x43781,x43783,x43785,x43787),x43789),f332(f74(x43782,x43784,x43786,x43788),x437810))) % 165.28/165.04 [4384]E(f332(f272(x43841,x43842,x43843,x43844,x43845,x43846),f332(f272(x43847,x43841,x43848,x43843,x43849,x438410),x438411)),f332(f272(x43847,x43842,x43848,x43844,f332(f74(x43841,x43842,x43847,x43845),x43849),f332(f74(x43843,x43844,x43848,x43846),x438410)),x438411)) % 165.28/165.04 [4562]~P94(x45621)+E(f92(x45621),a329) % 165.28/165.04 [4563]~P27(x45631)+P27(f872(x45631)) % 165.28/165.04 [4564]~P59(x45641)+P59(f872(x45641)) % 165.28/165.04 [4565]~P102(x45651)+P102(f869(x45651)) % 165.28/165.04 [4568]~P141(x45681)+~E(f79(x45681),f2(x45681)) % 165.28/165.04 [4570]~E(x45701,f2(a102))+E(f332(a20,x45701),f2(a1)) % 165.28/165.04 [4571]~E(x45711,f2(a1))+E(f83(a1,x45711),f2(a1)) % 165.28/165.04 [4577]~P142(x45771)+P34(x45771,f2(x45771)) % 165.28/165.04 [4579]~P106(x45791)+P32(x45791,f116(x45791)) % 165.28/165.04 [4588]P24(x45881)+P24(f332(a327,x45881)) % 165.28/165.04 [4631]~P142(x46311)+~P34(x46311,f79(x46311)) % 165.28/165.04 [4678]~P24(x46781)+~P24(f332(a327,x46781)) % 165.28/165.04 [4701]E(f332(a107,x47011),f2(a868))+~P24(f332(a201,x47011)) % 165.28/165.04 [4767]~P99(x47671)+P11(x47671,x47671,f113(x47671)) % 165.28/165.04 [4768]~P100(x47681)+P11(x47681,x47681,f104(x47681)) % 165.28/165.04 [4769]~P95(x47691)+P11(x47691,x47691,f82(x47691)) % 165.28/165.04 [4770]~P106(x47701)+P11(x47701,x47701,f244(x47701)) % 165.28/165.04 [4771]~P106(x47711)+P11(x47711,x47711,f245(x47711)) % 165.28/165.04 [4772]~P71(x47721)+P12(x47721,x47721,f82(x47721)) % 165.28/165.04 [4574]~E(x45741,f2(a868))+E(f332(f103(a1),x45741),f2(a1)) % 165.28/165.04 [4581]~P92(x45811)+E(f332(f106(x45811),a84),f2(x45811)) % 165.28/165.04 [4584]~E(f520(x45841),f2(a868))+E(f332(f167(a868),x45841),f2(a868)) % 165.28/165.04 [4585]~P105(x45851)+E(f248(x45851,f246(x45851)),f244(x45851)) % 165.28/165.04 [4586]~P105(x45861)+E(f249(x45861,f246(x45861)),f245(x45861)) % 165.28/165.04 [4587]~P88(x45871)+E(f83(x45871,f2(x45871)),f2(x45871)) % 165.28/165.04 [4596]~P142(x45961)+E(f332(f103(x45961),f79(a868)),f79(x45961)) % 165.28/165.04 [4597]~P142(x45971)+E(f332(f103(x45971),f2(a868)),f2(x45971)) % 165.28/165.04 [4598]~P138(x45981)+E(f332(f105(x45981),f79(a1)),f79(x45981)) % 165.28/165.04 [4599]~P138(x45991)+E(f332(f105(x45991),f2(a1)),f2(x45991)) % 165.28/165.04 [4600]E(x46001,f2(a868))+~E(f332(f103(a1),x46001),f2(a1)) % 165.28/165.04 [4625]~P81(x46251)+E(f332(f80(x46251),f196(x46251)),f255(x46251)) % 165.28/165.04 [4626]~P81(x46261)+E(f332(f80(x46261),f255(x46261)),f196(x46261)) % 165.28/165.04 [4627]~P67(x46271)+E(f332(f80(x46271),f2(x46271)),f2(x46271)) % 165.28/165.04 [4628]~P118(x46281)+E(f332(f76(x46281),f79(x46281)),f79(x46281)) % 165.28/165.04 [4629]~P85(x46291)+E(f332(f76(x46291),f2(x46291)),f2(x46291)) % 165.28/165.04 [4630]~P80(x46301)+E(f332(f167(x46301),f116(x46301)),f2(x46301)) % 165.28/165.04 [4651]~P40(x46511)+P42(f332(f174(a1),x46511)) % 165.28/165.04 [4683]~P92(x46831)+E(f332(f80(x46831),f79(x46831)),f332(f106(x46831),a100)) % 165.28/165.04 [4700]~P92(x47001)+P34(x47001,f332(f106(x47001),a84)) % 165.28/165.04 [4717]~P59(x47171)+E(f332(f174(x47171),f56(x47171)),f255(f875(x47171,a862))) % 165.28/165.04 [4727]P40(x47271)+~P42(f332(f174(a1),x47271)) % 165.28/165.04 [4728]~P59(x47281)+P24(f332(f138(x47281),f56(x47281))) % 165.28/165.04 [4773]E(f332(f103(a1),f332(a107,x47731)),x47731)+P24(f332(a201,x47731)) % 165.28/165.04 [4842]~P110(x48421)+E(f258(x48421,f79(x48421),f82(x48421)),f257(x48421)) % 165.28/165.04 [4872]~P92(x48721)+~P34(x48721,f332(f106(x48721),a100)) % 165.28/165.04 [4882]E(f332(a26,x48821),f209(a863))+P24(f332(a25,f332(a28,x48821))) % 165.28/165.04 [5015]E(f332(f76(a1),x50151),x50151)+P24(f332(f332(f247(a1),x50151),f2(a1))) % 165.28/165.04 [5036]~E(f332(a107,x50361),f2(a868))+P24(f332(f332(f246(a1),x50361),f2(a1))) % 165.28/165.04 [5098]~P24(f332(a201,x50981))+P24(f332(f332(f247(a1),x50981),f2(a1))) % 165.28/165.04 [5138]~P112(x51381)+P24(f332(f332(f246(x51381),f2(x51381)),f79(x51381))) % 165.28/165.04 [5139]~P138(x51391)+P24(f332(f332(f334(x51391),f79(x51391)),f112(x51391))) % 165.28/165.04 [5140]~P142(x51401)+P24(f332(f332(f334(x51401),f79(x51401)),f194(x51401))) % 165.28/165.04 [5141]~P138(x51411)+P24(f332(f332(f334(x51411),f2(x51411)),f112(x51411))) % 165.28/165.04 [5142]~P142(x51421)+P24(f332(f332(f334(x51421),f2(x51421)),f194(x51421))) % 165.28/165.04 [5143]~P112(x51431)+P24(f332(f332(f247(x51431),f2(x51431)),f79(x51431))) % 165.28/165.04 [5145]E(f332(f208(a863),f535(x51451)),f332(a26,x51451))+~P24(f332(a25,f332(a28,x51451))) % 165.28/165.04 [5146]E(f332(f208(a863),f705(x51461)),f332(a26,x51461))+~P24(f332(a25,f332(a28,x51461))) % 165.28/165.04 [5201]E(x52011,f2(a868))+~P24(f332(f332(f246(a868),x52011),f2(a868))) % 165.28/165.04 [5246]E(f332(a107,x52461),f2(a868))+~P24(f332(f332(f246(a1),x52461),f2(a1))) % 165.28/165.04 [5312]P24(f332(a201,x53121))+~P24(f332(f332(f247(a1),x53121),f2(a1))) % 165.28/165.04 [5317]~P106(x53171)+P12(x53171,f869(x53171),f149(x53171,x53171,f5(x53171))) % 165.28/165.04 [5334]P42(x53341)+~P24(f332(f332(f246(a1),f2(a1)),f339(x53341))) % 165.28/165.04 [5340]E(f332(f76(a1),x53401),f332(f80(a1),x53401))+~P24(f332(f332(f247(a1),x53401),f2(a1))) % 165.28/165.04 [5512]~P112(x55121)+~P24(f332(f332(f246(x55121),f79(x55121)),f2(x55121))) % 165.28/165.04 [5513]~P112(x55131)+~P24(f332(f332(f247(x55131),f79(x55131)),f2(x55131))) % 165.28/165.04 [5523]~E(x55231,f2(a868))+P24(f332(f332(f246(a1),f332(f103(a1),x55231)),f2(a1))) % 165.28/165.04 [5524]~E(x55241,f2(a1))+P24(f332(f332(f247(a1),f332(f76(a1),x55241)),f79(a1))) % 165.28/165.04 [5645]~P80(x56451)+E(f143(x56451,x56451,f81(x56451),f2(x56451)),f167(x56451)) % 165.28/165.04 [5817]~P101(x58171)+P21(a868,x58171,f103(x58171),f255(f875(a868,a862))) % 165.28/165.04 [6013]E(x60131,f2(a868))+~P24(f332(f332(f246(a1),f332(f103(a1),x60131)),f2(a1))) % 165.28/165.04 [6014]E(x60141,f2(a1))+~P24(f332(f332(f247(a1),f332(f76(a1),x60141)),f79(a1))) % 165.28/165.04 [6814]~P24(f332(f332(f247(a1),x68141),f2(a1)))+P24(f332(f332(f247(a1),f332(f332(f81(a1),x68141),x68141)),f2(a1))) % 165.28/165.04 [7356]P24(f332(f332(f247(a1),x73561),f2(a1)))+~P24(f332(f332(f247(a1),f332(f332(f81(a1),x73561),x73561)),f2(a1))) % 165.28/165.04 [7910]E(x79101,f332(a3,f2(a868)))+P24(f332(f332(f247(a868),f332(f332(f22(a868),f332(a19,x79101)),f332(a115,f2(a868)))),f332(a19,x79101))) % 165.28/165.04 [8654]~P24(f332(f332(f247(a1),x86541),f2(a1)))+P24(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f81(a1),x86541),x86541)),a100)),f2(a1))) % 165.28/165.04 [8740]~P24(f332(f332(f247(a1),x87401),f2(a1)))+P24(f332(f332(f247(a1),f332(f332(f81(a1),f332(f332(f81(a1),f79(a1)),x87401)),x87401)),f2(a1))) % 165.28/165.04 [9053]P24(f332(f332(f247(a1),x90531),f2(a1)))+~P24(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f81(a1),x90531),x90531)),a100)),f2(a1))) % 165.28/165.04 [9114]P24(f332(f332(f247(a1),x91141),f2(a1)))+~P24(f332(f332(f247(a1),f332(f332(f81(a1),f332(f332(f81(a1),f79(a1)),x91141)),x91141)),f2(a1))) % 165.28/165.04 [4671]~E(a84,x46711)+E(f332(f332(f81(a1),x46711),x46711),a84) % 165.28/165.04 [4672]~E(x46721,a84)+E(f332(f332(f81(a1),x46721),x46721),a84) % 165.28/165.04 [4686]E(x46861,f2(a1))+E(f332(f332(f39(a1),x46861),x46861),f79(a1)) % 165.28/165.04 [4818]E(x48181,a84)+~E(f332(f332(f81(a1),x48181),x48181),a84) % 165.28/165.04 [4819]E(a84,x48191)+~E(f332(f332(f81(a1),x48191),x48191),a84) % 165.28/165.04 [4832]~P106(x48321)+E(f140(x48321,f196(f875(x48321,a862))),f116(x48321)) % 165.28/165.04 [4833]~P30(x48331)+E(f40(x48331,f196(f875(x48331,a862))),f196(x48331)) % 165.28/165.04 [4834]~P30(x48341)+E(f40(x48341,f255(f875(x48341,a862))),f255(x48341)) % 165.28/165.04 [4835]~P30(x48351)+E(f41(x48351,f196(f875(x48351,a862))),f255(x48351)) % 165.28/165.04 [4836]~P30(x48361)+E(f41(x48361,f255(f875(x48361,a862))),f196(x48361)) % 165.28/165.04 [4973]E(x49731,f2(a868))+P24(f332(f332(f247(a868),f2(a868)),x49731)) % 165.28/165.04 [4992]~P31(x49921)+P24(f332(f332(f246(a1),f2(a1)),x49921)) % 165.28/165.04 [5027]~E(f332(f106(a868),x50271),f2(a868))+P24(f332(f332(f246(a1),x50271),a84)) % 165.28/165.04 [5032]P42(x50321)+P24(f332(f332(f334(a1),f339(x50321)),x50321)) % 165.28/165.04 [5033]E(x50331,f332(a3,f2(a868)))+P24(f332(f332(f246(a102),f79(a102)),x50331)) % 165.28/165.04 [5072]P24(f332(a201,x50721))+P24(f332(f332(f246(a1),f2(a1)),x50721)) % 165.28/165.04 [5120]E(f332(f103(a1),f332(a107,x51201)),f2(a1))+P24(f332(f332(f246(a1),f2(a1)),x51201)) % 165.28/165.04 [5187]E(f332(f103(a1),f332(f106(a868),x51871)),f332(f106(a1),x51871))+P24(f332(a201,f332(f106(a1),x51871))) % 165.28/165.04 [5207]E(f332(f106(a868),x52071),f2(a868))+~P24(f332(a201,f332(f106(a1),x52071))) % 165.28/165.04 [5208]E(f332(f106(a868),x52081),f2(a868))+~P24(f332(f332(f246(a1),x52081),a84)) % 165.28/165.04 [5243]P31(x52431)+~P24(f332(f332(f246(a1),f2(a1)),x52431)) % 165.28/165.04 [5320]E(f332(a115,f790(x53201)),x53201)+~P24(f332(f332(f247(a868),f2(a868)),x53201)) % 165.28/165.04 [5328]E(f332(a115,f332(f106(a868),x53281)),f79(a868))+~P24(f332(a201,f332(f106(a1),x53281))) % 165.28/165.04 [5336]E(f332(f103(a1),f396(x53361)),x53361)+~P24(f332(f332(f247(a1),f2(a1)),x53361)) % 165.28/165.04 [5343]~E(x53431,f332(a3,f2(a868)))+~P24(f332(f332(f246(a102),f79(a102)),x53431)) % 165.28/165.04 [5350]E(f332(f103(a1),f332(f106(a868),x53501)),f2(a1))+~P24(f332(a201,f332(f106(a1),x53501))) % 165.28/165.04 [5376]E(f332(f167(a868),x53761),f2(a868))+P24(f332(f332(f334(a868),f520(x53761)),f332(f174(a868),x53761))) % 165.28/165.04 [5397]E(f332(f103(a1),f332(a107,x53971)),x53971)+~P24(f332(f332(f246(a1),f2(a1)),x53971)) % 165.28/165.04 [5406]~P24(f332(a201,x54061))+~P24(f332(f332(f246(a1),f2(a1)),x54061)) % 165.28/165.04 [5505]E(f332(f332(f81(a868),f79(a868)),f332(f106(a868),x55051)),f79(a868))+~P24(f332(f332(f247(a1),x55051),a84)) % 165.28/165.04 [5565]E(x55651,f2(a868))+~P24(f332(f332(f247(a868),x55651),f332(a115,f2(a868)))) % 165.28/165.04 [5604]E(f332(f332(f22(a868),f332(f106(a868),x56041)),f79(a868)),f2(a868))+~P24(f332(f332(f246(a1),x56041),a84)) % 165.28/165.04 [5605]E(f332(f332(f81(a868),f332(f106(a868),x56051)),f79(a868)),f79(a868))+~P24(f332(f332(f247(a1),x56051),a84)) % 165.28/165.04 [5615]~P42(x56151)+E(f332(f38(a868),f332(f311(a1,a868,a107),x56151)),f332(f38(a1),x56151)) % 165.28/165.04 [5646]~P106(x56461)+E(f248(x56461,f332(f7(x56461,x56461,a862),f246(x56461))),f245(x56461)) % 165.28/165.04 [5647]~P106(x56471)+E(f249(x56471,f332(f7(x56471,x56471,a862),f246(x56471))),f244(x56471)) % 165.28/165.04 [5657]E(f45(a868,f332(a115,f2(a868)),f332(f106(a868),x56571)),f332(a115,f2(a868)))+~P24(f332(a201,f332(f106(a1),x56571))) % 165.28/165.04 [5666]~P24(f332(f332(f247(a1),f2(a1)),x56661))+P24(f332(f332(f246(a1),f79(a1)),x56661)) % 165.28/165.04 [5667]P24(f332(f332(f247(a1),f2(a1)),x56671))+~P24(f332(f332(f246(a1),f79(a1)),x56671)) % 165.28/165.04 [5678]E(f332(a115,f332(f332(f22(a868),x56781),f79(a868))),x56781)+~P24(f332(f332(f247(a868),f2(a868)),x56781)) % 165.28/165.04 [5736]P24(f332(f332(f247(a868),f2(a868)),f396(x57361)))+~P24(f332(f332(f247(a1),f2(a1)),x57361)) % 165.28/165.04 [5795]E(f45(a1,f332(f106(a1),a100),x57951),f332(f332(f22(a1),x57951),f79(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x57951)) % 165.28/165.04 [5829]~P24(f332(f332(f247(a1),a84),x58291))+P24(f332(f332(f247(a868),f2(a868)),f332(f106(a868),x58291))) % 165.28/165.04 [5879]P24(f332(f332(f247(a868),f2(a868)),f332(a107,x58791)))+~P24(f332(f332(f247(a1),f2(a1)),x58791)) % 165.28/165.04 [5930]~P24(f332(f332(f247(a868),f2(a868)),x59301))+P24(f332(f332(f247(a1),f2(a1)),f332(f103(a1),x59301))) % 165.28/165.04 [5965]~P24(f332(f332(f247(a868),f2(a868)),f332(a107,x59651)))+P24(f332(f332(f247(a1),f2(a1)),x59651)) % 165.28/165.04 [5979]~P42(x59791)+E(f332(f311(a868,a1,f103(a1)),f332(f311(a1,a868,a107),x59791)),x59791) % 165.28/165.04 [5994]P24(f332(f332(f247(a1),a84),x59941))+~P24(f332(f332(f247(a868),f2(a868)),f332(f106(a868),x59941))) % 165.28/165.04 [6042]~P59(x60421)+E(f332(f332(f152(f872(x60421)),f209(x60421)),f332(f332(f155(x60421,f872(x60421)),f208(x60421)),f56(x60421))),f56(f872(x60421))) % 165.28/165.04 [6053]P24(f332(f332(f247(a868),f2(a868)),x60531))+~P24(f332(f332(f247(a1),f2(a1)),f332(f103(a1),x60531))) % 165.28/165.04 [6170]E(f332(f311(a868,a1,f103(a1)),f332(f253(a868),f332(a107,x61701))),f332(f302(a1,f2(a1)),x61701))+~P24(f332(f332(f246(a1),f2(a1)),x61701)) % 165.28/165.04 [6186]~P112(x61861)+P24(f332(f332(f247(x61861),f2(x61861)),f332(f332(f81(x61861),f79(x61861)),f79(x61861)))) % 165.28/165.04 [6237]P24(f332(f332(f247(a868),f332(a115,f2(a868))),f332(a107,x62371)))+~P24(f332(f332(f247(a1),f79(a1)),x62371)) % 165.28/165.04 [6331]E(x63311,f2(a1))+P24(f332(f49(f2(a1),x63311),f332(f332(f267(a1,a1),f2(a1)),f2(a1)))) % 165.28/165.04 [6499]~P24(f332(f332(f247(a868),f332(a115,f2(a868))),f332(a107,x64991)))+P24(f332(f332(f247(a1),f79(a1)),x64991)) % 165.28/165.04 [6924]~P111(x69241)+P41(x69241,f332(f252(f874(x69241,x69241)),f332(f271(x69241,x69241,a862),f247(x69241)))) % 165.28/165.04 [5552]E(f332(f106(a868),f332(f332(f22(a1),x55521),a100)),f332(a115,f332(f106(a868),x55521)))+P24(f332(a201,f332(f106(a1),x55521))) % 165.28/165.04 [5568]~P40(x55681)+E(f332(f332(f155(a868,a1),f103(a1)),f332(f332(f155(a1,a868),a107),x55681)),x55681) % 165.28/165.04 [5684]E(f332(f80(a1),f332(f103(a1),f332(a115,f365(x56841)))),x56841)+~P24(f332(f332(f247(a1),x56841),f2(a1))) % 165.28/165.04 [5694]E(f332(f332(f81(a868),f79(a868)),f332(f106(a868),x56941)),f332(f106(a868),f332(f332(f22(a1),x56941),a100)))+P24(f332(f332(f247(a1),x56941),a84)) % 165.28/165.04 [5738]E(f332(f332(f39(a1),f332(f106(a1),a100)),x57381),f332(f106(a1),a100))+~P24(f332(f332(f247(a1),f2(a1)),x57381)) % 165.28/165.04 [5825]E(f332(f332(f22(a868),f332(f106(a868),x58251)),f79(a868)),f332(f106(a868),f332(f332(f81(a1),x58251),a100)))+P24(f332(f332(f246(a1),x58251),a84)) % 165.28/165.04 [5826]E(f332(f332(f81(a868),f332(f106(a868),x58261)),f79(a868)),f332(f106(a868),f332(f332(f22(a1),x58261),a100)))+P24(f332(f332(f247(a1),x58261),a84)) % 165.28/165.04 [5867]E(f332(a107,f332(f332(f81(a1),f79(a1)),x58671)),f332(a115,f332(a107,x58671)))+~P24(f332(f332(f246(a1),f2(a1)),x58671)) % 165.28/165.04 [5903]E(f332(a115,f332(f332(f22(a868),x59031),f332(a115,f2(a868)))),x59031)+~P24(f332(f332(f247(a868),f2(a868)),x59031)) % 165.28/165.04 [6113]E(f45(a868,f332(a115,f2(a868)),f332(f106(a868),x61131)),f332(a107,f45(a1,f79(a1),f332(f106(a1),x61131))))+P24(f332(a201,f332(f106(a1),x61131))) % 165.28/165.04 [6160]~P24(f332(f332(f246(a1),a84),x61601))+P24(f332(f332(f246(a1),a84),f332(f332(f81(a1),x61601),x61601))) % 165.28/165.04 [6161]~P24(f332(f332(f247(a1),a100),x61611))+P24(f332(f332(f246(a1),a100),f332(f332(f81(a1),x61611),x61611))) % 165.28/165.04 [6162]~P24(f332(f332(f247(a1),a84),x61621))+P24(f332(f332(f247(a1),a84),f332(f332(f81(a1),x61621),x61621))) % 165.28/165.04 [6163]~P24(f332(f332(f247(a1),a100),x61631))+P24(f332(f332(f247(a1),a100),f332(f332(f81(a1),x61631),x61631))) % 165.28/165.04 [6164]~P24(f332(f332(f92(a1),a84),x61641))+P24(f332(f332(f92(a1),a84),f332(f332(f81(a1),x61641),x61641))) % 165.28/165.04 [6344]~P24(f332(f62(x63441),f255(f875(x63441,a862))))+P24(f332(f62(f872(x63441)),f255(f875(f872(x63441),a862)))) % 165.28/165.04 [6431]~P24(f332(f332(f246(a1),f2(a1)),x64311))+P24(f332(f332(f247(a1),f2(a1)),f332(f332(f81(a1),f79(a1)),x64311))) % 165.28/165.04 [6438]E(f332(f266(a1,a1),f47(f79(a1),f332(f106(a1),x64381))),f332(f332(f39(a1),f79(a1)),f332(f106(a1),x64381)))+~P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x64381))) % 165.28/165.04 [6458]E(f332(f270(a1,a1),f47(f79(a1),f332(f106(a1),x64581))),f45(a1,f79(a1),f332(f106(a1),x64581)))+~P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x64581))) % 165.28/165.04 [6470]P24(f332(f62(x64701),f255(f875(x64701,a862))))+~P24(f332(f62(f872(x64701)),f255(f875(f872(x64701),a862)))) % 165.28/165.04 [6500]P24(f332(f332(f246(a1),a84),x65001))+~P24(f332(f332(f246(a1),a84),f332(f332(f81(a1),x65001),x65001))) % 165.28/165.04 [6501]P24(f332(f332(f247(a1),a84),x65011))+~P24(f332(f332(f247(a1),a84),f332(f332(f81(a1),x65011),x65011))) % 165.28/165.04 [6502]P24(f332(f332(f247(a1),a100),x65021))+~P24(f332(f332(f246(a1),a100),f332(f332(f81(a1),x65021),x65021))) % 165.28/165.04 [6503]P24(f332(f332(f247(a1),a100),x65031))+~P24(f332(f332(f247(a1),a100),f332(f332(f81(a1),x65031),x65031))) % 165.28/165.04 [6504]P24(f332(f332(f92(a1),a84),x65041))+~P24(f332(f332(f92(a1),a84),f332(f332(f81(a1),x65041),x65041))) % 165.28/165.04 [6818]~P24(f332(f62(x68181),f255(f875(x68181,a862))))+P24(f332(f332(f247(a868),f2(a868)),f332(f38(x68181),f255(f875(x68181,a862))))) % 165.28/165.04 [7399]P24(f332(f62(a868),x73991))+~P24(f332(f62(a1),f332(f311(a868,a1,f103(a1)),x73991))) % 165.28/165.04 [5480]~E(a100,x54801)+E(f332(f332(f22(a1),f332(f332(f81(a1),x54801),x54801)),a100),a100) % 165.28/165.04 [5481]~E(x54811,a100)+E(f332(f332(f22(a1),f332(f332(f81(a1),x54811),x54811)),a100),a100) % 165.28/165.04 [5987]E(x59871,a100)+~E(f332(f332(f22(a1),f332(f332(f81(a1),x59871),x59871)),a100),a100) % 165.28/165.04 [5988]E(a100,x59881)+~E(f332(f332(f22(a1),f332(f332(f81(a1),x59881),x59881)),a100),a100) % 165.28/165.04 [6400]~E(f332(f106(a868),x64001),f2(a868))+P24(f332(a201,f332(f106(a1),f332(f332(f81(a1),x64001),a100)))) % 165.28/165.04 [6744]~P24(f332(a201,f332(f106(a1),x67441)))+P24(f332(a201,f332(f106(a1),f332(f332(f81(a1),x67441),x67441)))) % 165.28/165.04 [6745]~P24(f332(f332(f246(a1),x67451),a84))+P24(f332(f332(f246(a1),f332(f332(f81(a1),x67451),x67451)),a84)) % 165.28/165.04 [6746]~P24(f332(f332(f246(a1),x67461),a100))+P24(f332(f332(f246(a1),f332(f332(f81(a1),x67461),x67461)),a100)) % 165.28/165.04 [6747]~P24(f332(f332(f247(a1),x67471),a84))+P24(f332(f332(f247(a1),f332(f332(f81(a1),x67471),x67471)),a84)) % 165.28/165.04 [6748]~P24(f332(f332(f246(a1),x67481),a100))+P24(f332(f332(f247(a1),f332(f332(f81(a1),x67481),x67481)),a100)) % 165.28/165.04 [6749]~P24(f332(f332(f92(a1),x67491),a84))+P24(f332(f332(f92(a1),f332(f332(f81(a1),x67491),x67491)),a84)) % 165.28/165.04 [7069]E(f332(f106(a868),x70691),f2(a868))+~P24(f332(a201,f332(f106(a1),f332(f332(f81(a1),x70691),a100)))) % 165.28/165.04 [7308]~P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x73081)))+P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),f332(f332(f81(a1),x73081),x73081)))) % 165.28/165.04 [7309]P24(f332(a201,f332(f106(a1),x73091)))+~P24(f332(a201,f332(f106(a1),f332(f332(f81(a1),x73091),x73091)))) % 165.28/165.04 [7310]P24(f332(f332(f246(a1),x73101),a84))+~P24(f332(f332(f246(a1),f332(f332(f81(a1),x73101),x73101)),a84)) % 165.28/165.04 [7311]P24(f332(f332(f246(a1),x73111),a100))+~P24(f332(f332(f246(a1),f332(f332(f81(a1),x73111),x73111)),a100)) % 165.28/165.04 [7312]P24(f332(f332(f246(a1),x73121),a100))+~P24(f332(f332(f247(a1),f332(f332(f81(a1),x73121),x73121)),a100)) % 165.28/165.04 [7313]P24(f332(f332(f247(a1),x73131),a84))+~P24(f332(f332(f247(a1),f332(f332(f81(a1),x73131),x73131)),a84)) % 165.28/165.04 [7314]P24(f332(f332(f92(a1),x73141),a84))+~P24(f332(f332(f92(a1),f332(f332(f81(a1),x73141),x73141)),a84)) % 165.28/165.04 [7681]E(f332(a109,f685(x76811)),x76811)+~P24(f332(f332(f334(f875(f874(a868,a868),a862)),x76811),a101)) % 165.28/165.04 [6317]~P92(x63171)+E(f332(f106(x63171),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f79(x63171)) % 165.28/165.04 [6796]~P24(f332(a201,f332(f106(a1),x67961)))+E(f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),x67961),x67961)),a100)),f2(a868)) % 165.28/165.04 [7856]~P24(f332(f332(f247(a1),f332(f106(a1),x78561)),f2(a1)))+E(f332(f266(a1,a1),f332(a51,f50(f332(f80(a1),f79(a1)),f332(f80(a1),f332(f106(a1),x78561))))),f332(f332(f39(a1),f79(a1)),f332(f106(a1),x78561))) % 165.28/165.04 [7869]~P24(f332(f332(f247(a1),f332(f106(a1),x78691)),f2(a1)))+E(f332(f270(a1,a1),f332(a51,f50(f332(f80(a1),f79(a1)),f332(f80(a1),f332(f106(a1),x78691))))),f45(a1,f79(a1),f332(f106(a1),x78691))) % 165.28/165.04 [7916]~P24(f332(f332(f246(a1),a84),x79161))+P24(f332(f332(f246(a1),a84),f332(f332(f22(a1),f332(f332(f81(a1),x79161),x79161)),a100))) % 165.28/165.04 [7917]~P24(f332(f332(f246(a1),a100),x79171))+P24(f332(f332(f246(a1),a100),f332(f332(f22(a1),f332(f332(f81(a1),x79171),x79171)),a100))) % 165.28/165.04 [7918]~P24(f332(f332(f246(a1),a84),x79181))+P24(f332(f332(f247(a1),a84),f332(f332(f22(a1),f332(f332(f81(a1),x79181),x79181)),a100))) % 165.28/165.04 [7919]~P24(f332(f332(f247(a1),a100),x79191))+P24(f332(f332(f247(a1),a100),f332(f332(f22(a1),f332(f332(f81(a1),x79191),x79191)),a100))) % 165.28/165.04 [7920]~P24(f332(f332(f92(a1),a100),x79201))+P24(f332(f332(f92(a1),a100),f332(f332(f22(a1),f332(f332(f81(a1),x79201),x79201)),a100))) % 165.28/165.04 [8219]~P92(x82191)+~P34(x82191,f332(f106(x82191),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))) % 165.28/165.04 [8394]P24(f332(f332(f246(a1),a84),x83941))+~P24(f332(f332(f246(a1),a84),f332(f332(f22(a1),f332(f332(f81(a1),x83941),x83941)),a100))) % 165.28/165.04 [8395]P24(f332(f332(f246(a1),a84),x83951))+~P24(f332(f332(f247(a1),a84),f332(f332(f22(a1),f332(f332(f81(a1),x83951),x83951)),a100))) % 165.28/165.04 [8396]P24(f332(f332(f246(a1),a100),x83961))+~P24(f332(f332(f246(a1),a100),f332(f332(f22(a1),f332(f332(f81(a1),x83961),x83961)),a100))) % 165.28/165.04 [8397]P24(f332(f332(f247(a1),a100),x83971))+~P24(f332(f332(f247(a1),a100),f332(f332(f22(a1),f332(f332(f81(a1),x83971),x83971)),a100))) % 165.28/165.04 [8398]P24(f332(f332(f92(a1),a100),x83981))+~P24(f332(f332(f92(a1),a100),f332(f332(f22(a1),f332(f332(f81(a1),x83981),x83981)),a100))) % 165.28/165.04 [8698]E(f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),x86981),x86981)),a100)),f332(f332(f87(a868,a868),f332(f106(a868),x86981)),f332(f332(f8(a868,a868,a868),a115),f332(f332(f18(a868,a868,a868),f81(a868)),f5(a868)))))+P24(f332(a201,f332(f106(a1),x86981))) % 165.28/165.04 [9511]E(x95111,f196(f875(f874(a868,a868),a862)))+P24(f332(f332(f334(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),x95111),f196(f875(f874(a868,a868),a862)))),a69)) % 165.28/165.04 [8629]~P24(f332(a201,f332(f106(a1),x86291)))+P24(f332(a201,f332(f106(a1),f332(f332(f22(a1),f332(f332(f81(a1),x86291),x86291)),a100)))) % 165.28/165.04 [8630]~P24(f332(f332(f247(a1),x86301),a84))+P24(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f81(a1),x86301),x86301)),a100)),a84)) % 165.28/165.04 [8631]~P24(f332(f332(f246(a1),x86311),a100))+P24(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f81(a1),x86311),x86311)),a100)),a100)) % 165.28/165.04 [8632]~P24(f332(f332(f247(a1),x86321),a84))+P24(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f81(a1),x86321),x86321)),a100)),a84)) % 165.28/165.04 [8633]~P24(f332(f332(f247(a1),x86331),a100))+P24(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f81(a1),x86331),x86331)),a100)),a100)) % 165.28/165.04 [8634]~P24(f332(f332(f92(a1),x86341),a100))+P24(f332(f332(f92(a1),f332(f332(f22(a1),f332(f332(f81(a1),x86341),x86341)),a100)),a100)) % 165.28/165.04 [8733]~P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x87331)))+P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),f332(f332(f22(a1),f332(f332(f81(a1),x87331),x87331)),a100)))) % 165.28/165.04 [8889]~P92(x88891)+E(f332(f332(f81(x88891),f79(x88891)),f79(x88891)),f332(f106(x88891),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))) % 165.28/165.04 [9037]P24(f332(a201,f332(f106(a1),x90371)))+~P24(f332(a201,f332(f106(a1),f332(f332(f22(a1),f332(f332(f81(a1),x90371),x90371)),a100)))) % 165.28/165.04 [9038]P24(f332(f332(f246(a1),x90381),a100))+~P24(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f81(a1),x90381),x90381)),a100)),a100)) % 165.28/165.04 [9039]P24(f332(f332(f247(a1),x90391),a84))+~P24(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f81(a1),x90391),x90391)),a100)),a84)) % 165.28/165.04 [9040]P24(f332(f332(f247(a1),x90401),a84))+~P24(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f81(a1),x90401),x90401)),a100)),a84)) % 165.28/165.04 [9041]P24(f332(f332(f247(a1),x90411),a100))+~P24(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f81(a1),x90411),x90411)),a100)),a100)) % 165.28/165.04 [9042]P24(f332(f332(f92(a1),x90421),a100))+~P24(f332(f332(f92(a1),f332(f332(f22(a1),f332(f332(f81(a1),x90421),x90421)),a100)),a100)) % 165.28/165.04 [9557]~P24(f332(f62(f874(a868,a868)),x95571))+P24(f332(f332(f334(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),f196(f875(f874(a868,a868),a862))),x95571)),a70)) % 165.28/165.04 [9349]~P142(x93491)+E(f332(f332(f257(x93491),f79(x93491)),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f79(x93491)) % 165.28/165.04 [9350]~P142(x93501)+E(f332(f332(f257(x93501),f2(x93501)),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f2(x93501)) % 165.28/165.04 [9786]~P24(f332(f332(f247(a868),f79(a868)),x97861))+P24(f332(f332(f247(a868),f2(a868)),f332(f332(f39(a868),x97861),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))) % 165.28/165.04 [9796]~P24(f332(f332(f247(a868),f2(a868)),x97961))+P24(f332(f332(f247(a868),f2(a868)),f332(f332(f39(a868),f332(f332(f81(a868),x97961),f79(a868))),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))) % 165.28/165.04 [9839]~E(f45(a868,x98391,f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f79(a868))+P24(f332(f332(f247(a868),f2(a868)),f45(a868,x98391,f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))) % 165.28/165.04 [9858]E(f45(a868,x98581,f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f79(a868))+~P24(f332(f332(f247(a868),f2(a868)),f45(a868,x98581,f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))) % 165.28/165.04 [4604]~P41(x46041,x46042)+P56(x46041,x46042) % 165.28/165.04 [4605]~P47(x46051,x46052)+P56(x46051,x46052) % 165.28/165.04 [4566]~E(x45661,x45662)+E(f279(x45661,x45662),f79(a102)) % 165.28/165.04 [4569]E(f228(x45691,x45692),x45691)+~E(x45692,f2(a868)) % 165.28/165.04 [4576]~E(x45762,f116(x45761))+E(f153(x45761,x45762),f116(x45761)) % 165.28/165.04 [4595]~E(f153(x45952,x45951),f116(x45952))+E(x45951,f116(x45952)) % 165.28/165.04 [4609]~P25(x46092)+P25(f875(x46091,x46092)) % 165.28/165.04 [4610]~P104(x46102)+P104(f875(x46101,x46102)) % 165.28/165.04 [4611]~P105(x46112)+P105(f875(x46111,x46112)) % 165.28/165.04 [4612]~P107(x46122)+P107(f875(x46121,x46122)) % 165.28/165.04 [4613]~P26(x46132)+P26(f875(x46131,x46132)) % 165.28/165.04 [4614]~P26(x46142)+P99(f875(x46141,x46142)) % 165.28/165.04 [4615]~P96(x46152)+P64(f875(x46151,x46152)) % 165.28/165.04 [4616]~P65(x46162)+P65(f875(x46161,x46162)) % 165.28/165.04 [4617]~P81(x46172)+P81(f875(x46171,x46172)) % 165.28/165.04 [4618]~P82(x46182)+P82(f875(x46181,x46182)) % 165.28/165.04 [4619]~P26(x46192)+P100(f875(x46191,x46192)) % 165.28/165.04 [4620]~P97(x46202)+P97(f875(x46201,x46202)) % 165.28/165.04 [4621]~P109(x46212)+P109(f875(x46211,x46212)) % 165.28/165.04 [4622]~P96(x46222)+P98(f875(x46221,x46222)) % 165.28/165.04 [4623]~P30(x46232)+P30(f875(x46231,x46232)) % 165.28/165.04 [4624]~P96(x46242)+P96(f875(x46241,x46242)) % 165.28/165.04 [4636]E(x46361,x46362)+~E(f332(a28,x46361),f332(a28,x46362)) % 165.28/165.04 [4638]E(x46381,x46382)+~E(f332(a115,x46381),f332(a115,x46382)) % 165.28/165.04 [4639]E(x46391,x46392)+~E(f332(a109,x46391),f332(a109,x46392)) % 165.28/165.04 [4640]E(x46401,x46402)+~E(f332(a3,x46401),f332(a3,x46402)) % 165.28/165.04 [4642]E(x46421,x46422)+~E(f332(a19,x46421),f332(a19,x46422)) % 165.28/165.04 [4746]~P28(x47461)+E(f45(x47461,x47462,x47462),f2(x47461)) % 165.28/165.04 [4780]~P41(x47801,x47802)+P41(f869(x47801),f146(x47801,x47802)) % 165.28/165.04 [4781]~P41(x47811,x47812)+P41(f869(x47811),f147(x47811,x47812)) % 165.28/165.04 [4877]~P41(x48771,x48772)+P41(f875(x48771,a862),f325(x48771,x48772)) % 165.28/165.04 [4878]~P41(x48781,x48782)+P41(f875(x48781,a862),f323(x48781,x48782)) % 165.28/165.04 [4998]~P31(x49981)+P42(f303(a1,x49981,x49982)) % 165.28/165.04 [5101]~P41(x51011,x51012)+P58(x51011,f68(x51011,x51011,x51012)) % 165.28/165.04 [5609]~P77(x56091)+P21(x56091,x56091,f80(x56091),x56092) % 165.28/165.04 [4590]~E(x45902,f116(x45901))+E(f332(f169(x45901),x45902),f116(x45901)) % 165.28/165.04 [4591]~E(x45912,f116(x45911))+E(f332(f170(x45911),x45912),f116(x45911)) % 165.28/165.04 [4646]E(x46461,f332(a107,x46462))+~E(f332(f103(a1),x46461),x46462) % 165.28/165.04 [4649]E(x46491,f116(x46492))+~E(f332(f169(x46492),x46491),f116(x46492)) % 165.28/165.04 [4650]E(x46501,f116(x46502))+~E(f332(f170(x46502),x46501),f116(x46502)) % 165.28/165.04 [4668]~P92(x46681)+E(f332(f106(x46681),x46682),f332(f105(x46681),x46682)) % 165.28/165.04 [4675]~E(x46752,f209(x46751))+E(f239(x46751,x46752),f196(f875(x46751,a862))) % 165.28/165.04 [4677]~P27(x46771)+P24(f332(f62(x46771),x46772)) % 165.28/165.04 [4684]E(x46841,f209(x46842))+E(f332(f208(x46842),f338(x46842,x46841)),x46841) % 165.28/165.04 [4685]E(x46851,f209(x46852))+E(f332(f208(x46852),f382(x46852,x46851)),x46851) % 165.28/165.04 [4687]~E(f568(x46872,x46871),f116(x46871))+E(f182(x46871,x46872),f116(f869(x46871))) % 165.28/165.04 [4696]~E(x46962,f116(x46961))+E(f332(f174(x46961),x46962),f196(f875(x46961,a862))) % 165.28/165.04 [4697]~E(x46972,f116(x46971))+E(f196(f875(x46971,a862)),f332(f174(x46971),x46972)) % 165.28/165.04 [4699]E(x46991,x46992)+~E(f332(f103(a1),x46991),f332(f103(a1),x46992)) % 165.28/165.04 [4702]E(f226(x47021,x47022),f2(a868))+P24(f332(f62(x47021),x47022)) % 165.28/165.04 [4722]~P118(x47221)+E(f83(x47221,f83(x47221,x47222)),f83(x47221,x47222)) % 165.28/165.04 [4735]~P113(x47351)+E(f332(f332(f257(x47351),x47352),f79(a868)),x47352) % 165.28/165.04 [4736]~P79(x47361)+E(f332(f332(f257(x47361),x47362),f79(a868)),x47362) % 165.28/165.04 [4740]E(x47401,x47402)+E(f279(x47401,x47402),f332(f332(f81(a102),x47402),f79(a102))) % 165.28/165.04 [4743]E(f332(f38(x47431),x47432),f2(a868))+P24(f332(f62(x47431),x47432)) % 165.28/165.04 [4747]~E(f153(x47471,x47472),x47472)+P24(f332(f138(x47471),x47472)) % 165.28/165.04 [4750]~P64(x47501)+E(f332(f332(f113(x47501),x47502),f196(x47501)),x47502) % 165.28/165.04 [4751]~P67(x47511)+E(f332(f332(f22(x47511),x47512),f2(x47511)),x47512) % 165.28/165.04 [4752]~P98(x47521)+E(f332(f332(f104(x47521),x47522),f255(x47521)),x47522) % 165.28/165.04 [4753]~P113(x47531)+E(f332(f332(f81(x47531),x47532),f2(x47531)),x47532) % 165.28/165.04 [4754]~P74(x47541)+E(f332(f332(f81(x47541),x47542),f2(x47541)),x47542) % 165.28/165.04 [4755]~P80(x47551)+E(f332(f332(f81(x47551),x47552),f2(x47551)),x47552) % 165.28/165.04 [4756]~P73(x47561)+E(f332(f332(f82(x47561),x47562),f79(x47561)),x47562) % 165.28/165.04 [4757]~P113(x47571)+E(f332(f332(f82(x47571),x47572),f79(x47571)),x47572) % 165.28/165.04 [4758]~P79(x47581)+E(f332(f332(f82(x47581),x47582),f79(x47581)),x47582) % 165.28/165.04 [4759]~P28(x47591)+E(f332(f332(f39(x47591),x47592),f79(x47591)),x47592) % 165.28/165.04 [4760]~P116(x47601)+E(f332(f332(f290(x47601),x47602),f79(x47601)),x47602) % 165.28/165.04 [4761]~P113(x47611)+E(f332(f332(f257(x47611),x47612),f2(a868)),f79(x47611)) % 165.28/165.04 [4762]~P110(x47621)+E(f332(f332(f257(x47621),x47622),f2(a868)),f79(x47621)) % 165.28/165.04 [4763]~E(x47632,f196(f875(x47631,a862)))+E(f332(f38(x47631),x47632),f2(a868)) % 165.28/165.04 [4774]~P28(x47741)+E(f45(x47741,x47742,f2(x47741)),x47742) % 165.28/165.04 [4782]~P98(x47821)+E(f332(f332(f113(x47821),x47822),f255(x47821)),f255(x47821)) % 165.28/165.04 [4783]~P64(x47831)+E(f332(f332(f104(x47831),x47832),f196(x47831)),f196(x47831)) % 165.28/165.04 [4784]~P113(x47841)+E(f332(f332(f82(x47841),x47842),f2(x47841)),f2(x47841)) % 165.28/165.04 [4785]~P128(x47851)+E(f332(f332(f82(x47851),x47852),f2(x47851)),f2(x47851)) % 165.28/165.04 [4786]~P28(x47861)+E(f332(f332(f39(x47861),x47862),f2(x47861)),f2(x47861)) % 165.28/165.04 [4787]~P117(x47871)+E(f332(f332(f290(x47871),x47872),f2(x47871)),f2(x47871)) % 165.28/165.04 [4788]E(x47881,f209(x47882))+~E(f239(x47882,x47881),f196(f875(x47882,a862))) % 165.28/165.04 [4790]~P28(x47901)+E(f45(x47901,x47902,f79(x47901)),f2(x47901)) % 165.28/165.04 [4791]~P28(x47911)+E(f45(x47911,f2(x47911),x47912),f2(x47911)) % 165.28/165.04 [4820]E(x48201,f2(a868))+E(f55(x48202,x48201,f116(x48202)),f116(f869(x48202))) % 165.28/165.04 [4844]P41(x48441,x48442)+~E(f689(x48442,x48441),f196(f875(x48441,a862))) % 165.28/165.04 [4845]E(x48451,f116(x48452))+~E(f332(f174(x48452),x48451),f196(f875(x48452,a862))) % 165.28/165.04 [4846]E(x48461,f116(x48462))+~E(f196(f875(x48462,a862)),f332(f174(x48462),x48461)) % 165.28/165.04 [4849]~E(x48491,x48492)+P24(f332(f332(a329,x48491),x48492)) % 165.28/165.04 [4859]P24(x48591)+P24(f332(f332(a335,x48591),x48592)) % 165.28/165.04 [4860]E(x48601,f116(x48602))+E(f332(f332(f166(x48602),x48601),f2(a868)),f332(f142(x48602),x48601)) % 165.28/165.04 [4863]E(f153(x48631,x48632),x48632)+~P24(f332(f138(x48631),x48632)) % 165.28/165.04 [4868]~P24(x48682)+P24(f332(f332(a331,x48681),x48682)) % 165.28/165.04 [4869]~P24(x48691)+P24(f332(f332(a331,x48691),x48692)) % 165.28/165.04 [4870]~P24(x48702)+P24(f332(f332(a335,x48701),x48702)) % 165.28/165.04 [4880]~E(f521(x48802,x48801),f532(x48802,x48801))+P24(f332(f138(x48801),x48802)) % 165.28/165.04 [4888]E(f332(f252(x48881),x48882),f196(f875(x48881,a862)))+P24(f332(x48882,f393(x48882))) % 165.28/165.04 [4889]E(f196(f875(x48891,a862)),f332(f252(x48891),x48892))+P24(f332(x48892,f425(x48892))) % 165.28/165.04 [4955]~P118(x49551)+E(f332(f332(f82(x49551),x49552),f83(x49551,x49552)),f332(f76(x49551),x49552)) % 165.28/165.04 [4966]~E(x49661,f2(a1))+E(f46(x49661,x49662),f332(f332(f267(a1,a1),f2(a1)),f2(a1))) % 165.28/165.04 [4997]~P56(x49971,x49972)+P56(x49971,f332(f287(x49971,x49971),x49972)) % 165.28/165.04 [5016]~E(f332(a26,x50161),f332(f208(a863),x50162))+P24(f332(a25,f332(a28,x50161))) % 165.28/165.04 [5021]E(x50211,x50212)+~P24(f332(f332(a329,x50211),x50212)) % 165.28/165.04 [5025]~P24(f332(a25,x50252))+P24(f332(a25,f33(x50251,x50252))) % 165.28/165.04 [5034]P24(x50341)+~P24(f332(f332(a330,x50342),x50341)) % 165.28/165.04 [5035]P24(x50351)+~P24(f332(f332(a330,x50351),x50352)) % 165.28/165.04 [5040]~P109(x50401)+P24(f332(f332(f246(x50401),x50402),f255(x50401))) % 165.28/165.04 [5044]E(x50441,x50442)+~E(f332(x50441,f427(x50442,x50441)),f332(x50442,f427(x50442,x50441))) % 165.28/165.04 [5074]E(x50741,f2(a868))+E(f228(x50741,f45(a868,x50742,x50741)),f228(x50742,x50741)) % 165.28/165.04 [5079]~P106(x50791)+P32(x50791,f332(f332(f152(x50791),x50792),f116(x50791))) % 165.28/165.04 [5081]E(x50811,f2(a1))+P24(f332(f49(x50812,x50811),f46(x50812,x50811))) % 165.28/165.04 [5099]~E(x50991,x50992)+P24(f332(f332(f247(a868),x50991),f332(a115,x50992))) % 165.28/165.04 [5109]~E(x51091,f2(a868))+P24(f332(f332(f247(a868),x51091),f332(a115,x51092))) % 165.28/165.04 [5119]P24(f332(x51191,x51192))+P24(f332(f332(f246(a1),f2(a1)),f359(x51191))) % 165.28/165.04 [5155]P24(f332(a25,x51551))+~P24(f332(a25,f33(x51552,x51551))) % 165.28/165.04 [5157]P24(f332(a25,x51571))+~P24(f332(a25,f34(x51572,x51571))) % 165.28/165.04 [5159]P24(f332(a25,x51591))+~P24(f332(a25,f34(x51591,x51592))) % 165.28/165.04 [5191]P56(x51911,x51912)+~P56(x51911,f332(f287(x51911,x51911),x51912)) % 165.28/165.04 [5194]~E(f45(a868,x51942,x51941),f2(a868))+E(f332(f332(f82(a868),x51941),f394(x51941,x51942)),x51942) % 165.28/165.04 [5195]~E(f45(a1,x51952,x51951),f2(a1))+E(f332(f332(f82(a1),x51951),f395(x51951,x51952)),x51952) % 165.28/165.04 [5222]~P24(f332(x52221,x52222))+P24(f332(f332(f246(a1),f2(a1)),f340(x52221))) % 165.28/165.04 [5234]E(f332(f332(f22(a868),f332(a107,x52341)),f332(a107,x52342)),f332(a107,x52341))+~P24(f332(a201,x52342)) % 165.28/165.04 [5267]E(f280(x52671,x52672),f79(a102))+~P24(f332(f332(f246(a102),x52671),f79(a102))) % 165.28/165.04 [5362]E(f332(f332(f166(x53621),x53622),f521(x53622,x53621)),f332(f332(f166(x53621),x53622),f532(x53622,x53621)))+P24(f332(f138(x53621),x53622)) % 165.28/165.04 [5407]~P24(f332(x54071,f91(x54072,x54071)))+P24(f332(x54071,f533(x54072,x54071))) % 165.28/165.04 [5470]P58(x54701,x54702)+~P24(f332(f320(x54701,x54702),f649(x54702,x54701))) % 165.28/165.04 [5616]~E(f332(a115,f45(a868,x56161,x56162)),x56162)+E(f45(a868,f332(a115,x56161),x56162),f2(a868)) % 165.28/165.04 [5673]P41(x56731,x56732)+P24(f332(f332(f334(x56731),f737(x56732,x56731)),f738(x56732,x56731))) % 165.28/165.04 [5680]~P138(x56801)+P24(f332(f332(f334(x56801),f332(f103(x56801),x56802)),f112(x56801))) % 165.28/165.04 [5681]~P142(x56811)+P24(f332(f332(f334(x56811),f332(f103(x56811),x56812)),f194(x56811))) % 165.28/165.04 [5682]~P138(x56821)+P24(f332(f332(f334(x56821),f332(f105(x56821),x56822)),f112(x56821))) % 165.28/165.04 [5683]~P92(x56831)+P24(f332(f332(f334(x56831),f332(f106(x56831),x56832)),f112(x56831))) % 165.28/165.04 [5828]E(f332(a115,f45(a868,x58281,x58282)),x58282)+E(f45(a868,f332(a115,x58281),x58282),f332(a115,f45(a868,x58281,x58282))) % 165.28/165.04 [6249]P41(x62491,x62492)+~P24(f332(f332(f334(x62491),f651(x62492,x62491)),f321(x62491,x62492))) % 165.28/165.04 [6283]~P112(x62831)+~P24(f332(f332(f247(x62831),f332(f103(x62831),x62832)),f2(x62831))) % 165.28/165.04 [6284]~P85(x62841)+~P24(f332(f332(f247(x62841),f332(f76(x62841),x62842)),f2(x62841))) % 165.28/165.04 [6373]P24(f332(f332(f247(a1),x63731),f45(a1,x63732,x63731)))+~P24(f332(f332(f247(a1),x63731),f2(a1))) % 165.28/165.04 [6472]E(f332(f332(f310(a868),f332(a115,x64721)),f303(a868,x64722,x64721)),f303(a868,x64722,f332(a115,x64721)))+~P24(f332(f332(f246(a868),x64722),f332(a115,x64721))) % 165.28/165.04 [6560]~P106(x65601)+P32(x65601,f151(x65601,x65601,f5(x65601),x65602)) % 165.28/165.04 [6688]E(f332(f169(x66881),x66882),x66882)+~P24(f332(f332(f246(a868),f332(f197(f869(x66881)),x66882)),f79(a868))) % 165.28/165.04 [6708]~P85(x67081)+P24(f332(f332(f246(x67081),f332(f80(x67081),f332(f76(x67081),x67082))),f2(x67081))) % 165.28/165.04 [6741]~P41(x67411,x67412)+P41(x67411,f332(f332(f289(x67411,x67411,x67411),x67412),f308(x67411,x67412))) % 165.28/165.04 [6962]~P24(f332(f332(f247(a1),x69622),f2(a1)))+P24(f332(f332(f246(a1),f45(a1,x69621,x69622)),f2(a1))) % 165.28/165.04 [7353]~P142(x73531)+E(f198(x73531,f332(f332(f7(x73531,x73531,x73531),f81(x73531)),f79(x73531)),x73532,f2(x73531)),f332(f103(x73531),x73532)) % 165.28/165.04 [7381]~P121(x73811)+~P24(f332(f332(f247(x73811),f332(f332(f82(x73811),x73812),x73812)),f2(x73811))) % 165.28/165.04 [9948]~P118(x99481)+~P24(f332(f332(f247(x99481),f332(f332(f257(x99481),x99482),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f2(x99481))) % 165.28/165.04 [4647]~E(x46472,f116(x46471))+E(f332(f197(f869(x46471)),x46472),f2(a868)) % 165.28/165.04 [4688]~E(x46881,f2(a868))+E(f332(f332(f81(a868),x46881),x46882),x46882) % 165.28/165.04 [4689]~E(x46892,f2(a868))+E(f332(f332(f82(a868),x46891),x46892),f2(a868)) % 165.28/165.04 [4691]~E(x46911,f2(a868))+E(f332(f332(f82(a868),x46911),x46912),f2(a868)) % 165.28/165.04 [4692]~E(x46922,f2(a868))+E(f332(f332(f257(a868),x46921),x46922),f79(a868)) % 165.28/165.04 [4693]~E(x46932,f2(a1))+E(f332(f332(f39(a1),x46931),x46932),f2(a1)) % 165.28/165.04 [4703]E(x47031,f116(x47032))+~E(f332(f197(f869(x47032)),x47031),f2(a868)) % 165.28/165.04 [4704]~P26(x47041)+E(f332(f332(f113(x47041),x47042),x47042),x47042) % 165.28/165.04 [4706]~P99(x47061)+E(f332(f332(f113(x47061),x47062),x47062),x47062) % 165.28/165.04 [4707]~P26(x47071)+E(f332(f332(f104(x47071),x47072),x47072),x47072) % 165.28/165.04 [4709]~P100(x47091)+E(f332(f332(f104(x47091),x47092),x47092),x47092) % 165.28/165.04 [4711]~P95(x47111)+E(f332(f332(f82(x47111),x47112),x47112),x47112) % 165.28/165.04 [4713]~P106(x47131)+E(f332(f332(f244(x47131),x47132),x47132),x47132) % 165.28/165.04 [4715]~P106(x47151)+E(f332(f332(f245(x47151),x47152),x47152),x47152) % 165.28/165.04 [4734]~P67(x47341)+E(f332(f332(f22(x47341),x47342),x47342),f2(x47341)) % 165.28/165.04 [4748]~P67(x47481)+E(f332(f80(x47481),f332(f80(x47481),x47482)),x47482) % 165.28/165.04 [4749]~P81(x47491)+E(f332(f80(x47491),f332(f80(x47491),x47492)),x47492) % 165.28/165.04 [4766]~E(x47662,f2(a868))+E(f332(f332(f257(a868),x47661),x47662),f332(a115,f2(a868))) % 165.28/165.04 [4799]~P64(x47991)+E(f332(f332(f113(x47991),f196(x47991)),x47992),x47992) % 165.28/165.04 [4800]~P98(x48001)+E(f332(f332(f104(x48001),f255(x48001)),x48002),x48002) % 165.28/165.04 [4801]~P113(x48011)+E(f332(f332(f81(x48011),f2(x48011)),x48012),x48012) % 165.28/165.04 [4802]~P74(x48021)+E(f332(f332(f81(x48021),f2(x48021)),x48022),x48022) % 165.28/165.04 [4803]~P80(x48031)+E(f332(f332(f81(x48031),f2(x48031)),x48032),x48032) % 165.28/165.04 [4804]~P73(x48041)+E(f332(f332(f82(x48041),f79(x48041)),x48042),x48042) % 165.28/165.04 [4805]~P113(x48051)+E(f332(f332(f82(x48051),f79(x48051)),x48052),x48052) % 165.28/165.04 [4806]~P79(x48061)+E(f332(f332(f82(x48061),f79(x48061)),x48062),x48062) % 165.28/165.04 [4825]~P98(x48251)+E(f332(f332(f113(x48251),f255(x48251)),x48252),f255(x48251)) % 165.28/165.04 [4826]~P64(x48261)+E(f332(f332(f104(x48261),f196(x48261)),x48262),f196(x48261)) % 165.28/165.04 [4827]~P113(x48271)+E(f332(f332(f82(x48271),f2(x48271)),x48272),f2(x48271)) % 165.28/165.04 [4828]~P128(x48281)+E(f332(f332(f82(x48281),f2(x48281)),x48282),f2(x48281)) % 165.28/165.04 [4829]~P79(x48291)+E(f332(f332(f257(x48291),f79(x48291)),x48292),f79(x48291)) % 165.28/165.04 [4830]~P28(x48301)+E(f332(f332(f39(x48301),f2(x48301)),x48302),f2(x48301)) % 165.28/165.04 [4831]~P116(x48311)+E(f332(f332(f290(x48311),f2(x48311)),x48312),f2(x48311)) % 165.28/165.04 [4839]E(x48391,f116(x48392))+E(f145(x48392,f332(f170(x48392),x48391)),f332(f142(x48392),x48391)) % 165.28/165.04 [4840]E(x48401,f116(x48402))+E(f332(f142(x48402),f332(f170(x48402),x48401)),f145(x48402,x48401)) % 165.28/165.04 [4841]E(x48411,f2(a868))+~E(f332(f332(f81(a868),x48412),x48411),x48412) % 165.28/165.04 [4847]~P138(x48471)+E(f332(f105(x48471),f332(f103(a1),x48472)),f332(f103(x48471),x48472)) % 165.28/165.04 [4848]~P92(x48481)+E(f332(f105(x48481),f332(f106(a1),x48482)),f332(f106(x48481),x48482)) % 165.28/165.04 [4855]E(x48551,f79(a868))+~E(f332(f332(f82(a868),x48552),x48551),f79(a868)) % 165.28/165.04 [4856]E(x48561,f79(a868))+~E(f332(f332(f82(a868),x48561),x48562),f79(a868)) % 165.28/165.04 [4857]E(x48571,f2(a868))+~E(f332(f332(f81(a868),x48572),x48571),f2(a868)) % 165.28/165.04 [4858]E(x48581,f2(a868))+~E(f332(f332(f81(a868),x48581),x48582),f2(a868)) % 165.28/165.04 [4873]~P85(x48731)+E(f332(f76(x48731),f332(f80(x48731),x48732)),f332(f76(x48731),x48732)) % 165.28/165.04 [4874]~P118(x48741)+E(f332(f76(x48741),f332(f103(x48741),x48742)),f332(f103(x48741),x48742)) % 165.28/165.04 [4875]~P85(x48751)+E(f332(f76(x48751),f332(f76(x48751),x48752)),f332(f76(x48751),x48752)) % 165.28/165.04 [4876]~P74(x48761)+E(f332(f167(x48761),f332(f170(x48761),x48762)),f332(f167(x48761),x48762)) % 165.28/165.04 [4881]~E(x48811,f332(a115,f2(a868)))+E(f332(f332(f257(a868),x48811),x48812),f332(a115,f2(a868))) % 165.28/165.04 [4891]~P67(x48911)+E(f332(f332(f22(x48911),f2(x48911)),x48912),f332(f80(x48911),x48912)) % 165.28/165.04 [4892]~E(x48922,f2(a868))+E(f140(a868,f332(f302(a868,x48921),x48922)),f116(a868)) % 165.28/165.04 [4901]~P92(x49011)+E(f332(f332(f81(x49011),x49012),f332(f106(x49011),a84)),x49012) % 165.28/165.04 [4902]E(x49021,f2(a1))+E(f47(f332(f76(a1),x49022),f332(f76(a1),x49021)),f53(x49022,x49021)) % 165.28/165.04 [4918]~E(x49181,x49182)+P24(f332(f332(f246(a868),x49181),x49182)) % 165.28/165.04 [4925]~E(x49251,f2(a102))+E(f332(f332(f81(a868),f332(a19,x49251)),x49252),x49252) % 165.28/165.04 [4926]~E(f332(f106(a1),x49262),f332(f103(a1),x49261))+E(x49261,f332(a107,f332(f106(a1),x49262))) % 165.28/165.04 [4935]~P31(x49351)+P31(f332(f332(f257(a1),x49351),x49352)) % 165.28/165.04 [4936]~P81(x49361)+E(f332(f332(f113(x49361),x49362),f332(f80(x49361),x49362)),f255(x49361)) % 165.28/165.04 [4937]~P81(x49371)+E(f332(f332(f104(x49371),x49372),f332(f80(x49371),x49372)),f196(x49371)) % 165.28/165.04 [4938]~P67(x49381)+E(f332(f332(f81(x49381),x49382),f332(f80(x49381),x49382)),f2(x49381)) % 165.28/165.04 [4963]E(x49631,f2(a868))+~E(f332(f80(a1),f332(f103(a1),x49632)),f332(f103(a1),x49631)) % 165.28/165.04 [4964]E(x49641,f2(a868))+~E(f332(f80(a1),f332(f103(a1),x49641)),f332(f103(a1),x49642)) % 165.28/165.04 [4974]E(f202(x49741,x49742),f2(a1))+P24(f332(f332(f246(a1),x49742),x49741)) % 165.28/165.04 [4975]E(f181(x49751,x49752),f116(a1))+P24(f332(f332(f246(a1),x49751),x49752)) % 165.28/165.04 [4988]E(x49881,f332(a115,f2(a868)))+~E(f332(f332(f82(a868),x49882),x49881),f332(a115,f2(a868))) % 165.28/165.04 [4989]E(x49891,f332(a115,f2(a868)))+~E(f332(f332(f82(a868),x49891),x49892),f332(a115,f2(a868))) % 165.28/165.04 [4990]~P104(x49901)+P24(f332(f332(f246(x49901),x49902),x49902)) % 165.28/165.04 [4991]~P94(x49911)+P24(f332(f332(f92(x49911),x49912),x49912)) % 165.28/165.04 [4994]~P92(x49941)+E(f332(f332(f82(x49941),x49942),f332(f106(x49941),a100)),f332(f80(x49941),x49942)) % 165.28/165.04 [5012]~P138(x50121)+E(f332(f80(x50121),f332(f105(x50121),x50122)),f332(f105(x50121),f332(f80(a1),x50122))) % 165.28/165.04 [5013]~P92(x50131)+E(f332(f80(x50131),f332(f106(x50131),x50132)),f332(f106(x50131),f332(f80(a1),x50132))) % 165.28/165.04 [5045]~E(x50451,f332(a115,x50452))+P24(f332(f332(f247(a868),f2(a868)),x50451)) % 165.28/165.04 [5062]~P106(x50621)+E(f332(f80(f875(x50621,a862)),f332(f253(x50621),x50622)),f332(f254(x50621),x50622)) % 165.28/165.04 [5063]~P106(x50631)+E(f332(f80(f875(x50631,a862)),f332(f304(x50631),x50632)),f332(f301(x50631),x50632)) % 165.28/165.04 [5064]~P106(x50641)+E(f332(f80(f875(x50641,a862)),f332(f254(x50641),x50642)),f332(f253(x50641),x50642)) % 165.28/165.04 [5065]~P106(x50651)+E(f332(f80(f875(x50651,a862)),f332(f301(x50651),x50652)),f332(f304(x50651),x50652)) % 165.28/165.04 [5073]~E(f332(f103(a1),x50732),x50731)+P24(f332(f332(f246(a1),f2(a1)),x50731)) % 165.28/165.04 [5080]~E(x50802,f2(a1))+E(f53(x50801,x50802),f332(f332(f267(a1,a1),f2(a1)),f332(f76(a1),x50801))) % 165.28/165.04 [5082]~P25(x50821)+P24(f332(f332(f246(x50821),f196(x50821)),x50822)) % 165.28/165.04 [5114]E(x51141,x51142)+~E(f332(f332(f81(a1),x51141),x51141),f332(f332(f81(a1),x51142),x51142)) % 165.28/165.04 [5118]~P24(f332(x51181,x51182))+P24(f332(x51181,f332(a107,f340(x51181)))) % 165.28/165.04 [5144]~P118(x51441)+E(f332(f332(f82(x51441),f83(x51441,x51442)),f332(f76(x51441),x51442)),x51442) % 165.28/165.04 [5153]~E(x51532,f2(a868))+E(f86(f874(a868,a868),f48(x51531,x51532)),f332(f332(f267(a868,a868),f2(a868)),x51531)) % 165.28/165.04 [5164]~E(x51641,x51642)+~P24(f332(f332(f247(a868),x51641),x51642)) % 165.28/165.04 [5165]~E(x51651,x51652)+~P24(f332(f332(f247(a1),x51651),x51652)) % 165.28/165.04 [5168]~P142(x51681)+E(f332(f332(f81(x51681),f79(x51681)),f332(f103(x51681),x51682)),f332(f103(x51681),f332(a115,x51682))) % 165.28/165.04 [5172]~E(x51721,f2(a868))+~P24(f332(f332(f247(a868),x51722),x51721)) % 165.28/165.04 [5188]E(f153(x51881,x51882),x51882)+~E(f332(f197(f869(x51881)),f153(x51881,x51882)),f332(f197(f869(x51881)),x51882)) % 165.28/165.04 [5189]E(f332(f38(x51891),f332(f174(x51891),x51892)),f332(f197(f869(x51891)),x51892))+~P24(f332(f138(x51891),x51892)) % 165.28/165.04 [5199]~P24(f332(x51991,f341(x51991)))+P24(f332(x51991,f332(f103(a1),x51992))) % 165.28/165.04 [5210]E(f181(x52101,x52102),f116(a1))+~P24(f332(f332(f247(a1),x52102),x52101)) % 165.28/165.04 [5211]E(f280(x52111,x52112),f79(a102))+~P24(f332(f332(f247(a102),x52112),x52111)) % 165.28/165.04 [5212]E(f126(x52121,x52122),f118(a1))+~P24(f332(f332(f247(a1),x52121),x52122)) % 165.28/165.04 [5215]~P107(x52151)+E(f303(x52151,x52152,x52152),f332(f332(f310(x52151),x52152),f196(f875(x52151,a862)))) % 165.28/165.04 [5237]~E(f332(f332(f22(a868),x52371),x52372),f2(a868))+P24(f332(f332(f246(a868),x52371),x52372)) % 165.28/165.04 [5238]~E(f332(f332(f22(a1),x52381),x52382),f2(a1))+P24(f332(f332(f92(a1),x52381),x52382)) % 165.28/165.04 [5264]~E(x52642,f2(a868))+E(f55(x52641,x52642,f116(x52641)),f332(f332(f152(f869(x52641)),f116(x52641)),f116(f869(x52641)))) % 165.28/165.04 [5268]~P104(x52681)+~P24(f332(f332(f247(x52681),x52682),x52682)) % 165.28/165.04 [5271]~E(f45(a1,x52711,x52712),f2(a1))+E(f45(a1,x52711,f332(f80(a1),x52712)),f2(a1)) % 165.28/165.04 [5273]~E(f45(a1,x52731,x52732),f2(a1))+E(f45(a1,f332(f80(a1),x52731),x52732),f2(a1)) % 165.28/165.04 [5282]E(f332(f302(a868,x52821),f332(a115,x52822)),f196(f875(a868,a862)))+P24(f332(f332(f246(a868),x52821),x52822)) % 165.28/165.04 [5303]E(f140(a868,f332(f302(a868,x53031),x53032)),f116(a868))+P24(f332(f332(f247(a868),x53031),x53032)) % 165.28/165.04 [5308]~E(f332(f38(x53081),f332(f174(x53081),x53082)),f332(f197(f869(x53081)),x53082))+P24(f332(f138(x53081),x53082)) % 165.28/165.04 [5313]~P24(f332(f138(x53131),x53132))+P24(f332(f138(x53131),f332(f169(x53131),x53132))) % 165.28/165.04 [5314]~P24(f332(f138(x53141),x53142))+P24(f332(f138(x53141),f332(f173(x53141),x53142))) % 165.28/165.04 [5315]~P24(f332(f138(x53151),x53152))+P24(f332(f138(x53151),f332(f170(x53151),x53152))) % 165.28/165.04 [5322]P24(f332(x53221,x53222))+~P24(f332(x53221,f332(a107,f359(x53221)))) % 165.28/165.04 [5323]P24(f332(f332(f246(a868),x53232),x53231))+P24(f332(f332(f246(a868),x53231),x53232)) % 165.28/165.04 [5324]P24(f332(f332(f246(a1),x53242),x53241))+P24(f332(f332(f246(a1),x53241),x53242)) % 165.28/165.04 [5326]~P85(x53261)+P24(f332(f332(f246(x53261),x53262),f332(f76(x53261),x53262))) % 165.28/165.04 [5329]P24(f332(x53291,f342(x53291)))+~P24(f332(x53291,f332(f103(a1),x53292))) % 165.28/165.04 [5354]E(f332(f332(f22(a868),x53541),x53542),f2(a868))+~P24(f332(f332(f246(a868),x53541),x53542)) % 165.28/165.04 [5355]E(f332(f332(f22(a1),x53551),x53552),f2(a1))+~P24(f332(f332(f92(a1),x53551),x53552)) % 165.28/165.04 [5356]E(f332(f332(f39(a868),x53561),x53562),f2(a868))+~P24(f332(f332(f247(a868),x53561),x53562)) % 165.28/165.04 [5374]E(f45(a868,x53741,x53742),x53741)+~P24(f332(f332(f247(a868),x53741),x53742)) % 165.28/165.04 [5383]E(f45(a1,x53831,f332(f80(a1),x53832)),f291(x53831,x53832))+P24(f332(f332(f246(a1),f2(a1)),x53832)) % 165.28/165.04 [5395]E(f332(f332(f22(a1),x53951),x53952),f202(x53951,x53952))+~P24(f332(f332(f246(a1),x53952),x53951)) % 165.28/165.04 [5414]P24(f332(f332(f246(a1),f2(a1)),f341(x54141)))+P24(f332(x54141,f332(f103(a1),x54142))) % 165.28/165.04 [5426]~P59(x54261)+P24(f332(f332(f334(x54261),x54262),f332(f174(x54261),f56(x54261)))) % 165.28/165.04 [5428]~P112(x54281)+P24(f332(f332(f246(x54281),f2(x54281)),f332(f103(x54281),x54282))) % 165.28/165.04 [5429]~P85(x54291)+P24(f332(f332(f246(x54291),f2(x54291)),f332(f76(x54291),x54292))) % 165.28/165.04 [5456]E(f332(f332(f81(a868),x54561),f791(x54562,x54561)),x54562)+~P24(f332(f332(f246(a868),x54561),x54562)) % 165.28/165.04 [5468]~E(f332(f106(a1),x54681),f332(f103(a1),x54682))+P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x54681))) % 165.28/165.04 [5471]E(f303(a1,x54711,x54712),f196(f875(a1,a862)))+~P24(f332(f332(f247(a1),x54712),x54711)) % 165.28/165.04 [5474]~P118(x54741)+E(f332(f332(f82(x54741),f332(f76(x54741),x54742)),f332(f76(x54741),x54742)),f332(f332(f82(x54741),x54742),x54742)) % 165.28/165.04 [5479]E(f140(a868,f332(f302(a868,x54791),f332(a115,x54792))),f116(a868))+P24(f332(f332(f246(a868),x54791),x54792)) % 165.28/165.04 [5483]E(f332(f332(f39(a1),x54831),x54832),f292(x54831,x54832))+~P24(f332(f332(f246(a1),f2(a1)),x54832)) % 165.28/165.04 [5503]P24(f332(f138(x55031),x55032))+~P24(f332(f138(x55031),f332(f169(x55031),x55032))) % 165.28/165.04 [5504]P24(f332(f138(x55041),x55042))+~P24(f332(f138(x55041),f332(f170(x55041),x55042))) % 165.28/165.04 [5525]P24(f332(f62(a868),x55251))+P24(f332(f332(f334(a868),f792(x55251,x55252)),x55251)) % 165.28/165.04 [5526]P24(f332(f62(a868),x55261))+P24(f332(f332(f334(a868),f814(x55261,x55262)),x55261)) % 165.28/165.04 [5529]P24(f332(f332(f247(a868),x55292),f332(a115,x55291)))+P24(f332(f332(f247(a868),x55291),x55292)) % 165.28/165.04 [5530]E(f45(a1,x55301,x55302),f291(x55301,x55302))+~P24(f332(f332(f246(a1),f2(a1)),x55302)) % 165.28/165.04 [5533]E(f140(a868,f332(f302(a868,x55331),x55332)),f116(a868))+~P24(f332(f332(f246(a868),x55332),x55331)) % 165.28/165.04 [5534]~P77(x55341)+E(f332(f311(x55341,x55341,f80(x55341)),f332(f253(x55341),x55342)),f332(f304(x55341),f332(f80(x55341),x55342))) % 165.28/165.04 [5535]~P77(x55351)+E(f332(f311(x55351,x55351,f80(x55351)),f332(f304(x55351),x55352)),f332(f253(x55351),f332(f80(x55351),x55352))) % 165.28/165.04 [5536]~P77(x55361)+E(f332(f311(x55361,x55361,f80(x55361)),f332(f254(x55361),x55362)),f332(f301(x55361),f332(f80(x55361),x55362))) % 165.28/165.04 [5537]~P77(x55371)+E(f332(f311(x55371,x55371,f80(x55371)),f332(f301(x55371),x55372)),f332(f254(x55371),f332(f80(x55371),x55372))) % 165.28/165.04 [5548]E(x55481,f196(f875(x55482,a862)))+P24(f332(f332(f334(x55482),f397(x55481,x55482)),x55481)) % 165.28/165.04 [5549]E(x55491,f196(f875(x55492,a862)))+P24(f332(f332(f334(x55492),f412(x55491,x55492)),x55491)) % 165.28/165.04 [5560]~P24(f332(f332(f247(a868),x55601),x55602))+P24(f332(f332(f246(a868),x55601),x55602)) % 165.28/165.04 [5561]~P24(f332(f332(f247(a1),x55611),x55612))+P24(f332(f332(f246(a1),x55611),x55612)) % 165.28/165.04 [5577]E(f47(x55771,x55772),f332(f332(f267(a1,a1),f2(a1)),x55771))+~P24(f332(f332(f247(a1),x55771),x55772)) % 165.28/165.04 [5579]E(f227(f332(f80(a1),x55791),f332(f80(a1),x55792)),f227(x55791,x55792))+~P24(f332(f332(f247(a1),x55792),f2(a1))) % 165.28/165.04 [5590]E(x55901,x55902)+~E(f332(a3,f332(a115,f332(a19,x55901))),f332(a3,f332(a115,f332(a19,x55902)))) % 165.28/165.04 [5595]E(f47(x55951,x55952),f332(f332(f267(a1,a1),f2(a1)),x55951))+~P24(f332(f332(f246(a1),x55952),f2(a1))) % 165.28/165.04 [5622]E(f45(a868,f332(f106(a868),x56221),f332(f106(a868),x56222)),f2(a868))+~P24(f332(a201,f332(f106(a1),x56221))) % 165.28/165.04 [5637]P24(f332(f332(f246(a1),f2(a1)),f342(x56371)))+~P24(f332(x56371,f332(f103(a1),x56372))) % 165.28/165.04 [5671]P42(f303(a1,x56711,x56712))+~P24(f332(f332(f246(a1),f2(a1)),x56711)) % 165.28/165.04 [5676]~P24(f332(f62(x56761),x56762))+P24(f332(f62(f875(x56761,a862)),f332(f309(x56761),x56762))) % 165.28/165.04 [5689]E(f332(f332(f81(a1),x56891),f332(f103(a1),f343(x56892,x56891))),x56892)+~P24(f332(f332(f246(a1),x56891),x56892)) % 165.28/165.04 [5697]P24(f332(f332(f246(a868),x56971),x56972))+P24(f332(f332(f246(a868),f332(a115,x56972)),x56971)) % 165.28/165.04 [5742]E(f332(f332(f39(a868),f332(f106(a868),x57421)),f332(f106(a868),x57422)),f2(a868))+~P24(f332(a201,f332(f106(a1),x57421))) % 165.28/165.04 [5743]E(f332(f332(f82(a868),f332(f106(a868),x57431)),f332(f106(a868),x57432)),f2(a868))+~P24(f332(f332(f247(a1),x57431),a84)) % 165.28/165.04 [5745]P24(f332(f332(f246(a868),x57451),f332(a115,x57452)))+~P24(f332(f332(f246(a868),x57451),x57452)) % 165.28/165.04 [5747]P24(f332(f332(f247(a868),x57471),f332(a115,x57472)))+~P24(f332(f332(f246(a868),x57471),x57472)) % 165.28/165.04 [5749]P24(f332(f332(f247(a868),x57491),f332(a115,x57492)))+~P24(f332(f332(f247(a868),x57491),x57492)) % 165.28/165.04 [5752]~E(x57521,x57522)+P24(f332(f332(f247(a1),x57521),f332(f332(f81(a1),x57522),f79(a1)))) % 165.28/165.04 [5755]E(f45(a1,x57551,x57552),f2(a1))+E(f332(f332(f22(a1),x57552),f45(a1,x57551,x57552)),f45(a1,f332(f80(a1),x57551),x57552)) % 165.28/165.04 [5764]E(x57641,f116(x57642))+P24(f332(f332(f334(x57642),f145(x57642,x57641)),f332(f174(x57642),x57641))) % 165.28/165.04 [5776]E(f86(f874(a868,a868),f48(x57761,x57762)),f332(f332(f267(a868,a868),f2(a868)),x57761))+~P24(f332(f332(f247(a868),x57761),x57762)) % 165.28/165.04 [5809]E(f332(f332(f22(a868),f332(f106(a868),x58091)),f332(f106(a868),x58092)),f332(f106(a868),x58091))+~P24(f332(f332(f247(a1),x58092),a84)) % 165.28/165.04 [5810]E(f332(f332(f81(a868),f332(f106(a868),x58101)),f332(f106(a868),x58102)),f332(f106(a868),x58102))+~P24(f332(f332(f247(a1),x58101),a84)) % 165.28/165.04 [5815]E(f332(a115,f332(f332(f81(a868),x58151),f816(x58152,x58151))),x58152)+~P24(f332(f332(f247(a868),x58151),x58152)) % 165.28/165.04 [5838]P24(f332(x58381,x58382))+~P24(f332(x58381,f332(a90,f684(x58382,x58381)))) % 165.28/165.04 [5846]~P24(f332(f332(f247(a868),x58461),f332(a115,x58462)))+P24(f332(f332(f246(a868),x58461),x58462)) % 165.28/165.04 [5892]E(f332(f332(f310(a868),x58921),f332(f302(a868,x58922),x58921)),f332(f302(a868,x58922),f332(a115,x58921)))+~P24(f332(f332(f246(a868),x58922),x58921)) % 165.28/165.04 [5896]E(x58961,f116(x58962))+E(f332(f332(f135(x58962),f117(x58962,x58961)),f332(f332(f152(x58962),f145(x58962,x58961)),f116(x58962))),x58961) % 165.28/165.04 [5910]P24(f332(f62(x59101),x59102))+~P24(f332(f332(f247(a868),f2(a868)),f332(f38(x59101),x59102))) % 165.28/165.04 [5912]~E(x59121,f196(f875(x59122,a862)))+~P24(f332(f332(f247(a868),f2(a868)),f332(f38(x59122),x59121))) % 165.28/165.04 [5924]~P24(f332(f332(f247(a868),x59241),x59242))+P24(f332(f332(f246(a868),f332(a115,x59241)),x59242)) % 165.28/165.04 [5931]~P106(x59311)+E(f151(x59311,x59311,f5(x59311),f153(x59311,x59312)),f140(x59311,f332(f174(x59311),x59312))) % 165.28/165.04 [5934]E(x59341,f116(x59342))+P24(f332(f332(f334(x59342),f332(f142(x59342),x59341)),f332(f174(x59342),x59341))) % 165.28/165.04 [5940]~P112(x59401)+P24(f332(f332(f247(x59401),x59402),f332(f332(f81(x59401),x59402),f79(x59401)))) % 165.28/165.04 [5942]~P85(x59421)+P24(f332(f332(f246(x59421),f332(f80(x59421),x59422)),f332(f76(x59421),x59422))) % 165.28/165.04 [5972]P24(f332(f62(a868),x59721))+~P24(f332(f332(f246(a868),f792(x59721,x59722)),x59722)) % 165.28/165.04 [5973]P24(f332(f62(a868),x59731))+~P24(f332(f332(f247(a868),f814(x59731,x59732)),x59732)) % 165.28/165.04 [5976]~P24(f332(f62(f874(x59761,x59761)),x59762))+P24(f332(f62(x59761),f332(f285(x59761),x59762))) % 165.28/165.04 [6034]~P24(f332(f332(f247(a868),x60342),f332(a115,x60341)))+~P24(f332(f332(f247(a868),x60341),x60342)) % 165.28/165.04 [6035]~P107(x60351)+E(f332(f332(f104(f875(x60351,a862)),f332(f301(x60351),x60352)),f332(f254(x60351),x60352)),f332(f332(f310(x60351),x60352),f196(f875(x60351,a862)))) % 165.28/165.04 [6048]P24(f332(f62(x60481),x60482))+~P24(f332(f62(f875(x60481,a862)),f332(f309(x60481),x60482))) % 165.28/165.04 [6072]P24(f332(f332(f246(a868),f332(a115,x60721)),f332(a115,x60722)))+~P24(f332(f332(f246(a868),x60721),x60722)) % 165.28/165.04 [6073]P24(f332(f332(f246(a868),f332(a19,x60731)),f332(a19,x60732)))+~P24(f332(f332(f246(a102),x60731),x60732)) % 165.28/165.04 [6074]P24(f332(f332(f246(a102),f332(a3,x60741)),f332(a3,x60742)))+~P24(f332(f332(f246(a868),x60741),x60742)) % 165.28/165.04 [6076]P24(f332(f332(f247(a868),f332(a115,x60761)),f332(a115,x60762)))+~P24(f332(f332(f247(a868),x60761),x60762)) % 165.28/165.04 [6077]P24(f332(f332(f247(a868),f332(a19,x60771)),f332(a19,x60772)))+~P24(f332(f332(f247(a102),x60771),x60772)) % 165.28/165.04 [6078]P24(f332(f332(f247(a102),f332(a3,x60781)),f332(a3,x60782)))+~P24(f332(f332(f247(a868),x60781),x60782)) % 165.28/165.04 [6081]E(x60811,x60812)+~E(f332(f311(a868,a1,f103(a1)),x60811),f332(f311(a868,a1,f103(a1)),x60812)) % 165.28/165.04 [6097]P24(f332(f332(f246(a868),x60971),x60972))+~P24(f332(f332(f246(a868),f332(a115,x60971)),x60972)) % 165.28/165.04 [6100]P24(f332(f332(f247(a868),x61001),x61002))+~P24(f332(f332(f246(a868),f332(a115,x61001)),x61002)) % 165.28/165.04 [6101]P24(f332(f332(f247(a868),x61011),x61012))+~P24(f332(f332(f247(a868),f332(a115,x61011)),x61012)) % 165.28/165.04 [6116]E(f45(a1,x61161,x61162),f2(a1))+E(f332(f332(f22(a1),f45(a1,x61161,x61162)),x61162),f45(a1,x61161,f332(f80(a1),x61162))) % 165.28/165.04 [6189]E(f332(f38(f875(x61891,a862)),f332(f309(x61891),x61892)),f332(f332(f257(a868),f332(a115,f332(a115,f2(a868)))),f332(f38(x61891),x61892)))+~P24(f332(f62(x61891),x61892)) % 165.28/165.04 [6192]E(x61921,f116(x61922))+E(f332(f332(f166(x61922),x61921),f332(f332(f22(a868),f332(f197(f869(x61922)),x61921)),f79(a868))),f145(x61922,x61921)) % 165.28/165.04 [6217]E(x62171,f116(x62172))+E(f332(f332(f135(x62172),f332(f173(x62172),x62171)),f332(f332(f152(x62172),f332(f142(x62172),x62171)),f116(x62172))),f332(f169(x62172),x62171)) % 165.28/165.04 [6246]~P24(f332(f62(x62461),f40(f875(x62461,a862),x62462)))+P24(f332(f62(f875(x62461,a862)),x62462)) % 165.28/165.04 [6268]P24(f332(f332(f246(a868),f332(f106(a868),x62681)),f332(f106(a868),x62682)))+~P24(f332(f332(f246(a1),x62681),a84)) % 165.28/165.04 [6285]~P24(f332(f332(f247(a1),x62851),x62852))+P24(f332(f332(f246(a1),x62851),f332(f332(f22(a1),x62852),f79(a1)))) % 165.28/165.04 [6286]~P24(f332(f332(f246(a1),x62861),x62862))+P24(f332(f332(f247(a1),x62861),f332(f332(f81(a1),x62862),f79(a1)))) % 165.28/165.04 [6287]~P24(f332(f332(f247(a1),x62871),x62872))+P24(f332(f332(f247(a1),x62871),f332(f332(f81(a1),x62872),f79(a1)))) % 165.28/165.04 [6289]~P24(f332(f332(f246(a1),x62891),x62892))+P24(f332(f332(f246(a868),f332(f106(a868),x62891)),f332(f106(a868),x62892))) % 165.28/165.04 [6291]~P24(f332(f332(f246(a868),x62911),x62912))+P24(f332(f332(f246(a1),f332(f103(a1),x62911)),f332(f103(a1),x62912))) % 165.28/165.04 [6292]~P24(f332(f332(f246(a1),x62921),x62922))+P24(f332(f332(f246(a1),f332(f106(a1),x62921)),f332(f106(a1),x62922))) % 165.28/165.04 [6294]~P24(f332(f332(f247(a868),x62941),x62942))+P24(f332(f332(f247(a1),f332(f103(a1),x62941)),f332(f103(a1),x62942))) % 165.28/165.04 [6295]~P24(f332(f332(f247(a1),x62951),x62952))+P24(f332(f332(f247(a1),f332(f106(a1),x62951)),f332(f106(a1),x62952))) % 165.28/165.04 [6296]~P24(f332(f332(f92(a1),x62961),x62962))+P24(f332(f332(f92(a1),f332(f106(a1),x62961)),f332(f106(a1),x62962))) % 165.28/165.04 [6314]~P24(f332(f332(f246(a868),x63141),x63142))+~P24(f332(f332(f246(a868),f332(a115,x63142)),x63141)) % 165.28/165.04 [6359]~P24(f332(f332(f246(a868),f332(a115,x63591)),f332(a115,x63592)))+P24(f332(f332(f246(a868),x63591),x63592)) % 165.28/165.04 [6360]~P24(f332(f332(f246(a102),f332(a3,x63601)),f332(a3,x63602)))+P24(f332(f332(f246(a868),x63601),x63602)) % 165.28/165.04 [6361]~P24(f332(f332(f246(a868),f332(a19,x63611)),f332(a19,x63612)))+P24(f332(f332(f246(a102),x63611),x63612)) % 165.28/165.04 [6363]~P24(f332(f332(f247(a868),f332(a115,x63631)),f332(a115,x63632)))+P24(f332(f332(f247(a868),x63631),x63632)) % 165.28/165.04 [6364]~P24(f332(f332(f247(a102),f332(a3,x63641)),f332(a3,x63642)))+P24(f332(f332(f247(a868),x63641),x63642)) % 165.28/165.04 [6365]~P24(f332(f332(f247(a868),f332(a107,x63651)),f332(a107,x63652)))+P24(f332(f332(f247(a1),x63651),x63652)) % 165.28/165.04 [6366]~P24(f332(f332(f247(a868),f332(a19,x63661)),f332(a19,x63662)))+P24(f332(f332(f247(a102),x63661),x63662)) % 165.28/165.04 [6406]~P24(f332(f332(f247(a868),f332(a107,x64062)),f332(a107,x64061)))+P24(f332(f332(f247(a1),f2(a1)),x64061)) % 165.28/165.04 [6437]P24(f332(f332(f246(a1),f2(a1)),f45(a1,x64371,x64372)))+~P24(f332(f332(f247(a1),f2(a1)),x64372)) % 165.28/165.04 [6595]P41(x65951,x65952)+~E(f332(f332(f289(x65951,x65951,x65951),x65952),x65952),f196(f875(f874(x65951,x65951),a862))) % 165.28/165.04 [6607]~P41(x66071,x66072)+P41(x66071,f332(f332(f289(x66071,x66071,x66071),x66072),x66072)) % 165.28/165.04 [6618]P24(f332(f332(f246(a1),x66181),x66182))+~P24(f332(f332(f247(a1),x66181),f332(f332(f81(a1),x66182),f79(a1)))) % 165.28/165.04 [6619]P24(f332(f332(f247(a1),x66191),x66192))+~P24(f332(f332(f246(a1),x66191),f332(f332(f22(a1),x66192),f79(a1)))) % 165.28/165.04 [6622]P24(f332(f332(f246(a868),x66221),x66222))+~P24(f332(f332(f246(a1),f332(f103(a1),x66221)),f332(f103(a1),x66222))) % 165.28/165.04 [6623]P24(f332(f332(f246(a1),x66231),x66232))+~P24(f332(f332(f246(a1),f332(f106(a1),x66231)),f332(f106(a1),x66232))) % 165.28/165.04 [6625]P24(f332(f332(f247(a868),x66251),x66252))+~P24(f332(f332(f247(a1),f332(f103(a1),x66251)),f332(f103(a1),x66252))) % 165.28/165.04 [6626]P24(f332(f332(f247(a1),x66261),x66262))+~P24(f332(f332(f247(a868),f332(f106(a868),x66261)),f332(f106(a868),x66262))) % 165.28/165.04 [6627]P24(f332(f332(f247(a1),x66271),x66272))+~P24(f332(f332(f247(a1),f332(f106(a1),x66271)),f332(f106(a1),x66272))) % 165.28/165.04 [6628]P24(f332(f332(f92(a1),x66281),x66282))+~P24(f332(f332(f92(a1),f332(f106(a1),x66281)),f332(f106(a1),x66282))) % 165.28/165.04 [6721]~E(f618(x67212,x67211),f116(x67211))+E(f332(f143(f869(x67211),f869(x67211),f135(x67211),f116(x67211)),x67212),f116(x67211)) % 165.28/165.04 [6722]~E(f619(x67222,x67221),f116(x67221))+E(f332(f143(f869(x67221),f869(x67221),f135(x67221),f116(x67221)),x67222),f116(x67221)) % 165.28/165.04 [6729]~P30(x67291)+E(f332(f143(x67291,x67291,f113(x67291),f196(x67291)),x67292),f40(x67291,f332(f174(x67291),x67292))) % 165.28/165.04 [6730]~P30(x67301)+E(f332(f143(x67301,x67301,f104(x67301),f255(x67301)),x67302),f41(x67301,f332(f174(x67301),x67302))) % 165.28/165.04 [6742]E(x67421,f2(a102))+E(f332(f332(f81(a868),f332(a19,f332(f332(f22(a102),x67421),f79(a102)))),f332(a115,x67422)),f332(f332(f81(a868),f332(a19,x67421)),x67422)) % 165.28/165.04 [6792]P24(f332(f332(f247(a1),f332(f332(f22(a1),x67921),x67922)),f2(a1)))+~P24(f332(f332(f247(a1),x67921),x67922)) % 165.28/165.04 [6820]~P106(x68201)+E(f332(f332(f113(f875(x68201,a862)),f332(f332(f310(x68201),x68202),f196(f875(x68201,a862)))),f332(f304(x68201),x68202)),f332(f254(x68201),x68202)) % 165.28/165.04 [6895]~P58(x68951,x68952)+P41(x68951,f332(f252(f874(x68951,x68951)),f332(f271(x68951,x68951,a862),x68952))) % 165.28/165.04 [6896]~P58(x68961,x68962)+P56(x68961,f332(f252(f874(x68961,x68961)),f332(f271(x68961,x68961,a862),x68962))) % 165.28/165.04 [6897]E(x68971,f196(f875(x68972,a862)))+~P24(f332(f332(f246(f875(x68972,a862)),x68971),f196(f875(x68972,a862)))) % 165.28/165.04 [6978]~P24(f332(f332(f247(a868),f2(a868)),x69782))+P24(f332(f332(f246(a868),f45(a868,x69781,x69782)),x69782)) % 165.28/165.04 [6979]~P24(f332(f332(f246(a1),f2(a1)),x69791))+P24(f332(f332(f246(a1),f45(a1,x69791,x69792)),x69791)) % 165.28/165.04 [6980]~P24(f332(f332(f247(a868),f2(a868)),x69802))+P24(f332(f332(f247(a868),f45(a868,x69801,x69802)),x69802)) % 165.28/165.04 [6982]~P24(f332(f332(f247(a1),f2(a1)),x69822))+P24(f332(f332(f247(a1),f45(a1,x69821,x69822)),x69822)) % 165.28/165.04 [7058]~P107(x70581)+E(f332(f332(f22(f875(x70581,a862)),f332(f332(f310(x70581),x70582),f196(f875(x70581,a862)))),f332(f253(x70581),x70582)),f332(f332(f310(x70581),x70582),f196(f875(x70581,a862)))) % 165.28/165.04 [7131]~P52(x71311,x71312)+P43(x71311,f255(f875(x71311,a862)),f332(f252(f874(x71311,x71311)),f332(f271(x71311,x71311,a862),x71312))) % 165.28/165.04 [7132]P24(f332(x71321,x71322))+P24(f332(f332(f334(f875(f874(a868,a868),a862)),f684(x71322,x71321)),a101)) % 165.28/165.04 [7177]E(f332(f332(f135(a868),f140(a868,f332(f302(a868,x71771),x71772))),f332(f332(f152(a868),x71772),f116(a868))),f140(a868,f332(f302(a868,x71771),f332(a115,x71772))))+~P24(f332(f332(f246(a868),x71771),x71772)) % 165.28/165.04 [7318]E(x73181,f2(a868))+~E(f332(f143(a868,a868,f81(a868),x73181),x73182),f2(a868)) % 165.28/165.04 [7343]~P24(f332(f332(f247(a1),f332(f332(f22(a1),x73431),x73432)),f2(a1)))+P24(f332(f332(f247(a1),x73431),x73432)) % 165.28/165.04 [7372]P41(x73721,x73722)+~P41(x73721,f332(f332(f289(x73721,x73721,x73721),x73722),x73722)) % 165.28/165.04 [7402]~P24(f332(f332(f246(a868),f332(a115,x74021)),x74022))+P24(f193(a862,a250,f332(f246(a868),x74021),x74022)) % 165.28/165.04 [7560]P21(a868,a868,f332(f332(f7(a868,a868,a868),f22(a868)),x75601),x75602)+P24(f332(f332(f334(a868),f836(x75601,x75602)),x75602)) % 165.28/165.04 [7616]E(f332(f332(f332(f66(a868,x76161,f81(a868)),f332(f16(a868,x76161),f79(a868))),f2(a868)),x76162),f332(f38(x76161),x76162))+~P24(f332(f62(x76161),x76162)) % 165.28/165.04 [7658]P21(a868,a868,f332(f332(f7(a868,a868,a868),f22(a868)),x76581),x76582)+~P24(f332(f332(f246(a868),x76581),f836(x76581,x76582))) % 165.28/165.04 [7716]P41(x77161,x77162)+P24(f332(f332(f246(f875(x77161,a862)),f689(x77162,x77161)),f332(f286(x77161,x77161,x77162),f689(x77162,x77161)))) % 165.28/165.04 [7721]P58(x77211,x77212)+~P41(x77211,f332(f252(f874(x77211,x77211)),f332(f271(x77211,x77211,a862),x77212))) % 165.28/165.04 [7789]P24(f332(f332(f246(a868),f332(a115,x77891)),x77892))+~P24(f193(a862,a250,f332(f246(a868),x77891),x77892)) % 165.28/165.04 [7844]P24(f332(f332(f334(f874(a868,a868)),f332(f332(f267(a868,a868),x78441),x78442)),f308(a868,a322)))+~P24(f332(f332(f246(a868),x78441),x78442)) % 165.28/165.04 [7940]P52(x79401,x79402)+~P43(x79401,f255(f875(x79401,a862)),f332(f252(f874(x79401,x79401)),f332(f271(x79401,x79401,a862),x79402))) % 165.28/165.04 [7995]~P24(f332(f138(x79951),x79952))+P24(f332(f138(f875(x79951,a862)),f332(f332(f155(f869(x79951),f875(x79951,a862)),f174(x79951)),f54(x79951,x79952)))) % 165.28/165.04 [8196]~P41(x81961,f332(f287(x81961,x81961),x81962))+P41(x81961,f332(f287(x81961,x81961),f332(f332(f289(x81961,x81961,x81961),x81962),f308(x81961,x81962)))) % 165.28/165.04 [8315]P24(f332(f62(f874(x83151,x83151)),f332(f332(f289(x83151,x83151,x83151),x83152),f308(x83151,x83152))))+~P24(f332(f62(f874(x83151,x83151)),x83152)) % 165.28/165.04 [8346]E(x83461,f2(a1))+P24(f332(f49(x83462,x83461),f332(f332(f267(a1,a1),f332(f332(f39(a1),x83462),x83461)),f45(a1,x83462,x83461)))) % 165.28/165.04 [8357]~P24(f332(f332(f334(f874(a868,a868)),f332(f332(f267(a868,a868),x83571),x83572)),f308(a868,a322)))+P24(f332(f332(f246(a868),x83571),x83572)) % 165.28/165.04 [8372]~P80(x83721)+E(f332(f143(x83721,x83721,f332(f7(x83721,x83721,x83721),f81(x83721)),f2(x83721)),f332(f170(x83721),x83722)),f332(f143(x83721,x83721,f81(x83721),f2(x83721)),x83722)) % 165.28/165.04 [8538]~P106(x85381)+E(f332(f143(f869(x85381),x85381,f332(f7(x85381,f869(x85381),f869(x85381)),f149(x85381,x85381,f5(x85381))),f116(x85381)),x85382),f151(x85381,x85381,f5(x85381),x85382)) % 165.28/165.04 [8639]~P56(x86391,f332(f252(f874(x86391,x86391)),f332(f271(x86391,x86391,a862),x86392)))+P56(x86391,f332(f252(f874(x86391,x86391)),f332(f271(x86391,x86391,a862),f256(x86391,x86391,x86392)))) % 165.28/165.04 [8653]P24(f332(f332(f334(f874(a868,a868)),f332(f332(f267(a868,a868),x86531),x86532)),f332(f332(f289(a868,a868,a868),a322),f308(a868,a322))))+~P24(f332(f332(f247(a868),x86531),x86532)) % 165.28/165.04 [8696]~P24(f332(f62(f874(x86961,x86961)),f332(f332(f289(x86961,x86961,x86961),x86962),f308(x86961,x86962))))+P24(f332(f62(f874(x86961,x86961)),x86962)) % 165.28/165.04 [8747]~P56(x87471,f332(f252(f874(x87471,x87471)),f332(f271(x87471,x87471,a862),f256(x87471,x87471,x87472))))+P56(x87471,f332(f252(f874(x87471,x87471)),f332(f271(x87471,x87471,a862),x87472))) % 165.28/165.04 [8940]P56(x89401,x89402)+P24(f332(f332(f334(f874(x89401,x89401)),f332(f332(f267(x89401,x89401),f728(x89402,x89401)),f728(x89402,x89401))),f332(f332(f289(x89401,x89401,x89401),x89402),f308(x89401,x89402)))) % 165.28/165.04 [8941]P56(x89411,x89412)+P24(f332(f332(f334(f874(x89411,x89411)),f332(f332(f267(x89411,x89411),f743(x89412,x89411)),f743(x89412,x89411))),f332(f332(f289(x89411,x89411,x89411),x89412),f308(x89411,x89412)))) % 165.28/165.04 [9056]~P24(f332(f332(f334(f874(a868,a868)),f332(f332(f267(a868,a868),x90561),x90562)),f332(f332(f289(a868,a868,a868),a322),f308(a868,a322))))+P24(f332(f332(f247(a868),x90561),x90562)) % 165.28/165.04 [5058]~P92(x50581)+E(f332(f332(f81(x50581),f332(f106(x50581),a84)),x50582),x50582) % 165.28/165.04 [5087]~P81(x50871)+E(f332(f332(f113(x50871),f332(f80(x50871),x50872)),x50872),f255(x50871)) % 165.28/165.04 [5088]~P81(x50881)+E(f332(f332(f104(x50881),f332(f80(x50881),x50882)),x50882),f196(x50881)) % 165.28/165.04 [5089]~P66(x50891)+E(f332(f332(f81(x50891),f332(f80(x50891),x50892)),x50892),f2(x50891)) % 165.28/165.04 [5090]~P67(x50901)+E(f332(f332(f81(x50901),f332(f80(x50901),x50902)),x50902),f2(x50901)) % 165.28/165.04 [5122]~P92(x51221)+E(f332(f332(f82(x51221),f332(f106(x51221),a100)),x51222),f332(f80(x51221),x51222)) % 165.28/165.04 [5296]~P108(x52961)+E(f332(f332(f82(x52961),f332(f80(x52961),f79(x52961))),x52962),f332(f80(x52961),x52962)) % 165.28/165.04 [5339]E(f332(f76(a1),x53391),f79(a1))+~E(f332(f76(a1),f332(f332(f82(a1),x53391),x53392)),f79(a1)) % 165.28/165.04 [5431]~P92(x54311)+E(f332(f332(f81(x54311),f79(x54311)),f332(f106(x54311),x54312)),f332(f106(x54311),f332(f332(f22(a1),x54312),a100))) % 165.28/165.04 [5484]~P26(x54841)+E(f10(x54841,f332(f332(f310(x54841),x54842),f196(f875(x54841,a862)))),x54842) % 165.28/165.04 [5485]~P26(x54851)+E(f11(x54851,f332(f332(f310(x54851),x54852),f196(f875(x54851,a862)))),x54852) % 165.28/165.04 [5486]~P106(x54861)+E(f14(x54861,f332(f332(f310(x54861),x54862),f196(f875(x54861,a862)))),x54862) % 165.28/165.04 [5487]~P106(x54871)+E(f15(x54871,f332(f332(f310(x54871),x54872),f196(f875(x54871,a862)))),x54872) % 165.28/165.04 [5488]~P30(x54881)+E(f40(x54881,f332(f332(f310(x54881),x54882),f196(f875(x54881,a862)))),x54882) % 165.28/165.04 [5489]~P30(x54891)+E(f41(x54891,f332(f332(f310(x54891),x54892),f196(f875(x54891,a862)))),x54892) % 165.28/165.04 [5511]E(f332(f332(f81(a868),x55111),f332(f332(f22(a868),x55112),x55111)),x55112)+P24(f332(f332(f247(a868),x55112),x55111)) % 165.28/165.04 [5543]E(x55431,f116(x55432))+P24(f332(f332(f247(a868),f2(a868)),f332(f197(f869(x55432)),x55431))) % 165.28/165.04 [5668]~P106(x56681)+E(f12(x56681,f244(x56681),f332(f332(f310(x56681),x56682),f196(f875(x56681,a862)))),x56682) % 165.28/165.04 [5669]~P106(x56691)+E(f13(x56691,f245(x56691),f332(f332(f310(x56691),x56692),f196(f875(x56691,a862)))),x56692) % 165.28/165.04 [5732]E(f332(f332(f22(a868),x57321),f332(f332(f22(a868),x57321),x57322)),x57322)+~P24(f332(f332(f246(a868),x57322),x57321)) % 165.28/165.04 [5733]E(f332(f332(f81(a868),x57331),f332(f332(f22(a868),x57332),x57331)),x57332)+~P24(f332(f332(f246(a868),x57331),x57332)) % 165.28/165.04 [5754]E(f45(a868,f332(f332(f22(a868),x57541),x57542),x57542),f45(a868,x57541,x57542))+P24(f332(f332(f247(a868),x57541),x57542)) % 165.28/165.04 [5765]E(f332(f80(a1),f332(f332(f39(a1),x57651),f332(f80(a1),x57652))),f292(x57651,x57652))+P24(f332(f332(f246(a1),f2(a1)),x57652)) % 165.28/165.04 [5767]~E(x57672,f2(a868))+P24(f332(f332(f247(a868),f2(a868)),f332(f332(f257(a868),x57671),x57672))) % 165.28/165.04 [5818]~P92(x58181)+E(f332(f332(f81(x58181),f332(f80(x58181),f79(x58181))),f332(f106(x58181),x58182)),f332(f106(x58181),f332(f332(f81(a1),x58182),a100))) % 165.28/165.04 [5819]E(f332(f332(f257(a868),f332(f106(a868),x58191)),x58192),f332(f332(f257(a868),f2(a868)),x58192))+~P24(f332(a201,f332(f106(a1),x58191))) % 165.28/165.04 [5916]E(f332(f142(a868),f140(a868,f332(f302(a868,x59161),x59162))),x59161)+~P24(f332(f332(f247(a868),x59161),x59162)) % 165.28/165.04 [5935]E(f332(f332(f82(a868),f332(f106(a868),x59351)),f332(f106(a868),x59352)),f332(f106(a868),f332(f332(f82(a1),x59351),x59352)))+P24(f332(f332(f247(a1),x59351),a84)) % 165.28/165.04 [5941]~P121(x59411)+P24(f332(f332(f246(x59411),f2(x59411)),f332(f332(f82(x59411),x59412),x59412))) % 165.28/165.04 [5953]E(f332(f332(f22(a868),f332(a115,x59531)),x59532),f332(a115,f332(f332(f22(a868),x59531),x59532)))+~P24(f332(f332(f246(a868),x59532),x59531)) % 165.28/165.04 [5956]E(f45(a868,f332(f332(f22(a868),x59561),x59562),x59562),f45(a868,x59561,x59562))+~P24(f332(f332(f246(a868),x59562),x59561)) % 165.28/165.04 [6009]E(f332(f332(f257(a868),f332(a107,x60091)),x60092),f332(a107,f332(f332(f257(a1),x60091),x60092)))+~P24(f332(f332(f246(a1),f2(a1)),x60091)) % 165.28/165.04 [6025]P24(f332(f138(x60251),x60252))+P24(f332(f332(f247(a868),f521(x60252,x60251)),f332(f197(f869(x60251)),x60252))) % 165.28/165.04 [6026]P24(f332(f138(x60261),x60262))+P24(f332(f332(f247(a868),f532(x60262,x60261)),f332(f197(f869(x60261)),x60262))) % 165.28/165.04 [6041]~E(x60411,f116(x60412))+~P24(f332(f332(f247(a868),f2(a868)),f332(f197(f869(x60412)),x60411))) % 165.28/165.04 [6055]E(f145(a868,f140(a868,f332(f302(a868,x60551),x60552))),f332(f332(f22(a868),x60552),f79(a868)))+~P24(f332(f332(f247(a868),x60551),x60552)) % 165.28/165.04 [6058]E(f332(f332(f81(a1),x60581),f332(f103(a1),f332(a115,f345(x60582,x60581)))),x60582)+~P24(f332(f332(f247(a1),x60581),x60582)) % 165.28/165.04 [6065]E(x60651,f2(a868))+E(f332(f332(f82(a868),x60652),f332(f332(f257(a868),x60652),f332(f332(f22(a868),x60651),f79(a868)))),f332(f332(f257(a868),x60652),x60651)) % 165.28/165.04 [6091]E(f332(f332(f82(a868),f332(a107,x60911)),f332(a107,x60912)),f332(a107,f332(f332(f82(a1),x60911),x60912)))+~P24(f332(f332(f246(a1),f2(a1)),x60911)) % 165.28/165.04 [6092]E(f332(f332(f39(a868),f332(a107,x60921)),f332(a107,x60922)),f332(a107,f332(f332(f39(a1),x60921),x60922)))+~P24(f332(f332(f246(a1),f2(a1)),x60921)) % 165.28/165.04 [6106]~P113(x61061)+E(f332(f332(f81(x61061),x61062),x61062),f332(f332(f82(x61061),f332(f332(f81(x61061),f79(x61061)),f79(x61061))),x61062)) % 165.28/165.04 [6125]E(f332(f332(f22(a1),f332(f103(a1),x61251)),f332(f103(a1),x61252)),f332(f103(a1),f332(f332(f22(a868),x61251),x61252)))+~P24(f332(f332(f246(a868),x61252),x61251)) % 165.28/165.04 [6127]E(f332(f332(f267(a1,a1),f332(f106(a1),a100)),f332(f332(f81(a1),x61271),x61272)),f50(x61271,x61272))+~P24(f332(f332(f246(a1),x61272),f2(a1))) % 165.28/165.04 [6167]E(f182(x61671,x61672),f116(f869(x61671)))+P24(f332(f332(f334(f869(x61671)),f568(x61672,x61671)),f332(f174(f869(x61671)),x61672))) % 165.28/165.04 [6176]E(f119(a1,f332(f127(a1),x61761),f126(x61762,f332(f332(f81(a1),x61761),f79(a1)))),f126(x61762,x61761))+P24(f332(f332(f247(a1),x61762),x61761)) % 165.28/165.04 [6252]E(f332(f332(f152(a1),x62521),f181(f332(f332(f81(a1),x62521),f79(a1)),x62522)),f181(x62521,x62522))+~P24(f332(f332(f246(a1),x62521),x62522)) % 165.28/165.04 [6288]~P24(f332(f332(f247(a868),x62882),x62881))+P24(f332(f332(f247(a868),f2(a868)),f332(f332(f22(a868),x62881),x62882))) % 165.28/165.04 [6319]~P24(f332(f332(f247(a868),x63191),f332(a107,x63192)))+P24(f332(f332(f247(a1),f332(f103(a1),x63191)),x63192)) % 165.28/165.04 [6350]~P106(x63501)+E(f332(f332(f113(f875(x63501,a862)),f332(f253(x63501),x63502)),f332(f332(f310(x63501),x63502),f196(f875(x63501,a862)))),f332(f301(x63501),x63502)) % 165.28/165.04 [6351]~P24(f332(f332(f246(a1),f2(a1)),x63511))+P24(f332(f332(f246(a1),f2(a1)),f332(f332(f257(a1),x63511),x63512))) % 165.28/165.04 [6354]~P24(f332(f332(f247(a868),f2(a868)),x63541))+P24(f332(f332(f247(a868),f2(a868)),f332(f332(f257(a868),x63541),x63542))) % 165.28/165.04 [6382]~E(f332(x63821,f2(a868)),f2(a868))+E(f332(f332(f6(a868,a868),x63821),f303(a868,f332(a115,f2(a868)),x63822)),f332(f332(f6(a868,a868),x63821),f303(a868,f2(a868),x63822))) % 165.28/165.04 [6445]~P92(x64451)+E(f332(f332(f82(x64451),f332(f332(f81(x64451),f79(x64451)),f79(x64451))),f332(f106(x64451),x64452)),f332(f106(x64451),f332(f332(f81(a1),x64452),x64452))) % 165.28/165.04 [6461]E(f332(f332(f310(a1),x64611),f303(a1,f332(f332(f81(a1),x64611),f79(a1)),x64612)),f303(a1,x64611,x64612))+P24(f332(f332(f247(a1),x64612),x64611)) % 165.28/165.04 [6462]P24(f332(f332(f247(a868),x64621),f332(a107,x64622)))+~P24(f332(f332(f247(a1),f332(f103(a1),x64621)),x64622)) % 165.28/165.04 [6563]E(f332(a107,f332(f332(f39(a1),f332(f106(a1),x65631)),f332(f106(a1),x65632))),f332(f332(f39(a868),f332(f106(a868),x65631)),f332(f106(a868),x65632)))+P24(f332(a201,f332(f106(a1),x65631))) % 165.28/165.04 [6620]P24(f332(f332(f247(a868),x66201),x66202))+~P24(f332(f332(f247(a868),f2(a868)),f332(f332(f22(a868),x66202),x66201))) % 165.28/165.04 [6664]P24(f332(f332(f247(a868),f2(a868)),x66641))+~P24(f332(f332(f247(a868),f2(a868)),f332(f332(f82(a868),x66642),x66641))) % 165.28/165.04 [6665]P24(f332(f332(f247(a868),f2(a868)),x66651))+~P24(f332(f332(f247(a868),f2(a868)),f332(f332(f82(a868),x66651),x66652))) % 165.28/165.04 [6682]~P24(f332(f332(f246(a1),x66821),f2(a1)))+E(f332(f332(f82(a868),f332(a107,f332(f80(a1),x66821))),f332(a107,f332(f80(a1),x66822))),f332(a107,f332(f332(f82(a1),x66821),x66822))) % 165.28/165.04 [6740]~E(x67402,f196(f875(x67401,a862)))+P24(f332(f332(f246(f875(x67401,a862)),x67402),f332(f80(f875(x67401,a862)),x67402))) % 165.28/165.04 [6803]~P92(x68031)+E(f332(f332(f81(x68031),f332(f332(f81(x68031),f2(x68031)),f332(f106(x68031),x68032))),f332(f106(x68031),x68032)),f332(f106(x68031),f332(f332(f81(a1),x68032),x68032))) % 165.28/165.04 [6860]~P24(f332(f332(f247(a1),x68601),x68602))+P24(f332(f332(f246(a1),f332(f332(f81(a1),x68601),f79(a1))),x68602)) % 165.28/165.04 [6925]E(x69251,f2(a868))+~P24(f332(f332(f246(a1),f332(f103(a1),x69252)),f332(f80(a1),f332(f103(a1),x69251)))) % 165.28/165.04 [6926]E(x69261,f2(a868))+~P24(f332(f332(f246(a1),f332(f103(a1),x69261)),f332(f80(a1),f332(f103(a1),x69262)))) % 165.28/165.04 [7029]E(f332(f332(f267(a1,a1),f332(f106(a1),a100)),f332(f332(f81(a1),x70291),x70292)),f50(x70291,x70292))+~P24(f332(f332(f246(a1),f2(a1)),f332(f332(f81(a1),x70291),x70292))) % 165.28/165.04 [7071]~P22(x70711,x70712)+P41(x70711,f332(f266(f875(f874(x70711,x70711),a862),f875(f874(x70711,x70711),a862)),x70712)) % 165.28/165.04 [7089]~P24(f332(f332(f246(a868),f332(a115,f2(a868))),x70891))+P24(f332(f332(f246(a868),f332(a115,f2(a868))),f332(f332(f257(a868),x70891),x70892))) % 165.28/165.04 [7259]~P24(f332(f332(f246(a1),x72591),x72592))+P24(f332(f332(f246(a1),f332(f332(f81(a1),x72591),x72591)),f332(f332(f81(a1),x72592),x72592))) % 165.28/165.04 [7264]~P24(f332(f332(f247(a1),x72641),x72642))+P24(f332(f332(f247(a1),f332(f332(f81(a1),x72641),x72641)),f332(f332(f81(a1),x72642),x72642))) % 165.28/165.04 [7265]~P24(f332(f332(f92(a1),x72651),x72652))+P24(f332(f332(f92(a1),f332(f332(f81(a1),x72651),x72651)),f332(f332(f81(a1),x72652),x72652))) % 165.28/165.04 [7320]~P24(f332(f332(f247(a868),f2(a868)),x73201))+P24(f332(f332(f247(a868),f332(f332(f22(a868),x73201),f332(a115,x73202))),x73201)) % 165.28/165.04 [7354]P24(f332(f332(f246(a868),f332(a115,f2(a868))),x73541))+~P24(f332(f332(f246(a868),f332(a115,f2(a868))),f332(f332(f82(a868),x73542),x73541))) % 165.28/165.04 [7355]P24(f332(f332(f246(a868),f332(a115,f2(a868))),x73551))+~P24(f332(f332(f246(a868),f332(a115,f2(a868))),f332(f332(f82(a868),x73551),x73552))) % 165.28/165.04 [7359]P24(f332(f332(f246(a868),f332(f332(f166(a868),x73591),x73592)),f332(f167(a868),x73591)))+~P24(f332(f332(f247(a868),x73592),f332(f197(f869(a868)),x73591))) % 165.28/165.04 [7401]P24(f332(f332(f247(a1),x74011),x74012))+~P24(f332(f332(f246(a1),f332(f332(f81(a1),x74011),f79(a1))),x74012)) % 165.28/165.04 [7445]P24(f332(f62(x74451),f255(f875(x74451,a862))))+~P24(f332(f62(f875(x74452,x74451)),f255(f875(f875(x74452,x74451),a862)))) % 165.28/165.04 [7446]P24(f332(f62(x74461),f255(f875(x74461,a862))))+~P24(f332(f62(f876(x74462,x74461)),f255(f875(f876(x74462,x74461),a862)))) % 165.28/165.04 [7447]P24(f332(f62(x74471),f255(f875(x74471,a862))))+~P24(f332(f62(f876(x74471,x74472)),f255(f875(f876(x74471,x74472),a862)))) % 165.28/165.04 [7489]E(x74891,f196(f875(x74892,a862)))+~P24(f332(f332(f246(f875(x74892,a862)),x74891),f332(f80(f875(x74892,a862)),x74891))) % 165.28/165.04 [7626]E(f332(f143(f869(x76261),f869(x76261),f135(x76261),f116(x76261)),x76262),f116(x76261))+P24(f332(f332(f334(f869(x76261)),f618(x76262,x76261)),f332(f174(f869(x76261)),x76262))) % 165.28/165.04 [7627]E(f332(f143(f869(x76271),f869(x76271),f135(x76271),f116(x76271)),x76272),f116(x76271))+P24(f332(f332(f334(f869(x76271)),f619(x76272,x76271)),f332(f174(f869(x76271)),x76272))) % 165.28/165.04 [7861]P24(f332(f332(f246(a1),x78611),x78612))+~P24(f332(f332(f246(a1),f332(f332(f81(a1),x78611),x78611)),f332(f332(f81(a1),x78612),x78612))) % 165.28/165.04 [7866]P24(f332(f332(f247(a1),x78661),x78662))+~P24(f332(f332(f247(a1),f332(f332(f81(a1),x78661),x78661)),f332(f332(f81(a1),x78662),x78662))) % 165.28/165.04 [7867]P24(f332(f332(f92(a1),x78671),x78672))+~P24(f332(f332(f92(a1),f332(f332(f81(a1),x78671),x78671)),f332(f332(f81(a1),x78672),x78672))) % 165.28/165.04 [7960]~P113(x79601)+E(f332(f332(f82(x79601),f332(f332(f81(x79601),f79(x79601)),f79(x79601))),f332(f332(f6(a868,x79601),f103(x79601)),f303(a868,f79(a868),x79602))),f332(f332(f82(x79601),f332(f103(x79601),x79602)),f332(f332(f81(x79601),f332(f103(x79601),x79602)),f79(x79601)))) % 165.28/165.04 [8009]P24(f332(f332(f334(a868),x80091),x80092))+~P24(f332(f332(f334(a1),f332(f103(a1),x80091)),f332(f311(a868,a1,f103(a1)),x80092))) % 165.28/165.04 [8167]~P24(f332(f62(x81671),x81672))+E(f332(f311(a868,x81671,f431(x81672,x81671)),f332(f252(a868),f332(f332(f7(a868,a868,a862),f247(a868)),f432(x81672,x81671)))),x81672) % 165.28/165.04 [8443]P45(x84431,x84432)+P24(f332(f332(f334(f874(x84431,x84431)),f332(f332(f267(x84431,x84431),f502(x84432,x84431)),f502(x84432,x84431))),x84432)) % 165.28/165.04 [8579]~P92(x85791)+E(f332(f332(f22(x85791),f79(x85791)),f332(f106(x85791),x85792)),f332(f106(x85791),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f80(a1),x85792)))) % 165.28/165.04 [8693]~P24(f332(f332(f247(f875(a868,a862)),x86931),x86932))+P24(f332(f332(f247(f875(a1,a862)),f332(f311(a868,a1,f103(a1)),x86931)),f332(f311(a868,a1,f103(a1)),x86932))) % 165.28/165.04 [8721]~P24(f332(f332(f247(a1),x87211),x87212))+P24(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f81(a1),x87211),x87211)),a100)),f332(f332(f81(a1),x87212),x87212))) % 165.28/165.04 [8723]~P24(f332(f332(f247(a1),x87231),x87232))+P24(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f81(a1),x87231),x87231)),a100)),f332(f332(f81(a1),x87232),x87232))) % 165.28/165.04 [8793]~P24(f332(f332(f334(a868),x87931),f332(f174(a868),x87932)))+P24(f332(f332(f246(a868),x87931),f332(f143(a868,a868,f81(a868),f2(a868)),x87932))) % 165.28/165.04 [8885]P49(x88851,x88852)+~P24(f332(f332(f334(f874(x88851,x88851)),f332(f332(f267(x88851,x88851),f496(x88852,x88851)),f496(x88852,x88851))),x88852)) % 165.28/165.04 [8956]P20(a864,x89561,f332(f332(f310(f867(a864)),f332(a94,f332(a28,x89562))),f196(f875(f867(a864),a862))))+~P20(a864,f332(f332(f310(f867(a864)),f332(a94,f332(a28,x89562))),x89561),f332(f332(f310(f867(a864)),f332(a94,f332(f243(a863),f332(a26,x89562)))),f196(f875(f867(a864),a862)))) % 165.28/165.04 [9022]~P24(f332(f332(f246(f875(a1,a862)),f332(f311(a868,a1,f103(a1)),x90221)),f332(f311(a868,a1,f103(a1)),x90222)))+P24(f332(f332(f246(f875(a868,a862)),x90221),x90222)) % 165.28/165.04 [9023]~P24(f332(f332(f247(f875(a1,a862)),f332(f311(a868,a1,f103(a1)),x90231)),f332(f311(a868,a1,f103(a1)),x90232)))+P24(f332(f332(f247(f875(a868,a862)),x90231),x90232)) % 165.28/165.04 [9103]P24(f332(f332(f247(a1),x91031),x91032))+~P24(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f81(a1),x91031),x91031)),a100)),f332(f332(f81(a1),x91032),x91032))) % 165.28/165.04 [9105]P24(f332(f332(f247(a1),x91051),x91052))+~P24(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f81(a1),x91051),x91051)),a100)),f332(f332(f81(a1),x91052),x91052))) % 165.28/165.04 [9968]~P102(x99681)+E(f119(f869(x99681),f332(f127(f869(x99681)),f116(x99681)),f332(f332(f332(f99(f870(f869(x99681))),f332(f332(f247(a1),f2(a1)),x99682)),f332(f121(f874(x99681,f869(x99681)),f869(x99681),f132(x99681,f869(x99681),f133(x99681,f332(f332(f22(a1),x99682),f79(a1))),f133(f869(x99681),f332(f332(f22(a1),x99682),f79(a1))))),f332(f271(x99681,f869(x99681),f870(f869(x99681))),f332(f332(f8(f875(f869(x99681),f869(x99681)),f875(f869(x99681),f870(f869(x99681))),x99681),f332(f8(f869(x99681),f870(f869(x99681)),f869(x99681)),f127(f869(x99681)))),f152(x99681))))),f118(f869(x99681)))),f133(f869(x99681),x99682)) % 165.28/165.04 [9989]~P24(f332(f62(x99891),x99892))+E(f332(f197(f869(x99891)),f91(f869(x99891),f332(f332(f18(f869(x99891),a862,a862),f332(f332(f8(a862,f875(a862,a862),f869(x99891)),a330),f332(f332(f7(f869(x99891),f875(x99891,a862),a862),f332(f332(f8(f875(x99891,a862),f875(f875(x99891,a862),a862),f869(x99891)),a329),f174(x99891))),x99892))),f138(x99891)))),f226(x99891,x99892)) % 165.28/165.04 [6054]E(f332(f332(f81(a868),f332(f332(f22(a868),x60541),x60542)),x60542),x60541)+~P24(f332(f332(f246(a868),x60542),x60541)) % 165.28/165.04 [6121]E(f332(f332(f39(a868),f332(f332(f82(a868),x61211),x61212)),x61212),x61211)+~P24(f332(f332(f247(a868),f2(a868)),x61212)) % 165.28/165.04 [6122]E(f332(f332(f39(a868),f332(f332(f82(a868),x61221),x61222)),x61221),x61222)+~P24(f332(f332(f247(a868),f2(a868)),x61221)) % 165.28/165.04 [6126]~P74(x61261)+E(f332(f332(f6(a868,x61261),f332(f166(x61261),x61262)),f332(f302(a868,f2(a868)),f332(f197(f869(x61261)),x61262))),f332(f167(x61261),x61262)) % 165.28/165.04 [6244]E(f45(a868,f332(a115,f332(f332(f82(a868),x62441),x62442)),x62441),f79(a868))+~P24(f332(f332(f247(a868),f79(a868)),x62441)) % 165.28/165.04 [6250]E(f332(a115,f332(f332(f81(a868),f332(f106(a868),x62501)),x62502)),f332(f332(f81(a868),f79(a868)),x62502))+~P24(f332(a201,f332(f106(a1),x62501))) % 165.28/165.04 [6277]E(f332(a107,f332(f332(f257(a1),f332(f106(a1),x62771)),x62772)),f332(f332(f257(a868),f332(f106(a868),x62771)),x62772))+P24(f332(a201,f332(f106(a1),x62771))) % 165.28/165.04 [6516]E(f332(f332(f22(a868),x65161),f332(f106(a868),f332(f332(f81(a1),x65162),a100))),f332(f332(f22(a868),f332(a115,x65161)),f332(f106(a868),x65162)))+~P24(f332(f332(f247(a1),a84),x65162)) % 165.28/165.04 [6594]E(x65941,f2(a868))+E(f332(a115,f332(f332(f81(a868),f332(f332(f22(a868),x65941),f79(a868))),x65942)),f332(f332(f81(a868),x65941),x65942)) % 165.28/165.04 [6634]E(x66341,f2(a1))+P24(f332(f332(f247(a1),f2(a1)),f332(f332(f257(a1),f332(f76(a1),x66341)),x66342))) % 165.28/165.04 [6649]~E(x66492,f2(a868))+P24(f332(f332(f247(a1),f2(a1)),f332(f332(f257(a1),f332(f76(a1),x66491)),x66492))) % 165.28/165.04 [6686]E(x66861,f2(a868))+E(f332(f332(f81(a868),x66862),f332(f332(f82(a868),f332(f332(f22(a868),x66861),f79(a868))),x66862)),f332(f332(f82(a868),x66861),x66862)) % 165.28/165.04 [6734]~P24(f332(f332(f246(a1),x67341),x67342))+P24(f332(f332(f247(a1),f332(f332(f81(a1),x67341),a100)),x67342)) % 165.28/165.04 [6863]E(f332(f332(f152(a868),x68631),f140(a868,f332(f302(a868,f332(a115,x68631)),x68632))),f140(a868,f332(f302(a868,x68631),x68632)))+~P24(f332(f332(f247(a868),x68631),x68632)) % 165.28/165.04 [7062]E(x70621,x70622)+~E(f332(f332(f22(a1),f332(f332(f81(a1),x70621),x70621)),a100),f332(f332(f22(a1),f332(f332(f81(a1),x70622),x70622)),a100)) % 165.28/165.04 [7065]E(x70651,f116(x70652))+E(f276(x70652,f332(f332(f155(x70652,f874(a102,x70652)),f332(f267(a102,x70652),f79(a102))),x70651)),f283(x70652,x70651)) % 165.28/165.04 [7289]P24(f332(f332(f246(a1),x72891),x72892))+~P24(f332(f332(f247(a1),f332(f332(f81(a1),x72891),a100)),x72892)) % 165.28/165.04 [7769]~P24(f332(f332(f247(a868),x77691),x77692))+P24(f332(f332(f334(f874(a868,a868)),f332(f332(f267(a868,a868),x77691),x77692)),a251)) % 165.28/165.04 [7986]~P24(f332(f332(f247(a102),f2(a102)),x79861))+P24(f332(f332(f247(a102),f332(f266(a102,f874(a102,a102)),f332(f277(x79861),x79862))),x79861)) % 165.28/165.04 [8293]~P85(x82931)+P24(f332(f332(f246(x82931),f332(f76(x82931),f332(f167(x82931),x82932))),f332(f167(x82931),f332(f332(f155(x82931,x82931),f76(x82931)),x82932)))) % 165.28/165.04 [8317]P24(f332(f332(f247(a868),x83171),x83172))+~P24(f332(f332(f334(f874(a868,a868)),f332(f332(f267(a868,a868),x83171),x83172)),a251)) % 165.28/165.04 [8463]E(f332(f332(f267(x84631,x84631),f742(x84632,x84631)),f742(x84632,x84631)),x84632)+~P24(f332(f332(f334(f874(x84631,x84631)),x84632),f308(x84631,f196(f875(f874(x84631,x84631),a862))))) % 165.28/165.04 [8504]E(f332(f302(a868,x85041),f332(f332(f81(a868),x85041),f332(f38(a868),x85042))),x85042)+~P24(f332(f332(f246(f875(a868,a862)),x85042),f332(f302(a868,x85041),f332(f332(f81(a868),x85041),f332(f38(a868),x85042))))) % 165.28/165.04 [8832]E(f332(f332(f39(a1),f332(f106(a1),f332(f332(f22(a1),f332(f332(f81(a1),x88321),x88321)),a100))),f332(f106(a1),f332(f332(f81(a1),x88322),x88322))),f332(f332(f39(a1),f332(f106(a1),x88321)),f332(f106(a1),x88322)))+~P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x88322))) % 165.28/165.04 [8951]E(f179(f869(x89511),f332(f332(f8(a862,a862,f869(x89511)),a327),f332(f332(f7(f869(x89511),f869(x89511),a862),a329),f116(x89511))),x89512),f182(x89511,f182(x89511,x89512)))+~P32(a868,f332(f170(a868),f332(f332(f155(f869(x89511),a868),f197(f869(x89511))),x89512))) % 165.28/165.04 [8954]E(f332(f332(f39(a1),f332(f106(a1),f332(f332(f22(a1),f332(f332(f81(a1),x89541),x89541)),a100))),f332(f106(a1),f332(f332(f81(a1),x89542),x89542))),f332(f332(f39(a1),f332(f332(f81(a1),f332(f106(a1),x89541)),f79(a1))),f332(f106(a1),x89542)))+P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x89542))) % 165.28/165.04 [9766]P24(f332(a201,x97662))+E(f332(f332(f87(a1,a868),f332(f332(f22(a1),x97661),x97662)),f332(f332(f18(a1,a868,a868),f332(f332(f7(a1,a868,f875(a868,a868)),f332(f332(f8(a862,f875(a868,f875(a868,a868)),a1),f99(a868)),a201)),f2(a868))),a107)),f332(f332(f22(a868),f332(a107,x97661)),f332(a107,x97662))) % 165.28/165.04 [9774]E(f332(f332(f87(a1,a868),f332(f106(a1),f332(f332(f81(a1),x97741),f332(f80(a1),x97742)))),f332(f332(f18(a1,a868,a868),f332(f332(f7(a1,a868,f875(a868,a868)),f332(f332(f8(a862,f875(a868,f875(a868,a868)),a1),f99(a868)),a201)),f2(a868))),a107)),f332(f332(f22(a868),f332(f106(a868),x97741)),f332(f106(a868),x97742)))+P24(f332(f332(f247(a1),x97742),a84)) % 165.28/165.04 [9776]~P22(x97761,x97762)+P24(f332(f332(f246(f875(f874(x97761,x97761),a862)),f332(f332(f289(x97761,x97761,x97761),f332(f266(f875(f874(x97761,x97761),a862),f875(f874(x97761,x97761),a862)),x97762)),f332(f270(f875(f874(x97761,x97761),a862),f875(f874(x97761,x97761),a862)),x97762))),f332(f266(f875(f874(x97761,x97761),a862),f875(f874(x97761,x97761),a862)),x97762))) % 165.28/165.04 [9840]~E(f332(f38(a868),f332(f252(a868),f332(f332(f18(a868,a862,a862),f332(f332(f8(a862,f875(a862,a862),a868),a330),f332(f332(f7(a868,f875(a868,a862),a862),f334(a868)),x98401))),f332(f332(f7(a868,a868,a862),f247(a868)),f332(a115,x98402))))),f2(a868))+~P24(f332(f332(f334(a868),f2(a868)),x98401)) % 165.28/165.04 [9896]E(f45(a1,f332(f106(a1),f332(f332(f22(a1),f332(f332(f81(a1),x98961),x98961)),a100)),f332(f106(a1),f332(f332(f81(a1),x98962),x98962))),f332(f332(f81(a1),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f45(a1,f332(f106(a1),x98961),f332(f106(a1),x98962)))),f79(a1)))+~P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x98962))) % 165.28/165.04 [9905]E(f45(a1,f332(f106(a1),f332(f332(f22(a1),f332(f332(f81(a1),x99051),x99051)),a100)),f332(f106(a1),f332(f332(f81(a1),x99052),x99052))),f332(f332(f22(a1),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f45(a1,f332(f332(f81(a1),f332(f106(a1),x99051)),f79(a1)),f332(f106(a1),x99052)))),f79(a1)))+P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x99052))) % 165.28/165.04 [9957]~P30(x99571)+E(f40(x99571,f332(f252(x99571),f332(f332(f8(f875(x99571,a862),a862,x99571),f89(x99571)),f332(f332(f8(f875(x99571,a862),f875(x99571,a862),x99571),f332(f18(x99571,a862,a862),f332(f332(f8(a862,f875(a862,a862),x99571),a335),f332(f332(f7(x99571,f875(x99571,a862),a862),f334(x99571)),x99572)))),f246(x99571))))),f41(x99571,x99572)) % 165.28/165.04 [9982]~P41(x99821,x99822)+P58(x99821,f332(f332(f7(x99821,f875(f874(x99821,x99821),a862),f875(x99821,a862)),f332(f332(f8(f875(x99821,f875(f875(f874(x99821,x99821),a862),a862)),f875(f875(f874(x99821,x99821),a862),f875(x99821,a862)),x99821),f7(x99821,f875(f874(x99821,x99821),a862),a862)),f332(f332(f8(f875(x99821,f874(x99821,x99821)),f875(x99821,f875(f875(f874(x99821,x99821),a862),a862)),x99821),f332(f8(f874(x99821,x99821),f875(f875(f874(x99821,x99821),a862),a862),x99821),f334(f874(x99821,x99821)))),f267(x99821,x99821)))),x99822)) % 165.28/165.04 [9983]~P6(x99831,f255(f875(x99831,a862)),x99832)+P5(x99831,f332(f332(f7(x99831,f875(f874(x99831,x99831),a862),f875(x99831,a862)),f332(f332(f8(f875(x99831,f875(f875(f874(x99831,x99831),a862),a862)),f875(f875(f874(x99831,x99831),a862),f875(x99831,a862)),x99831),f7(x99831,f875(f874(x99831,x99831),a862),a862)),f332(f332(f8(f875(x99831,f874(x99831,x99831)),f875(x99831,f875(f875(f874(x99831,x99831),a862),a862)),x99831),f332(f8(f874(x99831,x99831),f875(f875(f874(x99831,x99831),a862),a862),x99831),f334(f874(x99831,x99831)))),f267(x99831,x99831)))),x99832)) % 165.28/165.04 [10020]P41(x100201,x100202)+~P58(x100201,f332(f332(f7(x100201,f875(f874(x100201,x100201),a862),f875(x100201,a862)),f332(f332(f8(f875(x100201,f875(f875(f874(x100201,x100201),a862),a862)),f875(f875(f874(x100201,x100201),a862),f875(x100201,a862)),x100201),f7(x100201,f875(f874(x100201,x100201),a862),a862)),f332(f332(f8(f875(x100201,f874(x100201,x100201)),f875(x100201,f875(f875(f874(x100201,x100201),a862),a862)),x100201),f332(f8(f874(x100201,x100201),f875(f875(f874(x100201,x100201),a862),a862),x100201),f334(f874(x100201,x100201)))),f267(x100201,x100201)))),x100202)) % 165.28/165.04 [10021]P6(x100211,f255(f875(x100211,a862)),x100212)+~P5(x100211,f332(f332(f7(x100211,f875(f874(x100211,x100211),a862),f875(x100211,a862)),f332(f332(f8(f875(x100211,f875(f875(f874(x100211,x100211),a862),a862)),f875(f875(f874(x100211,x100211),a862),f875(x100211,a862)),x100211),f7(x100211,f875(f874(x100211,x100211),a862),a862)),f332(f332(f8(f875(x100211,f874(x100211,x100211)),f875(x100211,f875(f875(f874(x100211,x100211),a862),a862)),x100211),f332(f8(f874(x100211,x100211),f875(f875(f874(x100211,x100211),a862),a862),x100211),f334(f874(x100211,x100211)))),f267(x100211,x100211)))),x100212)) % 165.28/165.04 [7240]E(f332(f332(f81(a868),f332(f106(a868),f332(f332(f22(a1),x72401),a100))),x72402),f332(a115,f332(f332(f81(a868),f332(f106(a868),x72401)),x72402)))+P24(f332(a201,f332(f106(a1),x72401))) % 165.28/165.04 [7685]~P92(x76851)+E(f332(f332(f81(x76851),f332(f332(f81(x76851),f79(x76851)),f332(f106(x76851),x76852))),f332(f106(x76851),x76852)),f332(f106(x76851),f332(f332(f22(a1),f332(f332(f81(a1),x76852),x76852)),a100))) % 165.28/165.04 [8319]~P24(f332(f332(f246(a1),x83191),x83192))+P24(f332(f332(f246(a1),f332(f332(f81(a1),x83191),x83191)),f332(f332(f22(a1),f332(f332(f81(a1),x83192),x83192)),a100))) % 165.28/165.04 [8321]~P24(f332(f332(f246(a1),x83211),x83212))+P24(f332(f332(f247(a1),f332(f332(f81(a1),x83211),x83211)),f332(f332(f22(a1),f332(f332(f81(a1),x83212),x83212)),a100))) % 165.28/165.04 [8725]P24(f332(f332(f246(a1),x87251),x87252))+~P24(f332(f332(f246(a1),f332(f332(f81(a1),x87251),x87251)),f332(f332(f22(a1),f332(f332(f81(a1),x87252),x87252)),a100))) % 165.28/165.04 [8727]P24(f332(f332(f246(a1),x87271),x87272))+~P24(f332(f332(f247(a1),f332(f332(f81(a1),x87271),x87271)),f332(f332(f22(a1),f332(f332(f81(a1),x87272),x87272)),a100))) % 165.28/165.04 [9010]~P24(f332(f332(f246(a1),x90101),x90102))+P24(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f81(a1),x90101),x90101)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),x90102),x90102)),a100))) % 165.28/165.04 [9012]~P24(f332(f332(f247(a1),x90121),x90122))+P24(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f81(a1),x90121),x90121)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),x90122),x90122)),a100))) % 165.28/165.04 [9013]~P24(f332(f332(f92(a1),x90131),x90132))+P24(f332(f332(f92(a1),f332(f332(f22(a1),f332(f332(f81(a1),x90131),x90131)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),x90132),x90132)),a100))) % 165.28/165.04 [9264]P24(f332(f332(f246(a1),x92641),x92642))+~P24(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f81(a1),x92641),x92641)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),x92642),x92642)),a100))) % 165.28/165.04 [9266]P24(f332(f332(f247(a1),x92661),x92662))+~P24(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f81(a1),x92661),x92661)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),x92662),x92662)),a100))) % 165.28/165.04 [9267]P24(f332(f332(f92(a1),x92671),x92672))+~P24(f332(f332(f92(a1),f332(f332(f22(a1),f332(f332(f81(a1),x92671),x92671)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),x92672),x92672)),a100))) % 165.28/165.04 [9299]~P24(f332(f62(x92991),x92992))+P24(f332(f62(f875(x92991,a862)),f332(f252(f875(x92991,a862)),f332(f332(f7(f875(x92991,a862),f875(x92991,a862),a862),f246(f875(x92991,a862))),x92992)))) % 165.28/165.04 [9344]~E(f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),x93441),f196(f875(f874(a868,a868),a862)))),f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),x93442),f196(f875(f874(a868,a868),a862)))))+P24(f332(f332(f334(f874(f874(a868,a868),f874(a868,a868))),f332(f332(f267(f874(a868,a868),f874(a868,a868)),x93441),x93442)),a111)) % 165.28/165.04 [9426]E(f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),x94261),f196(f875(f874(a868,a868),a862)))),f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),x94262),f196(f875(f874(a868,a868),a862)))))+~P24(f332(f332(f334(f874(f874(a868,a868),f874(a868,a868))),f332(f332(f267(f874(a868,a868),f874(a868,a868)),x94261),x94262)),a111)) % 165.28/165.04 [9459]P24(f332(f332(f246(a1),f2(a1)),f774(x94591,x94592)))+E(f332(f252(a1),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f246(a1),f2(a1)))),x94591)),f332(f252(a1),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f246(a1),f2(a1)))),x94592))) % 165.28/165.04 [9967]~P30(x99671)+E(f41(x99671,f332(f252(x99671),f332(f332(f8(f875(x99671,a862),a862,x99671),f89(x99671)),f332(f332(f8(f875(x99671,a862),f875(x99671,a862),x99671),f332(f18(x99671,a862,a862),f332(f332(f8(a862,f875(a862,a862),x99671),a335),f332(f332(f7(x99671,f875(x99671,a862),a862),f334(x99671)),x99672)))),f332(f7(x99671,x99671,a862),f246(x99671)))))),f40(x99671,x99672)) % 165.28/165.04 [9988]P24(f332(f332(f334(a868),f2(a868)),x99881))+E(f332(f38(a868),f332(f252(a868),f332(f332(f18(a868,a862,a862),f332(f332(f8(a862,f875(a862,a862),a868),a330),f332(f332(f7(a868,f875(a868,a862),a862),f332(f332(f8(a868,f875(f875(a868,a862),a862),a868),f334(a868)),a115)),x99881))),f332(f332(f7(a868,a868,a862),f247(a868)),x99882)))),f332(f38(a868),f332(f252(a868),f332(f332(f18(a868,a862,a862),f332(f332(f8(a862,f875(a862,a862),a868),a330),f332(f332(f7(a868,f875(a868,a862),a862),f334(a868)),x99881))),f332(f332(f7(a868,a868,a862),f247(a868)),f332(a115,x99882)))))) % 165.28/165.04 [7554]~P92(x75541)+E(f332(f332(f82(x75541),x75542),f332(f106(x75541),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),x75542) % 165.28/165.04 [7814]~P92(x78141)+E(f332(f332(f81(x78141),f332(f106(x78141),x78142)),f79(x78141)),f332(f106(x78141),f332(f332(f81(a1),x78142),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))) % 165.28/165.04 [7958]P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x79582)))+E(f332(f332(f257(a1),x79581),f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),x79582),x79582)),a100))),f79(a1)) % 165.28/165.04 [9323]~P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x93232)))+E(f332(f332(f257(a1),x93231),f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),x93232),x93232)),a100))),f332(f332(f87(a1,a1),f332(f332(f257(a1),x93231),f332(f106(a868),x93232))),f332(f332(f18(a1,a1,a1),f332(f332(f8(a1,f875(a1,a1),a1),f82(a1)),f332(f82(a1),x93231))),f5(a1)))) % 165.28/165.04 [9680]~P24(f332(f332(f246(a868),f801(x96802,x96801)),f332(x96801,f801(x96802,x96801))))+P24(f332(f62(a868),f332(f252(a868),f332(f332(f7(a868,a868,a862),f332(f332(f8(a868,f875(a868,a862),a868),f246(a868)),x96801)),x96802)))) % 165.28/165.04 [9830]~P24(f332(f332(f246(a868),f332(f106(a868),x98301)),f332(a115,x98302)))+P24(f332(f332(f87(a1,a862),f332(f106(a1),f332(f332(f81(a1),x98301),a100))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a335),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f7(a1,a868,a862),f332(f332(f8(a868,f875(a868,a862),a1),f246(a868)),a107)),x98302)))) % 165.28/165.04 [9831]~P24(f332(f332(f247(a868),f332(f106(a868),x98311)),f332(a115,x98312)))+P24(f332(f332(f87(a1,a862),f332(f106(a1),f332(f332(f81(a1),x98311),a100))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a335),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f7(a1,a868,a862),f332(f332(f8(a868,f875(a868,a862),a1),f247(a868)),a107)),x98312)))) % 165.28/165.04 [9880]P24(f332(f332(f246(a868),f332(f106(a868),x98801)),f332(a115,x98802)))+~P24(f332(f332(f87(a1,a862),f332(f106(a1),f332(f332(f81(a1),x98801),a100))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a335),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f7(a1,a868,a862),f332(f332(f8(a868,f875(a868,a862),a1),f246(a868)),a107)),x98802)))) % 165.28/165.04 [9881]P24(f332(f332(f247(a868),f332(f106(a868),x98811)),f332(a115,x98812)))+~P24(f332(f332(f87(a1,a862),f332(f106(a1),f332(f332(f81(a1),x98811),a100))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a335),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f7(a1,a868,a862),f332(f332(f8(a868,f875(a868,a862),a1),f247(a868)),a107)),x98812)))) % 165.28/165.04 [9911]~P24(f332(f332(f246(a868),f332(a115,x99112)),f332(f106(a868),x99111)))+P24(f332(f332(f87(a1,a862),f332(f106(a1),f332(f332(f81(a1),x99111),a100))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a335),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f8(a868,a862,a1),f332(f246(a868),x99112)),a107))))) % 165.28/165.04 [9912]~P24(f332(f332(f247(a868),f332(a115,x99122)),f332(f106(a868),x99121)))+P24(f332(f332(f87(a1,a862),f332(f106(a1),f332(f332(f81(a1),x99121),a100))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a335),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f8(a868,a862,a1),f332(f247(a868),x99122)),a107))))) % 165.28/165.04 [9955]P24(f332(f332(f246(a868),f332(a115,x99551)),f332(f106(a868),x99552)))+~P24(f332(f332(f87(a1,a862),f332(f106(a1),f332(f332(f81(a1),x99552),a100))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a335),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f8(a868,a862,a1),f332(f246(a868),x99551)),a107))))) % 165.28/165.04 [9956]P24(f332(f332(f247(a868),f332(a115,x99561)),f332(f106(a868),x99562)))+~P24(f332(f332(f87(a1,a862),f332(f106(a1),f332(f332(f81(a1),x99562),a100))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a335),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f8(a868,a862,a1),f332(f247(a868),x99561)),a107))))) % 165.28/165.04 [10027]~P24(f332(f332(f334(a868),f2(a868)),x100271))+E(f332(a115,f332(f38(a868),f332(f252(a868),f332(f332(f18(a868,a862,a862),f332(f332(f8(a862,f875(a862,a862),a868),a330),f332(f332(f7(a868,f875(a868,a862),a862),f332(f332(f8(a868,f875(f875(a868,a862),a862),a868),f334(a868)),a115)),x100271))),f332(f332(f7(a868,a868,a862),f247(a868)),x100272))))),f332(f38(a868),f332(f252(a868),f332(f332(f18(a868,a862,a862),f332(f332(f8(a862,f875(a862,a862),a868),a330),f332(f332(f7(a868,f875(a868,a862),a862),f334(a868)),x100271))),f332(f332(f7(a868,a868,a862),f247(a868)),f332(a115,x100272)))))) % 165.28/165.04 [8488]~P92(x84881)+E(f332(f332(f82(x84881),f332(f106(x84881),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),x84882),x84882) % 165.28/165.04 [8547]~P92(x85471)+E(f332(f332(f81(x85471),f79(x85471)),f332(f106(x85471),x85472)),f332(f106(x85471),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),x85472))) % 165.28/165.04 [8604]~P92(x86041)+E(f332(f332(f22(x86041),f332(f106(x86041),x86042)),f79(x86041)),f332(f106(x86041),f332(f332(f81(a1),x86042),f332(f80(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))) % 165.28/165.04 [8743]~P24(f332(f332(f247(a868),f332(f106(a868),a84)),x87432))+E(f332(f332(f22(a868),x87431),f332(f332(f22(a868),x87432),f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(f332(f22(a868),f332(a115,x87431)),x87432)) % 165.28/165.04 [9360]~P113(x93601)+E(f332(f332(f82(x93601),x93602),x93602),f332(f332(f257(x93601),x93602),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))) % 165.28/165.04 [9361]~P79(x93611)+E(f332(f332(f257(x93611),x93612),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(f332(f82(x93611),x93612),x93612)) % 165.28/165.04 [9363]~P92(x93631)+E(f332(f332(f82(x93631),x93632),f332(f106(x93631),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(f332(f81(x93631),x93632),x93632)) % 165.28/165.04 [9598]~P138(x95981)+E(f332(f332(f257(x95981),f332(f80(x95981),x95982)),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(f332(f257(x95981),x95982),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))) % 165.28/165.04 [9599]~P118(x95991)+E(f332(f332(f257(x95991),f332(f76(x95991),x95992)),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(f332(f257(x95991),x95992),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))) % 165.28/165.04 [9595]~P92(x95951)+E(f332(f332(f82(x95951),f332(f106(x95951),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x95952),f332(f332(f81(x95951),x95952),x95952)) % 165.28/165.04 [9720]~P118(x97201)+E(f332(f76(x97201),f332(f332(f257(x97201),x97202),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x97201),x97202),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))) % 165.28/165.04 [9783]~P118(x97831)+P24(f332(f332(f246(x97831),f2(x97831)),f332(f332(f257(x97831),x97832),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))) % 165.28/165.04 [9946]~E(f332(a115,x99462),f332(f106(a868),x99461))+P24(f332(f332(f87(a1,a862),f332(f106(a1),f332(f332(f81(a1),x99461),a100))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a335),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f7(a1,a868,a862),f332(f332(f8(a868,f875(a868,a862),a1),a329),a107)),x99462))))) % 165.28/165.04 [9947]~E(f332(f106(a868),x99471),f332(a115,x99472))+P24(f332(f332(f87(a1,a862),f332(f106(a1),f332(f332(f81(a1),x99471),a100))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a335),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f7(a1,a868,a862),f332(f332(f8(a868,f875(a868,a862),a1),a329),a107)),x99472))))) % 165.28/165.04 [9991]E(f332(a115,x99911),f332(f106(a868),x99912))+~P24(f332(f332(f87(a1,a862),f332(f106(a1),f332(f332(f81(a1),x99912),a100))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a335),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f7(a1,a868,a862),f332(f332(f8(a868,f875(a868,a862),a1),a329),a107)),x99911))))) % 165.28/165.04 [9992]E(f332(f106(a868),x99921),f332(a115,x99922))+~P24(f332(f332(f87(a1,a862),f332(f106(a1),f332(f332(f81(a1),x99921),a100))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a335),f332(f332(f8(a862,a862,a1),a327),a201))),f332(f332(f7(a1,a868,a862),f332(f332(f8(a868,f875(a868,a862),a1),a329),a107)),x99922))))) % 165.28/165.04 [9781]~P92(x97811)+E(f332(f332(f257(x97811),f332(f106(x97811),a100)),f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x97812)),f79(x97811)) % 165.28/165.04 [9782]~P138(x97821)+E(f332(f332(f257(x97821),f332(f80(x97821),f79(x97821))),f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x97822)),f79(x97821)) % 165.28/165.04 [9785]~P79(x97851)+E(f332(f332(f257(x97851),x97852),f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),a100))),f332(f332(f82(x97851),f332(f332(f82(x97851),x97852),x97852)),x97852)) % 165.28/165.04 [9971]~P24(f332(f332(f246(a1),f2(a1)),x99712))+E(f45(a1,f332(f332(f81(a1),f79(a1)),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x99711)),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x99712)),f332(f332(f81(a1),f79(a1)),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f45(a1,x99711,x99712)))) % 165.28/165.04 [9994]~P24(f332(f332(f246(a1),f2(a1)),x99942))+E(f332(f332(f39(a1),f332(f332(f81(a1),f79(a1)),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x99941))),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x99942)),f332(f332(f39(a1),x99941),x99942)) % 165.28/165.04 [9996]~P24(f332(f332(f246(a1),x99962),f2(a1)))+E(f332(f332(f39(a1),f332(f332(f81(a1),f79(a1)),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x99961))),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x99962)),f332(f332(f39(a1),f332(f332(f81(a1),x99961),f79(a1))),x99962)) % 165.28/165.04 [9997]~P24(f332(f332(f246(a1),x99972),f2(a1)))+E(f45(a1,f332(f332(f81(a1),f79(a1)),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x99971)),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x99972)),f332(f332(f22(a1),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f45(a1,f332(f332(f81(a1),x99971),f79(a1)),x99972))),f79(a1))) % 165.28/165.04 [9871]~P92(x98711)+E(f332(f332(f257(x98711),f332(f106(x98711),a100)),f332(a115,f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x98712))),f332(f106(x98711),a100)) % 165.28/165.04 [9873]~P138(x98731)+E(f332(f332(f257(x98731),f332(f80(x98731),f79(x98731))),f332(a115,f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x98732))),f332(f80(x98731),f79(x98731))) % 165.28/165.04 [5095]~P20(x50951,x50952,x50953)+P23(x50951,x50952,x50953) % 165.28/165.04 [8024]~E(x80242,x80243)+P38(x80241,x80241,a329,x80242,x80243) % 165.28/165.04 [8560]E(x85601,x85602)+~P38(x85603,x85603,a329,x85601,x85602) % 165.28/165.04 [4738]E(f171(x47381,x47382,x47383),f116(x47381))+~E(x47382,f2(a868)) % 165.28/165.04 [4904]~E(f171(x49042,x49041,x49043),f116(x49042))+E(x49041,f2(a868)) % 165.28/165.04 [5100]~P41(x51001,x51003)+P41(x51001,f326(x51001,x51002,x51003)) % 165.28/165.04 [5276]P33(x52761,x52762,x52763)+~P33(x52761,f332(a115,x52762),x52763) % 165.28/165.04 [5363]~P6(x53631,x53632,x53633)+P6(f869(x53631),f162(x53631,x53632),f159(x53631,x53633)) % 165.28/165.04 [5364]~P43(x53641,x53642,x53643)+P43(f869(x53641),f162(x53641,x53642),f159(x53641,x53643)) % 165.28/165.04 [5476]P53(x54761,x54762,x54763)+~E(f706(x54763,x54762,x54761),f707(x54763,x54762,x54761)) % 165.28/165.04 [5477]P54(x54771,x54772,x54773)+~E(f732(x54773,x54772,x54771),f733(x54773,x54772,x54771)) % 165.28/165.04 [6420]P23(x64201,x64202,x64203)+~P33(x64201,f536(x64203,x64202,x64201),f552(x64203,x64202,x64201)) % 165.28/165.04 [4644]~E(x46441,f209(x46442))+~E(x46441,f332(f208(x46442),x46443)) % 165.28/165.04 [4694]~E(f332(f170(x46942),x46941),x46943)+E(x46941,f332(f170(x46942),x46943)) % 165.28/165.04 [4695]~E(x46952,f332(f170(x46951),x46953))+E(f332(f170(x46951),x46952),x46953) % 165.28/165.04 [4744]E(x47441,x47442)+~E(f332(f208(x47443),x47441),f332(f208(x47443),x47442)) % 165.28/165.04 [4745]E(x47451,x47452)+~E(f332(f170(x47453),x47451),f332(f170(x47453),x47452)) % 165.28/165.04 [4951]~P5(x49513,x49511)+P24(f332(f332(x49511,x49512),x49512)) % 165.28/165.04 [4952]~P52(x49523,x49521)+P24(f332(f332(x49521,x49522),x49522)) % 165.28/165.04 [4954]~P58(x49541,x49542)+P24(f332(f320(x49541,x49542),x49543)) % 165.28/165.04 [5017]~P41(x50171,x50172)+P41(f869(x50171),f332(f144(x50171,x50172),x50173)) % 165.28/165.04 [5022]~P24(f332(x50222,x50223))+~E(f332(f252(x50221),x50222),f196(f875(x50221,a862))) % 165.28/165.04 [5023]~P24(f332(x50232,x50233))+~E(f196(f875(x50231,a862)),f332(f252(x50231),x50232)) % 165.28/165.04 [5037]E(x50371,f2(a868))+E(f145(x50372,f171(x50372,x50371,x50373)),x50373) % 165.28/165.04 [5055]~P24(f332(x50551,x50553))+P24(f332(x50551,f91(x50552,x50551))) % 165.28/165.04 [5067]E(x50671,f2(a868))+E(f332(f142(x50672),f171(x50672,x50671,x50673)),x50673) % 165.28/165.04 [5180]~E(x51802,x51803)+P24(f332(f332(f334(x51801),x51802),f332(a329,x51803))) % 165.28/165.04 [5192]~E(x51922,f2(a868))+E(f332(f174(x51921),f171(x51921,x51922,x51923)),f196(f875(x51921,a862))) % 165.28/165.04 [5239]E(f332(f170(x52391),x52392),f332(f332(f152(x52391),x52393),f116(x52391)))+~E(x52392,f332(f332(f152(x52391),x52393),f116(x52391))) % 165.28/165.04 [5240]~E(x52403,f332(f332(f152(x52401),x52402),f116(x52401)))+E(f332(f332(f152(x52401),x52402),f116(x52401)),f332(f170(x52401),x52403)) % 165.28/165.04 [5269]~E(x52693,f332(f16(f872(x52692),x52691),f209(x52692)))+E(f186(x52691,x52692,x52693),f196(f875(x52691,a862))) % 165.28/165.04 [5291]~P37(x52911,x52912,x52913)+P37(x52911,x52912,f332(f170(x52911),x52913)) % 165.28/165.04 [5292]~P35(x52921,x52922,x52923)+P35(x52921,x52922,f332(f170(x52921),x52923)) % 165.28/165.04 [5295]E(f332(f38(x52951),f704(x52952,x52953,x52951)),x52952)+~E(f332(f38(x52951),x52953),f332(a115,x52952)) % 165.28/165.04 [5301]~P41(x53011,x53013)+P24(f332(f332(f334(x53011),x53012),f321(x53011,x53013))) % 165.28/165.04 [5305]~E(f332(f170(x53052),x53051),f332(f332(f152(x53052),x53053),f116(x53052)))+E(x53051,f332(f332(f152(x53052),x53053),f116(x53052))) % 165.28/165.04 [5306]~E(f332(f332(f152(x53062),x53063),f116(x53062)),f332(f170(x53062),x53061))+E(x53061,f332(f332(f152(x53062),x53063),f116(x53062))) % 165.28/165.04 [5321]E(x53211,f332(f16(f872(x53212),x53213),f209(x53212)))+~E(f186(x53213,x53212,x53211),f196(f875(x53213,a862))) % 165.28/165.04 [5327]E(f86(f874(a868,a868),f48(x53271,x53272)),x53273)+~P24(f332(f48(x53271,x53272),x53273)) % 165.28/165.04 [5335]~E(x53353,f332(f208(x53351),x53352))+P24(f332(f332(f334(x53351),x53352),f239(x53351,x53353))) % 165.28/165.04 [5367]P37(x53671,x53672,x53673)+~P37(x53671,x53672,f332(f170(x53671),x53673)) % 165.28/165.04 [5368]P35(x53681,x53682,x53683)+~P35(x53681,x53682,f332(f170(x53681),x53683)) % 165.28/165.04 [5430]~E(x54302,f116(x54301))+P24(f332(f332(f334(f869(x54301)),x54302),f162(x54301,x54303))) % 165.28/165.04 [5437]~P43(x54371,x54372,x54373)+P43(x54371,x54372,f332(f287(x54371,x54371),x54373)) % 165.28/165.04 [5438]~P54(x54381,x54382,x54383)+P54(x54381,x54382,f332(f287(x54381,x54381),x54383)) % 165.28/165.04 [5457]~P28(x54571)+E(f45(x54571,f45(x54571,x54572,x54573),x54573),f45(x54571,x54572,x54573)) % 165.28/165.04 [5554]E(x55541,x55542)+~P24(f332(f332(f334(x55543),x55541),f332(a329,x55542))) % 165.28/165.04 [5600]~P142(x56001)+E(f198(x56001,x56002,f2(a868),x56003),x56003) % 165.28/165.04 [5620]P43(x56201,x56202,x56203)+~P43(x56201,x56202,f332(f287(x56201,x56201),x56203)) % 165.28/165.04 [5621]P54(x56211,x56212,x56213)+~P54(x56211,x56212,f332(f287(x56211,x56211),x56213)) % 165.28/165.04 [5625]~P106(x56252)+E(f151(x56251,x56252,x56253,f116(x56251)),f116(x56251)) % 165.28/165.04 [5638]E(f172(x56381,x56382,f153(x56381,x56383)),f153(x56381,f172(x56381,x56382,x56383)))+~P24(f332(f138(x56381),x56383)) % 165.28/165.04 [5644]E(x56441,f332(f208(x56442),x56443))+~P24(f332(f332(f334(x56442),x56443),f239(x56442,x56441))) % 165.28/165.04 [5730]~P24(f332(a25,x57303))+P24(f332(a25,f30(x57301,x57302,x57303))) % 165.28/165.04 [5741]E(f332(f137(x57411,x57412),x57413),f116(x57411))+P24(f332(x57412,f569(x57413,x57412,x57411))) % 165.28/165.04 [5884]~P24(f332(f138(x58841),x58843))+P24(f332(f138(x58841),f172(x58841,x58842,x58843))) % 165.28/165.04 [5885]~P24(f332(f138(x58851),x58852))+P24(f332(f138(x58851),f178(x58851,x58852,x58853))) % 165.28/165.04 [5886]~P24(f332(f138(x58861),x58863))+P24(f332(f138(x58861),f179(x58861,x58862,x58863))) % 165.28/165.04 [5887]~P24(f332(f138(x58871),x58873))+P24(f332(f138(x58871),f141(x58871,x58872,x58873))) % 165.28/165.04 [5888]~P144(x58881,x58882,x58883)+P24(f332(x58881,f45(a1,x58882,x58883))) % 165.28/165.04 [5907]~P37(x59073,x59071,x59072)+P24(f332(x59071,f708(x59072,x59071,x59073))) % 165.28/165.04 [5908]~P39(x59083,x59081,x59082)+P24(f332(x59081,f794(x59082,x59081,x59083))) % 165.28/165.04 [5929]E(f332(f137(x59291,x59292),x59293),f179(x59291,x59292,x59293))+P24(f332(x59292,f632(x59293,x59292,x59291))) % 165.28/165.04 [5968]~P24(f332(f138(x59681),x59683))+P24(f332(f138(f869(x59681)),f55(x59681,x59682,x59683))) % 165.28/165.04 [5992]P24(f332(a25,f29(x59921,x59922,x59923)))+~P24(f332(a25,f332(a28,x59922))) % 165.28/165.04 [6004]~P107(x60041)+E(f332(f332(f104(f875(x60041,a862)),f332(f253(x60041),x60042)),f303(x60041,x60042,x60043)),f196(f875(x60041,a862))) % 165.28/165.04 [6005]~P107(x60051)+E(f332(f332(f104(f875(x60051,a862)),f332(f301(x60051),x60052)),f306(x60051,x60052,x60053)),f196(f875(x60051,a862))) % 165.28/165.04 [6006]~P107(x60061)+E(f332(f332(f104(f875(x60061,a862)),f332(f301(x60061),x60062)),f305(x60061,x60062,x60063)),f196(f875(x60061,a862))) % 165.28/165.04 [6155]P24(f332(a25,x61551))+~P24(f332(a25,f30(x61552,x61553,x61551))) % 165.28/165.04 [6157]P24(f332(a25,x61571))+~P24(f332(a25,f31(x61572,x61573,x61571))) % 165.28/165.04 [6159]P24(f332(a25,x61591))+~P24(f332(a25,f31(x61592,x61591,x61593))) % 165.28/165.04 [6240]E(f332(f137(x62401,x62402),x62403),x62403)+~P24(f332(x62402,f605(x62403,x62402,x62401))) % 165.28/165.04 [6242]E(f332(f332(f310(x62421),f853(x62422,x62423,x62421)),f704(x62422,x62423,x62421)),x62423)+~E(f332(f38(x62421),x62423),f332(a115,x62422)) % 165.28/165.04 [6257]P144(x62571,x62572,x62573)+~P24(f332(x62571,f45(a1,x62572,x62573))) % 165.28/165.04 [6304]P35(x63041,x63042,x63043)+~P24(f332(x63042,f782(x63042,x63043,x63041))) % 165.28/165.04 [6305]P35(x63051,x63052,x63053)+~P24(f332(x63052,f787(x63053,x63052,x63051))) % 165.28/165.04 [6306]P35(x63061,x63062,x63063)+~P24(f332(x63062,f788(x63063,x63062,x63061))) % 165.28/165.04 [6308]E(f179(x63081,x63082,x63083),x63083)+~P24(f332(x63082,f617(x63083,x63082,x63081))) % 165.28/165.04 [6346]~P24(f332(a25,f29(x63462,x63461,x63463)))+P24(f332(a25,f332(a28,x63461))) % 165.28/165.04 [6389]~P24(f332(x63892,f537(x63893,x63892,x63891)))+P24(f332(f260(x63891,x63892),x63893)) % 165.28/165.04 [6390]~P24(f332(x63902,f606(x63903,x63902,x63901)))+P24(f332(f161(x63901,x63902),x63903)) % 165.28/165.04 [6635]~P24(f332(f320(x66351,x66352),f486(x66353,x66352,x66351)))+P24(f332(f320(x66351,x66352),x66353)) % 165.28/165.04 [6636]~P24(f332(f320(x66361,x66362),f501(x66363,x66362,x66361)))+P24(f332(f320(x66361,x66362),x66363)) % 165.28/165.04 [7241]~P28(x72411)+E(f332(f332(f81(x72411),f332(f332(f82(x72411),x72412),f332(f332(f39(x72411),x72413),x72412))),f45(x72411,x72413,x72412)),x72413) % 165.28/165.04 [7708]E(f332(f332(f267(x77081,x77081),f517(x77082,x77083,x77081)),f517(x77082,x77083,x77081)),x77083)+~P24(f332(f332(f334(f874(x77081,x77081)),x77083),f264(x77081,x77082))) % 165.28/165.04 [7822]~P24(f332(f332(f334(x78221),f660(x78223,x78222,x78221)),f321(x78221,x78223)))+P24(f332(f332(f334(x78221),x78222),f321(x78221,x78223))) % 165.28/165.04 [7823]~P24(f332(f332(f334(x78231),f710(x78233,x78232,x78231)),f321(x78231,x78233)))+P24(f332(f332(f334(x78231),x78232),f321(x78231,x78233))) % 165.28/165.04 [7824]~P24(f332(f332(f334(x78241),f719(x78243,x78242,x78241)),f321(x78241,x78243)))+P24(f332(f332(f334(x78241),x78242),f321(x78241,x78243))) % 165.28/165.04 [8005]~P28(x80051)+E(f332(f332(f81(x80051),f332(f332(f82(x80051),f332(f332(f39(x80051),x80052),x80053)),x80053)),f45(x80051,x80052,x80053)),x80052) % 165.28/165.04 [8050]~E(f332(f38(x80501),x80502),f332(a115,x80503))+~P24(f332(f332(f334(x80501),f853(x80503,x80502,x80501)),f704(x80503,x80502,x80501))) % 165.28/165.04 [8655]P24(f332(f332(f246(f875(f874(x86551,x86551),a862)),f308(x86551,x86552)),f308(x86551,x86553)))+~P24(f332(f332(f246(f875(f874(x86551,x86551),a862)),x86552),f308(x86551,x86553))) % 165.28/165.04 [8920]E(x89201,f116(x89202))+~P24(f332(f332(f334(f874(f869(x89202),f869(x89202))),f332(f332(f267(f869(x89202),f869(x89202)),x89201),f116(x89202))),f159(x89202,x89203))) % 165.28/165.04 [8945]E(x89451,f116(x89452))+~P24(f332(f332(f334(f874(f869(x89452),f869(x89452))),f332(f332(f267(f869(x89452),f869(x89452)),f116(x89452)),x89451)),f159(x89452,x89453))) % 165.28/165.04 [9068]E(f332(f332(f152(x90681),f594(x90682,x90683,x90681)),f595(x90682,x90683,x90681)),x90683)+~P24(f332(f332(f334(f874(f869(x90681),f869(x90681))),f332(f332(f267(f869(x90681),f869(x90681)),f116(x90681)),x90683)),f148(x90681,x90682))) % 165.28/165.04 [9292]~P121(x92921)+~P24(f332(f332(f247(x92921),f332(f332(f81(x92921),f332(f332(f82(x92921),x92922),x92922)),f332(f332(f82(x92921),x92923),x92923))),f2(x92921))) % 165.28/165.04 [9339]P24(f332(f62(x93391),x93392))+~P24(f332(f332(f334(f874(f875(x93391,a862),f875(x93391,a862))),f332(f332(f267(f875(x93391,a862),f875(x93391,a862)),x93393),x93392)),f307(x93391))) % 165.28/165.04 [9621]~P50(x96211,x96212,x96213)+P24(f332(f332(f246(a1),f332(f332(f74(f874(a1,a1),a1,x96211,f266(a1,a1)),f224(x96211)),f235(x96211,x96212,f232(x96211,x96213)))),f2(a1))) % 165.28/165.04 [9622]~P51(x96221,x96222,x96223)+P24(f332(f332(f247(a1),f332(f332(f74(f874(a1,a1),a1,x96221,f266(a1,a1)),f224(x96221)),f235(x96221,x96222,f232(x96221,x96223)))),f2(a1))) % 165.28/165.04 [9750]P51(x97501,x97502,x97503)+~P24(f332(f332(f247(a1),f332(f332(f74(f874(a1,a1),a1,x97501,f266(a1,a1)),f224(x97501)),f235(x97501,x97502,f232(x97501,x97503)))),f2(a1))) % 165.28/165.04 [9751]P50(x97511,x97512,x97513)+~P24(f332(f332(f246(a1),f332(f332(f74(f874(a1,a1),a1,x97511,f266(a1,a1)),f224(x97511)),f235(x97511,x97512,f232(x97511,x97513)))),f2(a1))) % 165.28/165.04 [10070]~P118(x100701)+~P24(f332(f332(f247(x100701),f332(f332(f81(x100701),f332(f332(f257(x100701),x100702),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x100701),x100703),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))),f2(x100701))) % 165.28/165.04 [4725]~E(x47253,f116(x47251))+E(f332(f332(f135(x47251),x47252),x47253),x47252) % 165.28/165.04 [4726]~E(x47262,f116(x47261))+E(f332(f332(f135(x47261),x47262),x47263),x47263) % 165.28/165.04 [4733]~E(x47332,f2(a868))+E(f332(f332(f177(x47331),x47332),x47333),f116(x47331)) % 165.28/165.04 [4739]~E(x47393,f116(x47391))+E(f332(f332(f177(x47391),x47392),x47393),f116(x47391)) % 165.28/165.04 [4779]~E(x47791,x47793)+E(x47791,f332(f332(f135(x47792),f116(x47792)),x47793)) % 165.28/165.04 [4866]~P25(x48662)+E(f332(f196(f875(x48661,x48662)),x48663),f196(x48662)) % 165.28/165.04 [4867]~P109(x48672)+E(f332(f255(f875(x48671,x48672)),x48673),f255(x48672)) % 165.28/165.04 [4886]E(x48861,f116(x48862))+~E(f332(f332(f135(x48862),x48863),x48861),x48863) % 165.28/165.04 [4887]E(x48871,f116(x48872))+~E(f332(f332(f135(x48872),x48871),x48873),x48873) % 165.28/165.04 [4895]E(x48951,f116(x48952))+~E(f332(f332(f135(x48952),x48953),x48951),f116(x48952)) % 165.28/165.04 [4896]E(x48961,f116(x48962))+~E(f332(f332(f135(x48962),x48961),x48963),f116(x48962)) % 165.28/165.04 [4921]~E(x49212,f2(a868))+E(f332(f332(f82(a868),x49211),x49212),f332(f332(f82(a868),x49213),x49212)) % 165.28/165.04 [4923]~E(x49231,f2(a868))+E(f332(f332(f82(a868),x49231),x49232),f332(f332(f82(a868),x49231),x49233)) % 165.28/165.04 [4976]~P26(x49761)+E(f332(f332(f113(x49761),x49762),x49763),f332(f332(f113(x49761),x49763),x49762)) % 165.28/165.04 [4978]~P99(x49781)+E(f332(f332(f113(x49781),x49782),x49783),f332(f332(f113(x49781),x49783),x49782)) % 165.28/165.04 [4979]~P26(x49791)+E(f332(f332(f104(x49791),x49792),x49793),f332(f332(f104(x49791),x49793),x49792)) % 165.28/165.04 [4981]~P100(x49811)+E(f332(f332(f104(x49811),x49812),x49813),f332(f332(f104(x49811),x49813),x49812)) % 165.28/165.04 [4982]~P113(x49821)+E(f332(f332(f81(x49821),x49822),x49823),f332(f332(f81(x49821),x49823),x49822)) % 165.28/165.04 [4983]~P113(x49831)+E(f332(f332(f82(x49831),x49832),x49833),f332(f332(f82(x49831),x49833),x49832)) % 165.28/165.04 [4985]~P106(x49851)+E(f332(f332(f244(x49851),x49852),x49853),f332(f332(f244(x49851),x49853),x49852)) % 165.28/165.04 [4987]~P106(x49871)+E(f332(f332(f245(x49871),x49872),x49873),f332(f332(f245(x49871),x49873),x49872)) % 165.28/165.04 [5050]E(f45(a868,x50501,x50502),f2(a868))+~E(x50501,f332(f332(f82(a868),x50502),x50503)) % 165.28/165.04 [5051]E(f45(a1,x50511,x50512),f2(a1))+~E(x50511,f332(f332(f82(a1),x50512),x50513)) % 165.28/165.04 [5112]E(x51121,x51122)+~E(f332(f332(f81(a868),x51123),x51121),f332(f332(f81(a868),x51123),x51122)) % 165.28/165.04 [5113]E(x51131,x51132)+~E(f332(f332(f81(a868),x51131),x51133),f332(f332(f81(a868),x51132),x51133)) % 165.28/165.04 [5123]~P81(x51231)+E(f332(f332(f104(x51231),x51232),f332(f80(x51231),x51233)),f332(f332(f22(x51231),x51232),x51233)) % 165.28/165.04 [5124]~P66(x51241)+E(f332(f332(f81(x51241),x51242),f332(f80(x51241),x51243)),f332(f332(f22(x51241),x51242),x51243)) % 165.28/165.04 [5125]~P67(x51251)+E(f332(f332(f81(x51251),x51252),f332(f80(x51251),x51253)),f332(f332(f22(x51251),x51252),x51253)) % 165.28/165.04 [5126]~P108(x51261)+E(f332(f332(f81(x51261),x51262),f332(f80(x51261),x51263)),f332(f332(f22(x51261),x51262),x51263)) % 165.28/165.04 [5127]~P67(x51271)+E(f332(f332(f22(x51271),x51272),f332(f80(x51271),x51273)),f332(f332(f81(x51271),x51272),x51273)) % 165.28/165.04 [5173]~P24(f332(x51733,x51732))+P24(f332(f332(f334(x51731),x51732),x51733)) % 165.28/165.04 [5175]~P74(x51752)+E(f332(f332(f6(x51751,x51752),x51753),f196(f875(x51751,a862))),f2(x51752)) % 165.28/165.04 [5177]~P73(x51772)+E(f332(f332(f9(x51771,x51772),x51773),f196(f875(x51771,a862))),f79(x51772)) % 165.28/165.04 [5227]~E(x52272,f332(f332(f81(a868),x52271),x52273))+P24(f332(f332(f246(a868),x52271),x52272)) % 165.28/165.04 [5230]~E(x52302,f196(f875(x52301,a862)))+E(f332(f332(f61(x52301),x52302),x52303),f196(f875(f875(x52301,a862),a862))) % 165.28/165.04 [5231]~E(x52312,f196(f875(x52311,a862)))+E(f196(f875(f875(x52311,a862),a862)),f332(f332(f61(x52311),x52312),x52313)) % 165.28/165.04 [5310]~E(f332(f263(x53102,x53103),x53101),f196(f875(x53103,a862)))+E(x53101,f196(f875(f874(x53102,x53103),a862))) % 165.28/165.04 [5311]~E(f332(f265(x53112,x53113),x53111),f196(f875(x53112,a862)))+E(x53111,f196(f875(f874(x53112,x53113),a862))) % 165.28/165.04 [5341]E(f332(f263(x53411,x53412),x53413),f196(f875(x53412,a862)))+~E(x53413,f196(f875(f874(x53411,x53412),a862))) % 165.28/165.04 [5342]E(f332(f265(x53421,x53422),x53423),f196(f875(x53421,a862)))+~E(x53423,f196(f875(f874(x53421,x53422),a862))) % 165.28/165.04 [5345]E(f282(x53451,x53452,x53453),f332(f332(f22(a102),x53452),x53453))+P24(f332(f332(f247(a102),x53452),x53453)) % 165.28/165.04 [5361]P24(f332(x53611,x53612))+~P24(f332(f332(f334(x53613),x53612),x53611)) % 165.28/165.04 [5400]E(x54001,x54002)+~E(f332(f80(f875(x54003,a862)),x54001),f332(f80(f875(x54003,a862)),x54002)) % 165.28/165.04 [5405]E(f314(x54051,x54052,x54053),f209(f869(a328)))+~P24(f332(f332(f247(a1),x54052),x54053)) % 165.28/165.04 [5410]~E(x54101,f196(f875(x54102,a862)))+~P24(f332(f332(f334(x54102),x54103),x54101)) % 165.28/165.04 [5439]~E(x54392,f332(f332(f81(a1),x54391),f332(f103(a1),x54393)))+P24(f332(f332(f246(a1),x54391),x54392)) % 165.28/165.04 [5455]E(f332(f332(f310(x54551),x54552),x54553),x54553)+~P24(f332(f332(f334(x54551),x54552),x54553)) % 165.28/165.04 [5466]E(x54661,f196(f875(x54662,a862)))+~E(f332(f332(f61(x54662),x54661),x54663),f196(f875(f875(x54662,a862),a862))) % 165.28/165.04 [5467]E(x54671,f196(f875(x54672,a862)))+~E(f196(f875(f875(x54672,a862),a862)),f332(f332(f61(x54672),x54671),x54673)) % 165.28/165.04 [5473]~P125(x54731)+E(f332(f332(f82(x54731),f332(f80(x54731),x54732)),f332(f80(x54731),x54733)),f332(f332(f82(x54731),x54732),x54733)) % 165.28/165.04 [5475]~P60(x54751)+E(f332(f332(f290(x54751),f332(f80(x54751),x54752)),f332(f80(x54751),x54753)),f332(f332(f290(x54751),x54752),x54753)) % 165.28/165.04 [5507]~P24(f332(x55073,x55072))+P24(f332(f332(f334(x55071),x55072),f332(f252(x55071),x55073))) % 165.28/165.04 [5528]E(x55281,f2(a868))+E(f332(f174(x55282),f171(x55282,x55281,x55283)),f332(f332(f310(x55282),x55283),f196(f875(x55282,a862)))) % 165.28/165.04 [5547]E(f172(x55471,x55472,x55473),x55473)+P24(f332(f332(f334(x55471),x55472),f332(f174(x55471),x55473))) % 165.28/165.04 [5629]~P24(f332(f138(x56291),x56293))+P24(f332(f138(x56291),f332(f137(x56291,x56292),x56293))) % 165.28/165.04 [5674]~P28(x56741)+E(f332(f332(f39(x56741),f45(x56741,x56742,x56743)),x56743),f2(x56741)) % 165.28/165.04 [5693]E(f178(x56931,f332(f332(f152(x56931),x56932),f116(x56931)),x56933),f116(x56931))+P24(f332(f332(f334(a868),f2(a868)),x56933)) % 165.28/165.04 [5699]E(x56991,f2(a868))+E(f332(f173(x56992),f171(x56992,x56991,x56993)),f171(x56992,f332(f332(f22(a868),x56991),f79(a868)),x56993)) % 165.28/165.04 [5751]E(f332(f332(f152(x57511),x57512),x57513),f141(x57511,x57512,x57513))+P24(f332(f332(f334(x57511),x57512),f332(f174(x57511),x57513))) % 165.28/165.04 [5760]E(x57601,x57602)+~E(f332(f332(f82(a868),f332(a115,x57603)),x57601),f332(f332(f82(a868),f332(a115,x57603)),x57602)) % 165.28/165.04 [5761]~E(x57612,f332(f332(f81(a1),x57611),f332(f103(a1),f332(a115,x57613))))+P24(f332(f332(f247(a1),x57611),x57612)) % 165.28/165.04 [5866]~E(x58663,f116(x58661))+E(f332(f332(f332(f191(f869(x58661),f869(x58661)),x58662),f169(x58661)),x58663),f116(x58661)) % 165.28/165.04 [5870]P24(f332(x58701,x58702))+~P24(f332(f332(f334(x58703),x58702),f332(f252(x58703),x58701))) % 165.28/165.04 [5902]E(x59021,x59022)+~E(f332(f332(f310(x59023),x59021),f196(f875(x59023,a862))),f332(f332(f310(x59023),x59022),f196(f875(x59023,a862)))) % 165.28/165.04 [5913]~P107(x59131)+E(f332(f332(f104(f875(x59131,a862)),f332(f253(x59131),x59132)),f332(f302(x59131,x59132),x59133)),f196(f875(x59131,a862))) % 165.28/165.04 [5955]E(f141(x59551,x59552,x59553),x59553)+~P24(f332(f332(f334(x59551),x59552),f332(f174(x59551),x59553))) % 165.28/165.04 [5975]~P77(x59751)+E(f332(f311(x59751,x59751,f80(x59751)),f332(f302(x59751,x59752),x59753)),f305(x59751,f332(f80(x59751),x59753),f332(f80(x59751),x59752))) % 165.28/165.04 [5986]E(f332(f197(f869(x59861)),f172(x59861,x59862,x59863)),f332(f197(f869(x59861)),x59863))+P24(f332(f332(f334(x59861),x59862),f332(f174(x59861),x59863))) % 165.28/165.04 [6040]~P107(x60401)+E(f332(f332(f104(f875(x60401,a862)),f332(f302(x60401,x60402),x60403)),f332(f254(x60401),x60403)),f196(f875(x60401,a862))) % 165.28/165.04 [6063]~P77(x60631)+E(f332(f311(x60631,x60631,f80(x60631)),f306(x60631,x60632,x60633)),f306(x60631,f332(f80(x60631),x60633),f332(f80(x60631),x60632))) % 165.28/165.04 [6064]~P77(x60641)+E(f332(f311(x60641,x60641,f80(x60641)),f303(x60641,x60642,x60643)),f303(x60641,f332(f80(x60641),x60643),f332(f80(x60641),x60642))) % 165.28/165.04 [6123]E(f178(x61231,f332(f332(f152(x61231),x61232),f116(x61231)),x61233),f332(f332(f152(x61231),x61232),f116(x61231)))+~P24(f332(f332(f334(a868),f2(a868)),x61233)) % 165.28/165.04 [6130]~P77(x61301)+E(f332(f311(x61301,x61301,f80(x61301)),f305(x61301,x61302,x61303)),f332(f302(x61301,f332(f80(x61301),x61303)),f332(f80(x61301),x61302))) % 165.28/165.04 [6150]~P29(x61501)+E(f45(x61501,f332(f80(x61501),f45(x61501,x61502,x61503)),x61503),f45(x61501,f332(f80(x61501),x61502),x61503)) % 165.28/165.04 [6255]~P24(f332(f62(f874(x62552,x62551)),x62553))+P24(f332(f62(x62551),f332(f263(x62552,x62551),x62553))) % 165.28/165.04 [6256]~P24(f332(f62(f874(x62561,x62562)),x62563))+P24(f332(f62(x62561),f332(f265(x62561,x62562),x62563))) % 165.28/165.04 [6261]~P107(x62611)+E(f332(f332(f104(f875(x62611,a862)),f306(x62611,x62612,x62613)),f332(f254(x62611),x62613)),f196(f875(x62611,a862))) % 165.28/165.04 [6262]~P107(x62621)+E(f332(f332(f104(f875(x62621,a862)),f305(x62621,x62622,x62623)),f332(f304(x62621),x62623)),f196(f875(x62621,a862))) % 165.28/165.04 [6263]~P107(x62631)+E(f332(f332(f104(f875(x62631,a862)),f303(x62631,x62632,x62633)),f332(f304(x62631),x62633)),f196(f875(x62631,a862))) % 165.28/165.04 [6329]E(f332(f332(f166(x63291),x63292),f534(x63292,x63293,x63291)),x63293)+~P24(f332(f332(f334(x63291),x63293),f332(f174(x63291),x63292))) % 165.28/165.04 [6471]E(x64711,f116(x64712))+~E(f332(f332(f332(f191(f869(x64712),f869(x64712)),x64713),f169(x64712)),x64711),f116(x64712)) % 165.28/165.04 [6573]~P24(f332(f62(f874(x65732,x65731)),x65733))+P24(f332(f62(f874(x65731,x65732)),f332(f287(x65732,x65731),x65733))) % 165.28/165.04 [6723]P54(x67231,x67232,x67233)+P24(f332(f332(f334(x67231),f733(x67233,x67232,x67231)),x67232)) % 165.28/165.04 [6724]P54(x67241,x67242,x67243)+P24(f332(f332(f334(x67241),f732(x67243,x67242,x67241)),x67242)) % 165.28/165.04 [6736]P24(f332(f320(x67361,x67362),x67363))+P24(f332(f332(x67362,f486(x67363,x67362,x67361)),x67363)) % 165.28/165.04 [6737]P24(f332(f320(x67371,x67372),x67373))+P24(f332(f332(x67372,f501(x67373,x67372,x67371)),x67373)) % 165.28/165.04 [6768]E(f332(f197(f869(x67681)),f172(x67681,x67682,x67683)),f332(f332(f22(a868),f332(f197(f869(x67681)),x67683)),f79(a868)))+~P24(f332(f332(f334(x67681),x67682),f332(f174(x67681),x67683))) % 165.28/165.04 [6808]P24(f332(f260(x68081,x68082),x68083))+P24(f332(f332(f334(x68081),f537(x68083,x68082,x68081)),x68083)) % 165.28/165.04 [6819]~P24(f332(f62(f874(x68192,x68191)),f332(f287(x68191,x68192),x68193)))+P24(f332(f62(f874(x68191,x68192)),x68193)) % 165.28/165.04 [6875]~P24(f332(f332(f334(x68751),x68752),f332(f174(x68751),f117(x68751,x68753))))+P24(f332(f332(f334(x68751),x68752),f332(f174(x68751),x68753))) % 165.28/165.04 [6880]P23(x68801,x68802,x68803)+P24(f332(f332(f334(f867(x68801)),f552(x68803,x68802,x68801)),x68803)) % 165.28/165.04 [6908]E(f332(f137(x69081,x69082),x69083),x69083)+P24(f332(f332(f334(x69081),f605(x69083,x69082,x69081)),f332(f174(x69081),x69083))) % 165.28/165.04 [6923]E(f332(f137(x69231,x69232),x69233),f116(x69231))+P24(f332(f332(f334(x69231),f569(x69233,x69232,x69231)),f332(f174(x69231),x69233))) % 165.28/165.04 [6946]P35(x69461,x69462,x69463)+P24(f332(f332(f334(x69461),f787(x69463,x69462,x69461)),f332(f174(x69461),x69463))) % 165.28/165.04 [6947]P35(x69471,x69472,x69473)+P24(f332(f332(f334(x69471),f788(x69473,x69472,x69471)),f332(f174(x69471),x69473))) % 165.28/165.04 [6948]P35(x69481,x69482,x69483)+P24(f332(f332(f334(x69481),f782(x69482,x69483,x69481)),f332(f174(x69481),x69483))) % 165.28/165.04 [6951]E(f179(x69511,x69512,x69513),x69513)+P24(f332(f332(f334(x69511),f617(x69513,x69512,x69511)),f332(f174(x69511),x69513))) % 165.28/165.04 [7030]P24(f332(f161(x70301,x70302),x70303))+P24(f332(f332(f334(x70301),f606(x70303,x70302,x70301)),f332(f174(x70301),x70303))) % 165.28/165.04 [7039]~P37(x70391,x70393,x70392)+P24(f332(f332(f334(x70391),f708(x70392,x70393,x70391)),f332(f174(x70391),x70392))) % 165.28/165.04 [7040]~P39(x70401,x70403,x70402)+P24(f332(f332(f334(x70401),f794(x70402,x70403,x70401)),f332(f174(x70401),x70402))) % 165.28/165.04 [7075]P24(f332(f332(f334(x70751),x70752),f772(x70753,x70752,x70751)))+~P24(f332(f332(f334(x70751),x70752),f40(f875(x70751,a862),x70753))) % 165.28/165.04 [7076]~P74(x70761)+E(f332(f332(f81(x70761),f332(f332(f6(a868,x70761),x70762),f332(f253(a868),x70763))),f332(x70762,x70763)),f332(f332(f6(a868,x70761),x70762),f332(f253(a868),f332(a115,x70763)))) % 165.28/165.04 [7165]~P37(x71652,x71651,x71653)+P24(f332(x71651,f332(f332(f166(x71652),x71653),f723(x71653,x71651,x71652)))) % 165.28/165.04 [7178]~P24(f332(f332(f334(x71781),x71782),f724(x71782,x71783,x71781)))+P24(f332(f332(f334(x71781),x71782),f41(f875(x71781,a862),x71783))) % 165.28/165.04 [7208]~P74(x72081)+E(f332(f332(f81(x72081),f332(f332(f6(a868,x72081),x72082),f332(f301(a868),x72083))),f332(x72082,f332(a115,x72083))),f332(f332(f6(a868,x72081),x72082),f332(f301(a868),f332(a115,x72083)))) % 165.28/165.04 [7341]P24(f332(f332(f334(f869(x73411)),x73412),f162(x73411,x73413)))+P24(f332(f332(f334(x73411),f572(x73413,x73412,x73411)),f332(f174(x73411),x73412))) % 165.28/165.04 [7357]~P24(f332(f332(f334(f869(x73571)),x73572),f162(x73571,f321(x73571,x73573))))+P24(f332(f332(f334(f869(x73571)),x73572),f321(f869(x73571),f158(x73571,x73573)))) % 165.28/165.04 [7383]~P24(f332(f332(f334(f869(x73831)),x73832),f321(f869(x73831),f158(x73831,x73833))))+P24(f332(f332(f334(f869(x73831)),x73832),f162(x73831,f321(x73831,x73833)))) % 165.28/165.04 [7419]E(f332(f332(f332(f191(f869(x74191),f869(x74191)),x74192),f169(x74191)),x74193),x74193)+~P24(f332(f332(f246(a868),f332(f197(f869(x74191)),x74193)),f79(a868))) % 165.28/165.04 [7454]E(f332(f332(f135(x74541),f740(x74542,x74543,x74541)),f332(f332(f152(x74541),x74543),f764(x74542,x74543,x74541))),x74542)+~P24(f332(f332(f334(x74541),x74543),f332(f174(x74541),x74542))) % 165.28/165.04 [7455]E(f332(f332(f135(x74551),f741(x74552,x74553,x74551)),f332(f332(f152(x74551),x74553),f760(x74552,x74553,x74551))),x74552)+~P24(f332(f332(f334(x74551),x74553),f332(f174(x74551),x74552))) % 165.28/165.04 [7456]E(f332(f332(f135(x74561),f761(x74562,x74563,x74561)),f332(f332(f152(x74561),x74563),f763(x74562,x74563,x74561))),x74562)+~P24(f332(f332(f334(x74561),x74563),f332(f174(x74561),x74562))) % 165.28/165.04 [7480]~P21(x74801,x74802,x74803,f255(f875(x74801,a862)))+P21(f869(x74801),f869(x74802),f332(f155(x74801,x74802),x74803),f255(f875(f869(x74801),a862))) % 165.28/165.04 [7629]E(x76291,f332(f332(f81(a868),f332(f332(f82(a868),f332(f266(a868,a868),x76292)),x76293)),f332(f270(a868,a868),x76292)))+~P24(f332(f48(x76291,x76293),x76292)) % 165.28/165.04 [7637]P21(x76371,x76372,x76373,f255(f875(x76371,a862)))+~P21(f869(x76371),f869(x76372),f332(f155(x76371,x76372),x76373),f255(f875(f869(x76371),a862))) % 165.28/165.04 [7680]P24(f332(f332(f334(f875(x76801,a862)),f724(x76802,x76803,x76801)),x76803))+P24(f332(f332(f334(x76801),x76802),f41(f875(x76801,a862),x76803))) % 165.28/165.04 [7772]P24(f332(f332(f334(f869(x77721)),x77722),f162(x77721,x77723)))+~P24(f332(f332(f334(x77721),f572(x77723,x77722,x77721)),x77723)) % 165.28/165.04 [7871]P35(x78711,x78712,x78713)+~P24(f332(x78712,f332(f332(f166(x78711),x78713),f783(x78713,x78712,x78711)))) % 165.28/165.04 [7895]E(x78951,x78952)+~E(f332(f332(f7(x78953,f875(x78953,a862),a862),f334(x78953)),x78951),f332(f332(f7(x78953,f875(x78953,a862),a862),f334(x78953)),x78952)) % 165.28/165.04 [7901]~P24(f332(f332(f334(f874(x79011,x79011)),x79013),f264(x79011,x79012)))+P24(f332(f332(f334(x79011),f517(x79012,x79013,x79011)),x79012)) % 165.28/165.04 [7903]~P24(f332(f332(f334(x79031),x79033),f40(f875(x79031,a862),x79032)))+P24(f332(f332(f334(f875(x79031,a862)),f772(x79032,x79033,x79031)),x79032)) % 165.28/165.04 [8077]~P24(f332(f332(f334(x80771),x80772),f332(f174(x80771),f741(x80773,x80772,x80771))))+~P24(f332(f332(f334(x80771),x80772),f332(f174(x80771),x80773))) % 165.28/165.04 [8078]~P24(f332(f332(f334(x80781),x80782),f332(f174(x80781),f763(x80783,x80782,x80781))))+~P24(f332(f332(f334(x80781),x80782),f332(f174(x80781),x80783))) % 165.28/165.04 [8166]E(f332(f241(f872(f869(a328)),f869(a328),f314(x81661,x81662,f332(f332(f81(a1),x81663),f79(a1))),f208(f869(a328))),f332(x81661,x81663)),f314(x81661,x81662,x81663))+P24(f332(f332(f247(a1),x81662),x81663)) % 165.28/165.04 [8266]E(x82661,f116(x82662))+P24(f332(f332(f334(x82662),f332(f266(x82662,f874(a102,a102)),f332(f283(x82662,x82661),x82663))),f332(f174(x82662),x82661))) % 165.28/165.04 [8362]~P70(x83621)+E(f332(f143(x83621,x83621,f332(f7(x83621,x83621,x83621),f81(x83621)),x83622),f332(f170(x83621),x83623)),f332(f143(x83621,x83621,f81(x83621),x83622),x83623)) % 165.28/165.04 [8838]~P106(x88381)+E(f332(f174(x88381),f150(x88381,x88381,f5(x88381),x88382,x88383)),f332(f332(f310(x88381),x88382),f332(f174(x88381),x88383))) % 165.28/165.04 [8849]P24(f332(f332(f247(a868),f2(a868)),f735(x88491,x88492,x88493)))+~P24(f332(f332(f334(f874(x88493,x88493)),x88492),f332(f332(f289(x88493,x88493,x88493),x88491),f308(x88493,x88491)))) % 165.28/165.04 [9125]~P56(x91251,x91252)+~P24(f332(f332(f334(f874(x91251,x91251)),f332(f332(f267(x91251,x91251),x91253),x91253)),f332(f332(f289(x91251,x91251,x91251),x91252),f308(x91251,x91252)))) % 165.28/165.04 [9247]~E(f332(f332(f104(f875(f874(x92471,x92471),a862)),f332(f287(x92471,x92471),x92472)),f308(x92471,x92472)),f196(f875(f874(x92471,x92471),a862)))+~P24(f332(f332(f334(f874(x92471,x92471)),f332(f332(f267(x92471,x92471),x92473),x92473)),f332(f332(f289(x92471,x92471,x92471),x92472),f308(x92471,x92472)))) % 165.28/165.04 [9422]~P24(f332(f62(x94221),x94222))+P24(f332(f332(f246(a868),f332(f38(x94221),f332(f332(f22(f875(x94221,a862)),x94222),f332(f332(f310(x94221),x94223),f196(f875(x94221,a862)))))),f332(f38(x94221),x94222))) % 165.28/165.04 [5039]~E(x50393,f116(x50391))+E(f145(x50391,f332(f332(f152(x50391),x50392),x50393)),x50392) % 165.28/165.04 [5047]~E(x50473,f116(x50471))+E(f117(x50471,f332(f332(f152(x50471),x50472),x50473)),f116(x50471)) % 165.28/165.04 [5076]E(x50761,f116(x50762))+E(f145(x50762,f332(f332(f152(x50762),x50763),x50761)),f145(x50762,x50761)) % 165.28/165.04 [5078]E(x50781,f116(x50782))+E(f145(x50782,f332(f332(f135(x50782),x50783),x50781)),f145(x50782,x50781)) % 165.28/165.04 [5083]~E(x50833,f116(x50831))+E(f117(x50831,f332(f332(f135(x50831),x50832),x50833)),f117(x50831,x50832)) % 165.28/165.04 [5085]~E(x50853,f116(x50851))+E(f145(x50851,f332(f332(f135(x50851),x50852),x50853)),f145(x50851,x50852)) % 165.28/165.04 [5117]E(x51171,f116(x51172))+E(f332(f142(x51172),f332(f332(f135(x51172),x51171),x51173)),f332(f142(x51172),x51171)) % 165.28/165.04 [5147]~E(x51472,f116(x51471))+E(f332(f142(x51471),f332(f332(f135(x51471),x51472),x51473)),f332(f142(x51471),x51473)) % 165.28/165.04 [5202]~P26(x52021)+E(f332(f332(f113(x52021),x52022),f332(f332(f104(x52021),x52022),x52023)),x52022) % 165.28/165.04 [5203]~P26(x52031)+E(f332(f332(f104(x52031),x52032),f332(f332(f113(x52031),x52032),x52033)),x52032) % 165.28/165.04 [5204]~P106(x52041)+E(f332(f332(f244(x52041),x52042),f332(f332(f245(x52041),x52042),x52043)),x52042) % 165.28/165.04 [5205]~P106(x52051)+E(f332(f332(f245(x52051),x52052),f332(f332(f244(x52051),x52052),x52053)),x52052) % 165.28/165.04 [5225]~P28(x52251)+E(f45(x52251,f332(f332(f82(x52251),x52252),x52253),x52253),f2(x52251)) % 165.28/165.04 [5226]~P28(x52261)+E(f45(x52261,f332(f332(f82(x52261),x52262),x52263),x52262),f2(x52261)) % 165.28/165.04 [5304]~P66(x53041)+E(f332(f80(x53041),f332(f332(f22(x53041),x53042),x53043)),f332(f332(f22(x53041),x53043),x53042)) % 165.28/165.04 [5365]E(x53651,f116(x53652))+E(f117(x53652,f332(f332(f152(x53652),x53653),x53651)),f332(f332(f152(x53652),x53653),f117(x53652,x53651))) % 165.28/165.04 [5366]E(x53661,f116(x53662))+E(f117(x53662,f332(f332(f135(x53662),x53663),x53661)),f332(f332(f135(x53662),x53663),f117(x53662,x53661))) % 165.28/165.04 [5369]~P30(x53691)+E(f40(x53691,f332(f332(f310(x53691),x53692),x53693)),f332(f332(f113(x53691),x53692),f40(x53691,x53693))) % 165.28/165.04 [5370]~P30(x53701)+E(f41(x53701,f332(f332(f310(x53701),x53702),x53703)),f332(f332(f104(x53701),x53702),f41(x53701,x53703))) % 165.28/165.04 [5415]~P26(x54151)+E(f332(f332(f113(x54151),x54152),f332(f332(f113(x54151),x54152),x54153)),f332(f332(f113(x54151),x54152),x54153)) % 165.28/165.04 [5417]~P99(x54171)+E(f332(f332(f113(x54171),x54172),f332(f332(f113(x54171),x54172),x54173)),f332(f332(f113(x54171),x54172),x54173)) % 165.28/165.04 [5418]~P26(x54181)+E(f332(f332(f104(x54181),x54182),f332(f332(f104(x54181),x54182),x54183)),f332(f332(f104(x54181),x54182),x54183)) % 165.28/165.04 [5420]~P100(x54201)+E(f332(f332(f104(x54201),x54202),f332(f332(f104(x54201),x54202),x54203)),f332(f332(f104(x54201),x54202),x54203)) % 165.28/165.04 [5421]~P95(x54211)+E(f332(f332(f82(x54211),x54212),f332(f332(f82(x54211),x54212),x54213)),f332(f332(f82(x54211),x54212),x54213)) % 165.28/165.04 [5423]~P106(x54231)+E(f332(f332(f244(x54231),x54232),f332(f332(f244(x54231),x54232),x54233)),f332(f332(f244(x54231),x54232),x54233)) % 165.28/165.04 [5425]~P106(x54251)+E(f332(f332(f245(x54251),x54252),f332(f332(f245(x54251),x54252),x54253)),f332(f332(f245(x54251),x54252),x54253)) % 165.28/165.04 [5433]~P28(x54331)+E(f45(x54331,f332(f332(f81(x54331),x54332),x54333),x54333),f45(x54331,x54332,x54333)) % 165.28/165.04 [5434]~P28(x54341)+E(f45(x54341,f332(f332(f81(x54341),x54342),x54343),x54342),f45(x54341,x54343,x54342)) % 165.28/165.04 [5440]~P125(x54401)+E(f332(f332(f82(x54401),x54402),f332(f80(x54401),x54403)),f332(f80(x54401),f332(f332(f82(x54401),x54402),x54403))) % 165.28/165.04 [5441]~P60(x54411)+E(f332(f332(f290(x54411),x54412),f332(f80(x54411),x54413)),f332(f80(x54411),f332(f332(f290(x54411),x54412),x54413))) % 165.28/165.04 [5442]~P80(x54421)+E(f332(f332(f81(x54421),x54422),f332(f167(x54421),x54423)),f332(f167(x54421),f332(f332(f152(x54421),x54422),x54423))) % 165.28/165.04 [5472]~P125(x54721)+E(f332(f332(f82(x54721),f332(f80(x54721),x54722)),x54723),f332(f332(f82(x54721),x54722),f332(f80(x54721),x54723))) % 165.28/165.04 [5478]~P6(x54781,x54782,x54783)+E(f40(f875(x54781,a862),f332(f332(f61(x54781),x54782),x54783)),x54782) % 165.28/165.04 [5539]~P110(x55391)+E(f332(f332(f82(x55391),x55392),f332(f332(f257(x55391),x55392),x55393)),f332(f332(f257(x55391),x55392),f332(a115,x55393))) % 165.28/165.04 [5540]~P113(x55401)+E(f332(f332(f82(x55401),x55402),f332(f332(f257(x55401),x55402),x55403)),f332(f332(f257(x55401),x55402),f332(a115,x55403))) % 165.28/165.04 [5550]~P67(x55501)+E(f332(f332(f81(x55501),f332(f80(x55501),x55502)),f332(f332(f81(x55501),x55502),x55503)),x55503) % 165.28/165.04 [5573]~P142(x55731)+E(f332(f332(f257(x55731),f332(f103(x55731),x55732)),x55733),f332(f103(x55731),f332(f332(f257(a868),x55732),x55733))) % 165.28/165.04 [5574]~P138(x55741)+E(f332(f332(f257(x55741),f332(f105(x55741),x55742)),x55743),f332(f105(x55741),f332(f332(f257(a1),x55742),x55743))) % 165.28/165.04 [5580]~P85(x55801)+E(f332(f76(x55801),f332(f332(f22(x55801),x55802),x55803)),f332(f76(x55801),f332(f332(f22(x55801),x55803),x55802))) % 165.28/165.04 [5582]~P118(x55821)+E(f332(f332(f82(x55821),f83(x55821,x55822)),f83(x55821,x55823)),f83(x55821,f332(f332(f82(x55821),x55822),x55823))) % 165.28/165.04 [5586]E(x55861,f116(x55862))+E(f332(f332(f135(x55862),f332(f173(x55862),x55861)),x55863),f332(f173(x55862),f332(f332(f135(x55862),x55861),x55863))) % 165.28/165.04 [5591]~E(x55912,f332(a115,f332(f332(f81(a868),x55911),x55913)))+P24(f332(f332(f247(a868),x55911),x55912)) % 165.28/165.04 [5592]~P125(x55921)+E(f332(f332(f82(x55921),f332(f80(x55921),x55922)),x55923),f332(f80(x55921),f332(f332(f82(x55921),x55922),x55923))) % 165.28/165.04 [5593]~P116(x55931)+E(f332(f332(f290(x55931),f332(f80(x55931),x55932)),x55933),f332(f80(x55931),f332(f332(f290(x55931),x55932),x55933))) % 165.28/165.04 [5594]~P118(x55941)+E(f332(f332(f257(x55941),f332(f76(x55941),x55942)),x55943),f332(f76(x55941),f332(f332(f257(x55941),x55942),x55943))) % 165.28/165.04 [5692]E(f650(x56921,x56922,x56923),f691(x56921,x56922,x56923))+E(f332(f332(f104(f875(x56923,a862)),x56922),x56921),f196(f875(x56923,a862))) % 165.28/165.04 [5707]~P74(x57072)+E(f332(f332(f6(x57071,x57072),f332(f16(x57072,x57071),f2(x57072))),x57073),f2(x57072)) % 165.28/165.04 [5708]~P73(x57082)+E(f332(f332(f9(x57081,x57082),f332(f16(x57082,x57081),f79(x57082))),x57083),f79(x57082)) % 165.28/165.04 [5710]~P142(x57101)+E(f332(f332(f81(x57101),f332(f103(x57101),x57102)),f332(f103(x57101),x57103)),f332(f103(x57101),f332(f332(f81(a868),x57102),x57103))) % 165.28/165.04 [5711]~P142(x57111)+E(f332(f332(f82(x57111),f332(f103(x57111),x57112)),f332(f103(x57111),x57113)),f332(f103(x57111),f332(f332(f82(a868),x57112),x57113))) % 165.28/165.04 [5712]~P138(x57121)+E(f332(f332(f22(x57121),f332(f105(x57121),x57122)),f332(f105(x57121),x57123)),f332(f105(x57121),f332(f332(f22(a1),x57122),x57123))) % 165.28/165.04 [5713]~P138(x57131)+E(f332(f332(f81(x57131),f332(f105(x57131),x57132)),f332(f105(x57131),x57133)),f332(f105(x57131),f332(f332(f81(a1),x57132),x57133))) % 165.28/165.04 [5714]~P138(x57141)+E(f332(f332(f82(x57141),f332(f105(x57141),x57142)),f332(f105(x57141),x57143)),f332(f105(x57141),f332(f332(f82(a1),x57142),x57143))) % 165.28/165.04 [5715]~P92(x57151)+E(f332(f332(f22(x57151),f332(f106(x57151),x57152)),f332(f106(x57151),x57153)),f332(f106(x57151),f332(f332(f22(a1),x57152),x57153))) % 165.28/165.04 [5718]~P92(x57181)+E(f332(f332(f81(x57181),f332(f106(x57181),x57182)),f332(f106(x57181),x57183)),f332(f106(x57181),f332(f332(f81(a1),x57182),x57183))) % 165.28/165.04 [5719]~P92(x57191)+E(f332(f332(f82(x57191),f332(f106(x57191),x57192)),f332(f106(x57191),x57193)),f332(f106(x57191),f332(f332(f82(a1),x57192),x57193))) % 165.28/165.04 [5768]~E(x57683,x57682)+P24(f332(f332(f246(f875(x57681,a862)),x57682),x57683)) % 165.28/165.04 [5774]~E(x57742,x57743)+P24(f332(f332(f246(f875(x57741,a862)),x57742),x57743)) % 165.28/165.04 [5779]~P81(x57791)+E(f332(f332(f104(x57791),f332(f80(x57791),x57792)),f332(f80(x57791),x57793)),f332(f80(x57791),f332(f332(f113(x57791),x57792),x57793))) % 165.28/165.04 [5780]~P81(x57801)+E(f332(f332(f113(x57801),f332(f80(x57801),x57802)),f332(f80(x57801),x57803)),f332(f80(x57801),f332(f332(f104(x57801),x57802),x57803))) % 165.28/165.04 [5781]~P67(x57811)+E(f332(f332(f81(x57811),f332(f80(x57811),x57812)),f332(f80(x57811),x57813)),f332(f80(x57811),f332(f332(f81(x57811),x57813),x57812))) % 165.28/165.04 [5782]~P66(x57821)+E(f332(f332(f81(x57821),f332(f80(x57821),x57822)),f332(f80(x57821),x57823)),f332(f80(x57821),f332(f332(f81(x57821),x57822),x57823))) % 165.28/165.04 [5783]~P75(x57831)+E(f332(f332(f245(x57831),f332(f80(x57831),x57832)),f332(f80(x57831),x57833)),f332(f80(x57831),f332(f332(f244(x57831),x57832),x57833))) % 165.28/165.04 [5784]~P75(x57841)+E(f332(f332(f244(x57841),f332(f80(x57841),x57842)),f332(f80(x57841),x57843)),f332(f80(x57841),f332(f332(f245(x57841),x57842),x57843))) % 165.28/165.04 [5785]~P118(x57851)+E(f332(f332(f82(x57851),f332(f76(x57851),x57852)),f332(f76(x57851),x57853)),f332(f76(x57851),f332(f332(f82(x57851),x57852),x57853))) % 165.28/165.04 [5786]~P62(x57861)+E(f332(f332(f290(x57861),f332(f76(x57861),x57862)),f332(f76(x57861),x57863)),f332(f76(x57861),f332(f332(f290(x57861),x57862),x57863))) % 165.28/165.04 [5787]~P80(x57871)+E(f332(f332(f81(x57871),f332(f167(x57871),x57872)),f332(f167(x57871),x57873)),f332(f167(x57871),f332(f332(f135(x57871),x57872),x57873))) % 165.28/165.04 [5788]E(x57881,f196(f875(x57882,a862)))+~E(f332(f332(f113(f875(x57882,a862)),x57883),x57881),f196(f875(x57882,a862))) % 165.28/165.04 [5789]E(x57891,f196(f875(x57892,a862)))+~E(f332(f332(f113(f875(x57892,a862)),x57891),x57893),f196(f875(x57892,a862))) % 165.28/165.04 [5790]~P145(x57901,x57902,x57903)+P24(f332(x57901,f332(f332(f39(a1),x57902),x57903))) % 165.28/165.04 [5840]~P24(f332(f62(x58401),x58403))+P24(f332(f62(x58401),f332(f332(f310(x58401),x58402),x58403))) % 165.28/165.04 [5841]~P24(f332(f138(x58411),x58413))+P24(f332(f138(x58411),f332(f332(f177(x58411),x58412),x58413))) % 165.28/165.04 [5842]~P24(f332(f138(x58421),x58423))+P24(f332(f138(x58421),f332(f332(f139(x58421),x58422),x58423))) % 165.28/165.04 [5871]~P26(x58711)+P24(f332(f332(f246(x58711),x58712),f332(f332(f113(x58711),x58713),x58712))) % 165.28/165.04 [5872]~P99(x58721)+P24(f332(f332(f246(x58721),x58722),f332(f332(f113(x58721),x58723),x58722))) % 165.28/165.04 [5873]~P26(x58731)+P24(f332(f332(f246(x58731),x58732),f332(f332(f113(x58731),x58732),x58733))) % 165.28/165.04 [5874]~P99(x58741)+P24(f332(f332(f246(x58741),x58742),f332(f332(f113(x58741),x58742),x58743))) % 165.28/165.04 [5875]~P106(x58751)+P24(f332(f332(f246(x58751),x58752),f332(f332(f245(x58751),x58753),x58752))) % 165.28/165.04 [5876]~P106(x58761)+P24(f332(f332(f246(x58761),x58762),f332(f332(f245(x58761),x58762),x58763))) % 165.28/165.04 [5890]~E(x58901,f2(a868))+E(f332(f332(f39(a868),f332(f332(f82(a868),x58901),x58902)),f332(f332(f82(a868),x58901),x58903)),f2(a868)) % 165.28/165.04 [5970]~P92(x59701)+E(f332(f332(f22(x59701),f332(f106(x59701),x59702)),f332(f106(x59701),x59703)),f332(f106(x59701),f332(f332(f81(a1),x59702),f332(f80(a1),x59703)))) % 165.28/165.04 [6027]E(x60271,f2(a868))+E(f332(f332(f39(a868),f332(f332(f82(a868),x60271),x60272)),f332(f332(f82(a868),x60271),x60273)),f332(f332(f39(a868),x60272),x60273)) % 165.28/165.04 [6061]E(f153(x60611,f332(f332(f152(x60611),x60612),x60613)),f332(f332(f152(x60611),x60612),f153(x60611,x60613)))+P24(f332(f332(f334(x60611),x60612),f332(f174(x60611),x60613))) % 165.28/165.04 [6095]P145(x60951,x60952,x60953)+~P24(f332(x60951,f332(f332(f39(a1),x60952),x60953))) % 165.28/165.04 [6172]E(x61721,f116(x61722))+E(f332(f332(f152(x61722),f332(f142(x61722),x61721)),f332(f332(f177(x61722),x61723),f332(f173(x61722),x61721))),f332(f332(f177(x61722),f332(a115,x61723)),x61721)) % 165.28/165.04 [6179]E(f332(f332(f22(f875(x61791,a862)),x61792),x61793),x61792)+~E(f332(f332(f104(f875(x61791,a862)),x61792),x61793),f196(f875(x61791,a862))) % 165.28/165.04 [6193]E(f153(x61931,f332(f332(f152(x61931),x61932),x61933)),f153(x61931,x61933))+~P24(f332(f332(f334(x61931),x61932),f332(f174(x61931),x61933))) % 165.28/165.04 [6225]~P24(f332(f332(f246(a868),x62251),x62253))+P24(f332(f332(f246(a868),x62251),f332(f332(f81(a868),x62252),x62253))) % 165.28/165.04 [6227]~P24(f332(f332(f246(a868),x62271),x62272))+P24(f332(f332(f246(a868),x62271),f332(f332(f81(a868),x62272),x62273))) % 165.28/165.04 [6229]~P24(f332(f332(f247(a868),x62291),x62293))+P24(f332(f332(f247(a868),x62291),f332(f332(f81(a868),x62292),x62293))) % 165.28/165.04 [6231]~P24(f332(f332(f247(a868),x62311),x62312))+P24(f332(f332(f247(a868),x62311),f332(f332(f81(a868),x62312),x62313))) % 165.28/165.04 [6269]P24(f332(f62(x62691),x62692))+~P24(f332(f62(x62691),f332(f332(f310(x62691),x62693),x62692))) % 165.28/165.04 [6270]P24(f332(f138(x62701),x62702))+~P24(f332(f138(x62701),f332(f332(f152(x62701),x62703),x62702))) % 165.28/165.04 [6271]P24(f332(f138(x62711),x62712))+~P24(f332(f138(x62711),f332(f332(f135(x62711),x62713),x62712))) % 165.28/165.04 [6272]P24(f332(f138(x62721),x62722))+~P24(f332(f138(x62721),f332(f332(f135(x62721),x62722),x62723))) % 165.28/165.04 [6318]~P113(x63181)+E(f332(f332(f81(x63181),x63182),f332(f332(f82(x63181),x63183),x63182)),f332(f332(f82(x63181),f332(f332(f81(x63181),x63183),f79(x63181))),x63182)) % 165.28/165.04 [6367]~E(x63671,x63672)+~P24(f332(f332(f247(f875(x63673,a862)),x63671),x63672)) % 165.28/165.04 [6411]P24(f332(f332(f334(x64111),x64112),x64113))+P24(f332(f332(f334(x64111),x64112),f332(f80(f875(x64111,a862)),x64113))) % 165.28/165.04 [6417]E(f145(x64171,f332(f332(f139(x64171),x64172),x64173)),f145(x64171,x64173))+~P24(f332(f332(f247(a868),x64172),f332(f197(f869(x64171)),x64173))) % 165.28/165.04 [6418]E(f332(f332(f177(x64181),x64182),f117(x64181,x64183)),f332(f332(f177(x64181),x64182),x64183))+~P24(f332(f332(f247(a868),x64182),f332(f197(f869(x64181)),x64183))) % 165.28/165.04 [6473]E(f332(f332(f332(f191(f869(x64731),f869(x64731)),x64732),f169(x64731)),x64733),x64733)+~E(f45(a868,x64732,f332(f197(f869(x64731)),x64733)),f2(a868)) % 165.28/165.04 [6480]~P6(x64801,x64803,x64802)+E(f332(f332(f289(x64801,x64801,x64801),f332(f287(x64801,x64801),x64802)),x64802),x64802) % 165.28/165.04 [6523]~E(f332(f332(f113(f875(x65231,a862)),x65232),x65233),x65233)+P24(f332(f332(f246(f875(x65231,a862)),x65232),x65233)) % 165.28/165.04 [6528]~P53(x65281,x65281,x65283)+P53(x65281,x65281,f332(f332(f191(f874(x65281,x65281),a862),x65282),x65283)) % 165.28/165.04 [6530]~P24(f332(f332(f334(x65301),x65303),f332(f174(x65301),x65302)))+P24(f332(f332(f247(a868),f2(a868)),f332(f197(f869(x65301)),x65302))) % 165.28/165.04 [6556]~P85(x65561)+E(f332(f76(x65561),f332(f332(f81(x65561),f332(f76(x65561),x65562)),f332(f76(x65561),x65563))),f332(f332(f81(x65561),f332(f76(x65561),x65562)),f332(f76(x65561),x65563))) % 165.28/165.04 [6566]E(f332(f332(f39(a868),f332(f332(f82(a868),x65661),x65662)),f332(f332(f82(a868),x65661),x65663)),f332(f332(f39(a868),x65662),x65663))+~P24(f332(f332(f247(a868),f2(a868)),x65661)) % 165.28/165.04 [6702]~P24(f332(f62(x67021),x67023))+E(f332(f332(f65(x67021,f875(x67021,a862),f310(x67021)),x67022),x67023),f332(f332(f113(f875(x67021,a862)),x67023),x67022)) % 165.28/165.04 [6761]E(f332(f332(f113(f875(x67611,a862)),x67612),x67613),x67612)+~P24(f332(f332(f246(f875(x67611,a862)),x67613),x67612)) % 165.28/165.04 [6763]E(f332(f332(f113(f875(x67631,a862)),x67632),x67633),x67633)+~P24(f332(f332(f246(f875(x67631,a862)),x67632),x67633)) % 165.28/165.04 [6764]E(f332(f332(f104(f875(x67641,a862)),x67642),x67643),x67643)+~P24(f332(f332(f246(f875(x67641,a862)),x67643),x67642)) % 165.28/165.04 [6765]E(f332(f332(f104(f875(x67651,a862)),x67652),x67653),x67652)+~P24(f332(f332(f246(f875(x67651,a862)),x67652),x67653)) % 165.28/165.04 [6817]~P24(f332(f138(x68171),x68172))+E(f332(f332(f22(f875(x68171,a862)),f332(f174(x68171),x68172)),f332(f332(f310(x68171),x68173),f196(f875(x68171,a862)))),f332(f174(x68171),f172(x68171,x68173,x68172))) % 165.28/165.04 [6870]P41(x68701,x68702)+~P41(x68701,f332(f332(f191(f874(x68701,x68701),a862),x68703),x68702)) % 165.28/165.04 [6934]P24(f332(f49(x69341,x69342),f332(a51,x69343)))+~P24(f332(f49(f332(f80(a1),x69341),f332(f80(a1),x69342)),x69343)) % 165.28/165.04 [6939]E(f332(f332(f22(f875(x69391,a862)),f332(f332(f310(x69391),x69392),x69393)),f332(f332(f310(x69391),x69392),f196(f875(x69391,a862)))),x69393)+P24(f332(f332(f334(x69391),x69392),x69393)) % 165.28/165.04 [6960]E(f332(f332(f104(f875(x69601,a862)),f332(f174(x69601),x69602)),f332(f174(x69601),x69603)),f196(f875(x69601,a862)))+~P24(f332(f138(x69601),f332(f332(f135(x69601),x69602),x69603))) % 165.28/165.04 [6976]~P24(f332(f332(f334(x69761),x69762),f332(f174(x69761),x69763)))+~P24(f332(f138(x69761),f332(f332(f152(x69761),x69762),x69763))) % 165.28/165.04 [7046]P35(x70461,x70462,x70463)+P24(f332(f332(f247(a868),f783(x70463,x70462,x70461)),f332(f197(f869(x70461)),x70463))) % 165.28/165.04 [7056]E(f332(f332(f104(f875(x70561,a862)),x70562),x70563),f196(f875(x70561,a862)))+P24(f332(f332(f334(x70561),f650(x70563,x70562,x70561)),x70562)) % 165.28/165.04 [7057]E(f332(f332(f104(f875(x70571,a862)),x70572),x70573),f196(f875(x70571,a862)))+P24(f332(f332(f334(x70571),f691(x70573,x70572,x70571)),x70573)) % 165.28/165.04 [7061]E(f117(x70611,f332(f332(f177(x70611),x70612),x70613)),f332(f332(f177(x70611),f332(f332(f22(a868),x70612),f79(a868))),x70613))+~P24(f332(f332(f246(a868),x70612),f332(f197(f869(x70611)),x70613))) % 165.28/165.04 [7120]~P37(x71203,x71202,x71201)+P24(f332(f332(f247(a868),f723(x71201,x71202,x71203)),f332(f197(f869(x71203)),x71201))) % 165.28/165.04 [7138]P24(f332(f332(f247(a868),f2(a868)),x71381))+P24(f332(f332(f246(a868),f332(f332(f82(a868),x71382),x71381)),f332(f332(f82(a868),x71383),x71381))) % 165.28/165.04 [7139]P24(f332(f332(f247(a868),f2(a868)),x71391))+P24(f332(f332(f246(a868),f332(f332(f82(a868),x71391),x71392)),f332(f332(f82(a868),x71391),x71393))) % 165.28/165.04 [7142]~P24(f332(f332(f334(x71421),x71422),x71423))+~P24(f332(f332(f334(x71421),x71422),f332(f80(f875(x71421,a862)),x71423))) % 165.28/165.04 [7149]~P24(f332(f332(f247(f875(x71491,a862)),x71492),x71493))+P24(f332(f332(f246(f875(x71491,a862)),x71492),x71493)) % 165.28/165.04 [7248]~P24(f332(f332(f246(a868),x72483),x72482))+P24(f332(f332(f246(a868),f332(f332(f22(a868),x72481),x72482)),f332(f332(f22(a868),x72481),x72483))) % 165.28/165.04 [7249]~P24(f332(f332(f246(a868),x72491),x72493))+P24(f332(f332(f246(a868),f332(f332(f22(a868),x72491),x72492)),f332(f332(f22(a868),x72493),x72492))) % 165.28/165.04 [7250]~P24(f332(f332(f246(a868),x72502),x72503))+P24(f332(f332(f246(a868),f332(f332(f81(a868),x72501),x72502)),f332(f332(f81(a868),x72501),x72503))) % 165.28/165.04 [7251]~P24(f332(f332(f246(a868),x72511),x72513))+P24(f332(f332(f246(a868),f332(f332(f81(a868),x72511),x72512)),f332(f332(f81(a868),x72513),x72512))) % 165.28/165.04 [7253]~P24(f332(f332(f246(a868),x72532),x72533))+P24(f332(f332(f246(a868),f332(f332(f82(a868),x72531),x72532)),f332(f332(f82(a868),x72531),x72533))) % 165.28/165.04 [7255]~P24(f332(f332(f246(a868),x72551),x72553))+P24(f332(f332(f246(a868),f332(f332(f82(a868),x72551),x72552)),f332(f332(f82(a868),x72553),x72552))) % 165.28/165.04 [7256]~P24(f332(f332(f246(a868),x72561),x72563))+P24(f332(f332(f246(a868),f332(f332(f39(a868),x72561),x72562)),f332(f332(f39(a868),x72563),x72562))) % 165.28/165.04 [7257]~P24(f332(f332(f246(a1),x72572),x72573))+P24(f332(f332(f246(a1),f332(f332(f81(a1),x72571),x72572)),f332(f332(f81(a1),x72571),x72573))) % 165.28/165.04 [7260]~P24(f332(f332(f247(a868),x72602),x72603))+P24(f332(f332(f247(a868),f332(f332(f81(a868),x72601),x72602)),f332(f332(f81(a868),x72601),x72603))) % 165.28/165.04 [7261]~P24(f332(f332(f247(a868),x72611),x72613))+P24(f332(f332(f247(a868),f332(f332(f81(a868),x72611),x72612)),f332(f332(f81(a868),x72613),x72612))) % 165.28/165.04 [7262]~P24(f332(f332(f247(a1),x72621),x72623))+P24(f332(f332(f247(a1),f332(f332(f81(a1),x72621),x72622)),f332(f332(f81(a1),x72623),x72622))) % 165.28/165.04 [7340]E(x73401,x73402)+~P24(f332(f332(f334(x73403),x73401),f332(f332(f310(x73403),x73402),f196(f875(x73403,a862))))) % 165.28/165.04 [7342]~E(f332(f332(f104(f875(x73421,a862)),x73422),x73423),f196(f875(x73421,a862)))+P24(f332(f332(f246(f875(x73421,a862)),x73422),f332(f80(f875(x73421,a862)),x73423))) % 165.28/165.04 [7349]P24(f332(f332(f334(f875(x73491,a862)),x73492),f332(f309(x73491),x73493)))+~P24(f332(f332(f246(f875(x73491,a862)),x73492),x73493)) % 165.28/165.04 [7403]E(f332(f332(f152(x74031),f332(f332(f166(x74031),x74032),x74033)),f332(f332(f139(x74031),f332(a115,x74033)),x74032)),f332(f332(f139(x74031),x74033),x74032))+~P24(f332(f332(f247(a868),x74033),f332(f197(f869(x74031)),x74032))) % 165.28/165.04 [7430]P24(f332(f332(f334(f874(x74301,x74301)),x74302),f308(x74301,x74303)))+~P24(f332(f332(f334(f874(x74301,x74301)),x74302),x74303)) % 165.28/165.04 [7440]~P24(f332(f332(f334(f875(x74401,a862)),x74402),f332(f309(x74401),x74403)))+P24(f332(f332(f246(f875(x74401,a862)),x74402),x74403)) % 165.28/165.04 [7486]P24(f332(f332(f246(f875(x74861,a862)),x74862),f40(f875(x74861,a862),x74863)))+~P24(f332(f332(f334(f875(x74861,a862)),x74862),x74863)) % 165.28/165.04 [7511]~P138(x75111)+E(f332(f332(f82(x75111),f332(f332(f257(x75111),f332(f80(x75111),f79(x75111))),x75112)),f332(f332(f257(x75111),x75113),x75112)),f332(f332(f257(x75111),f332(f80(x75111),x75113)),x75112)) % 165.28/165.04 [7533]E(f332(f332(f166(x75331),x75332),f332(f332(f22(a868),f332(f197(f869(x75331)),x75332)),f332(a115,x75333))),f332(f332(f166(x75331),f332(f170(x75331),x75332)),x75333))+~P24(f332(f332(f247(a868),x75333),f332(f197(f869(x75331)),x75332))) % 165.28/165.04 [7550]~E(f332(f332(f104(f875(x75501,a862)),f639(x75503,x75502,x75501)),x75503),f196(f875(x75501,a862)))+E(f332(f332(f104(f875(x75501,a862)),f40(f875(x75501,a862),x75502)),x75503),f196(f875(x75501,a862))) % 165.28/165.04 [7611]~P24(f332(f332(f334(x76113),x76112),f332(f174(x76113),x76111)))+P24(f332(f332(f247(a868),f534(x76111,x76112,x76113)),f332(f197(f869(x76113)),x76111))) % 165.28/165.04 [7619]P24(f332(f332(f334(x76191),f332(f332(f166(x76191),x76192),x76193)),f332(f174(x76191),x76192)))+~P24(f332(f332(f247(a868),x76193),f332(f197(f869(x76191)),x76192))) % 165.28/165.04 [7719]~P24(f332(x77192,f623(x77193,x77192,x77191)))+E(f332(f332(f139(x77191),f332(f197(f869(x77191)),f179(x77191,x77192,x77193))),x77193),f116(x77191)) % 165.28/165.04 [7730]P24(f332(f332(f246(f875(f869(x77301),a862)),f162(x77301,x77302)),f162(x77301,x77303)))+~P24(f332(f332(f246(f875(x77301,a862)),x77302),x77303)) % 165.28/165.04 [7731]P24(f332(f332(f246(f875(f869(x77311),a862)),f161(x77311,x77312)),f161(x77311,x77313)))+~P24(f332(f332(f246(f875(x77311,a862)),x77312),x77313)) % 165.28/165.04 [7758]E(f332(f332(f104(f875(x77581,a862)),f40(f875(x77581,a862),x77582)),x77583),f196(f875(x77581,a862)))+P24(f332(f332(f334(f875(x77581,a862)),f639(x77583,x77582,x77581)),x77582)) % 165.28/165.04 [7761]~P24(f332(f332(f334(f875(x77611,a862)),x77613),x77612))+P24(f332(f332(f246(f875(x77611,a862)),f41(f875(x77611,a862),x77612)),x77613)) % 165.28/165.04 [7763]E(f332(f332(f104(f875(x77631,a862)),x77632),x77633),f196(f875(x77631,a862)))+~P24(f332(f332(f246(f875(x77631,a862)),x77632),f332(f80(f875(x77631,a862)),x77633))) % 165.28/165.04 [7809]E(f332(f332(f22(a868),f332(f332(f81(a868),f332(f167(a868),x78091)),x78092)),f332(f332(f166(a868),x78091),x78093)),f332(f167(a868),f332(f332(f160(a868,x78091),x78093),x78092)))+~P24(f332(f332(f247(a868),x78093),f332(f197(f869(a868)),x78091))) % 165.28/165.04 [7859]P24(f332(f332(f246(a868),x78591),x78592))+~P24(f332(f332(f246(a868),f332(f332(f81(a868),x78593),x78591)),f332(f332(f81(a868),x78593),x78592))) % 165.28/165.04 [7862]P24(f332(f332(f247(a868),x78621),x78622))+~P24(f332(f332(f247(a868),f332(f332(f81(a868),x78623),x78621)),f332(f332(f81(a868),x78623),x78622))) % 165.28/165.04 [7863]P24(f332(f332(f247(a868),x78631),x78632))+~P24(f332(f332(f247(a868),f332(f332(f82(a868),x78633),x78631)),f332(f332(f82(a868),x78633),x78632))) % 165.28/165.04 [7864]P24(f332(f332(f247(a868),x78641),x78642))+~P24(f332(f332(f247(a868),f332(f332(f82(a868),x78641),x78643)),f332(f332(f82(a868),x78642),x78643))) % 165.28/165.04 [7893]P24(f332(f332(f247(a868),f2(a868)),x78931))+~P24(f332(f332(f247(a868),f332(f332(f82(a868),x78932),x78931)),f332(f332(f82(a868),x78933),x78931))) % 165.28/165.04 [7894]P24(f332(f332(f247(a868),f2(a868)),x78941))+~P24(f332(f332(f247(a868),f332(f332(f82(a868),x78941),x78942)),f332(f332(f82(a868),x78941),x78943))) % 165.28/165.04 [7968]E(f259(x79681,x79682,x79683),x79682)+~P24(f332(f332(f246(f875(x79681,a862)),x79683),f332(f332(f310(x79681),x79682),f196(f875(x79681,a862))))) % 165.28/165.04 [8018]~P24(f332(f138(x80181),x80183))+E(f332(f137(x80181,f332(f332(f8(a862,a862,x80181),a327),f332(a329,x80182))),x80183),f172(x80181,x80182,x80183)) % 165.28/165.04 [8041]E(f332(f332(f139(x80411),f332(f197(f869(x80411)),f179(x80411,x80412,x80413))),x80413),f116(x80411))+P24(f332(f332(f334(x80411),f623(x80413,x80412,x80411)),f332(f174(x80411),x80413))) % 165.28/165.04 [8045]E(f332(f332(f135(x80451),f332(f332(f177(x80451),x80452),x80453)),f332(f332(f152(x80451),f332(f332(f166(x80451),x80453),x80452)),f116(x80451))),f332(f332(f177(x80451),f332(a115,x80452)),x80453))+~P24(f332(f332(f247(a868),x80452),f332(f197(f869(x80451)),x80453))) % 165.28/165.04 [8106]E(f332(f137(x81061,f332(f332(f8(a862,a862,x81061),a327),f332(a329,x81062))),x81063),x81063)+P24(f332(f332(f334(x81061),x81062),f332(f174(x81061),x81063))) % 165.28/165.04 [8113]P24(f332(f332(f246(f875(f875(x81131,a862),a862)),f260(x81131,x81132)),f260(x81131,x81133)))+~P24(f332(f332(f246(f875(x81131,a862)),x81132),x81133)) % 165.28/165.04 [8157]~P24(f332(f138(x81571),x81573))+P24(f332(f138(x81571),f332(f332(f332(f191(f869(x81571),f869(x81571)),x81572),f169(x81571)),x81573))) % 165.28/165.04 [8163]~P24(f332(f332(f247(a868),x81632),x81633))+P24(f332(f332(f247(a868),f332(f332(f82(a868),f332(a115,x81631)),x81632)),f332(f332(f82(a868),f332(a115,x81631)),x81633))) % 165.28/165.04 [8185]P24(f332(f332(f246(f875(f875(x81851,a862),a862)),f332(f309(x81851),x81852)),f332(f309(x81851),x81853)))+~P24(f332(f332(f246(f875(x81851,a862)),x81852),x81853)) % 165.28/165.04 [8345]~P24(f332(f332(f246(f875(x83451,a862)),x83453),x83452))+P24(f332(f332(f246(f875(x83451,a862)),f332(f80(f875(x83451,a862)),x83452)),f332(f80(f875(x83451,a862)),x83453))) % 165.28/165.04 [8375]E(f332(f311(a868,a868,f332(f332(f7(a868,a868,a868),f22(a868)),x83751)),f332(f302(a868,x83752),x83753)),f332(f302(a868,f332(f332(f22(a868),x83752),x83751)),f332(f332(f22(a868),x83753),x83751)))+~P24(f332(f332(f247(a868),x83751),x83753)) % 165.28/165.04 [8402]~P80(x84021)+E(f332(f332(f81(x84021),x84022),f332(f143(x84021,x84021,f81(x84021),f2(x84021)),x84023)),f332(f143(x84021,x84021,f81(x84021),x84022),x84023)) % 165.28/165.04 [8475]~P85(x84751)+P24(f332(f332(f246(x84751),f332(f76(x84751),f332(f332(f22(x84751),x84752),x84753))),f332(f332(f81(x84751),f332(f76(x84751),x84752)),f332(f76(x84751),x84753)))) % 165.28/165.04 [8476]~P85(x84761)+P24(f332(f332(f246(x84761),f332(f76(x84761),f332(f332(f81(x84761),x84762),x84763))),f332(f332(f81(x84761),f332(f76(x84761),x84762)),f332(f76(x84761),x84763)))) % 165.28/165.04 [8486]E(f332(f332(f81(a1),f332(f332(f82(a1),x84861),f45(a1,f332(f332(f39(a1),x84862),x84861),x84863))),f45(a1,x84862,x84861)),f45(a1,x84862,f332(f332(f82(a1),x84861),x84863)))+~P24(f332(f332(f247(a1),f2(a1)),x84863)) % 165.28/165.04 [8492]E(f332(f332(f135(x84921),f332(f332(f177(x84921),x84922),x84923)),f332(f332(f152(x84921),f332(f142(x84921),f332(f332(f139(x84921),x84922),x84923))),f116(x84921))),f332(f332(f177(x84921),f332(a115,x84922)),x84923))+~P24(f332(f332(f247(a868),x84922),f332(f197(f869(x84921)),x84923))) % 165.28/165.04 [8511]E(f332(f278(x85111,f332(f332(f155(x85111,f874(a102,x85111)),f332(f267(a102,x85111),f79(a102))),x85112)),f332(a3,x85113)),f332(f332(f166(x85111),x85112),x85113))+~P24(f332(f332(f247(a868),x85113),f332(f197(f869(x85111)),x85112))) % 165.28/165.04 [8576]P24(f332(f332(f334(f874(x85761,x85761)),x85762),f332(f332(f289(x85761,x85761,x85761),x85763),f308(x85761,x85763))))+~P24(f332(f332(f334(f874(x85761,x85761)),x85762),x85763)) % 165.28/165.04 [8593]P24(f332(f332(f246(a868),x85931),x85932))+~P24(f332(f332(f246(a868),f332(f332(f82(a868),f332(a115,x85933)),x85931)),f332(f332(f82(a868),f332(a115,x85933)),x85932))) % 165.28/165.04 [8609]P24(f332(f332(f246(f875(x86091,a862)),x86092),x86093))+~P24(f332(f332(f246(f875(x86091,a862)),f332(f80(f875(x86091,a862)),x86093)),f332(f80(f875(x86091,a862)),x86092))) % 165.28/165.04 [8628]P24(f332(f138(x86281),x86282))+~P24(f332(f138(x86281),f332(f332(f332(f191(f869(x86281),f869(x86281)),x86283),f169(x86281)),x86282))) % 165.28/165.04 [8688]E(f332(f311(f874(x86881,x86882),x86882,f270(x86881,x86882)),f332(f174(f874(x86881,x86882)),x86883)),f188(x86881,x86882,f332(f180(x86881,x86882),x86883)))+~P24(f332(f138(x86881),f332(f332(f155(f874(x86881,x86882),x86881),f266(x86881,x86882)),x86883))) % 165.28/165.04 [8697]E(f332(f286(x86971,x86971,f308(x86971,x86972)),x86973),x86973)+~P24(f332(f332(f246(f875(x86971,a862)),f332(f286(x86971,x86971,x86972),x86973)),x86973)) % 165.28/165.04 [8739]~P106(x87391)+P32(x87391,f332(f137(x87391,f332(f332(f7(x87391,x87391,a862),a329),f332(x87392,x87393))),x87393)) % 165.28/165.04 [8745]~P24(f332(f332(f246(a868),x87451),x87452))+P24(f332(f332(f246(a868),x87451),f332(f143(a868,a868,f81(a868),x87452),x87453))) % 165.28/165.04 [8822]~P24(f332(f332(f334(f874(x88221,x88221)),x88222),f308(x88221,x88223)))+P24(f332(f332(f334(f874(x88221,x88221)),x88222),f332(f332(f191(f874(x88221,x88221),a862),f734(x88223,x88222,x88221)),x88223))) % 165.28/165.04 [8909]~P80(x89091)+E(f332(f332(f81(x89091),x89092),f332(f143(x89091,x89091,f332(f7(x89091,x89091,x89091),f81(x89091)),f2(x89091)),f332(f170(x89091),x89093))),f332(f143(x89091,x89091,f81(x89091),x89092),x89093)) % 165.28/165.04 [9171]P53(x91711,x91712,x91713)+P24(f332(f332(f334(f874(x91711,x91712)),f332(f332(f267(x91711,x91712),f730(x91713,x91712,x91711)),f707(x91713,x91712,x91711))),x91713)) % 165.28/165.04 [9172]P53(x91721,x91722,x91723)+P24(f332(f332(f334(f874(x91721,x91722)),f332(f332(f267(x91721,x91722),f730(x91723,x91722,x91721)),f706(x91723,x91722,x91721))),x91723)) % 165.28/165.04 [9234]~P24(f332(f332(f334(f874(x92341,x92341)),x92342),f332(f332(f289(x92341,x92341,x92341),x92343),f308(x92341,x92343))))+P24(f332(f332(f334(f874(x92341,x92341)),x92342),f332(f332(f191(f874(x92341,x92341),a862),f735(x92343,x92342,x92341)),x92343))) % 165.28/165.04 [9235]~P24(f332(x92351,f332(f332(f166(x92352),x92353),f332(f197(f869(x92352)),f179(x92352,x92351,x92353)))))+~P24(f332(f332(f247(a868),f332(f197(f869(x92352)),f179(x92352,x92351,x92353))),f332(f197(f869(x92352)),x92353))) % 165.28/165.04 [9321]~P24(f332(f332(f246(f875(x93211,a862)),x93212),x93213))+P24(f332(f332(f246(f875(x93211,a862)),f332(f332(f7(x93211,f875(x93211,a862),a862),f334(x93211)),x93212)),f332(f332(f7(x93211,f875(x93211,a862),a862),f334(x93211)),x93213))) % 165.28/165.04 [9372]~P24(f332(f332(f334(f874(f875(x93721,a862),f875(x93721,a862))),f332(f332(f267(f875(x93721,a862),f875(x93721,a862)),x93722),x93723)),f307(x93721)))+P24(f332(f332(f247(f875(x93721,a862)),x93722),x93723)) % 165.28/165.04 [9396]P54(x93961,x93962,x93963)+~P24(f332(f332(f334(f874(x93961,x93961)),f332(f332(f267(x93961,x93961),f733(x93963,x93962,x93961)),f732(x93963,x93962,x93961))),x93963)) % 165.28/165.04 [9397]P54(x93971,x93972,x93973)+~P24(f332(f332(f334(f874(x93971,x93971)),f332(f332(f267(x93971,x93971),f732(x93973,x93972,x93971)),f733(x93973,x93972,x93971))),x93973)) % 165.28/165.04 [9432]~P24(f332(f332(f334(f874(f869(x94321),f869(x94321))),f332(f332(f267(f869(x94321),f869(x94321)),x94322),x94322)),f148(x94321,x94323)))+P24(f332(f332(f334(f874(x94321,x94321)),f332(f332(f267(x94321,x94321),f557(x94322,x94323,x94321)),f557(x94322,x94323,x94321))),x94323)) % 165.28/165.04 [9480]P24(f332(f332(f246(f875(x94801,a862)),x94802),x94803))+~P24(f332(f332(f246(f875(x94801,a862)),f332(f332(f7(x94801,f875(x94801,a862),a862),f334(x94801)),x94802)),f332(f332(f7(x94801,f875(x94801,a862),a862),f334(x94801)),x94803))) % 165.28/165.04 [9561]E(f332(f332(f22(a868),f332(f332(f6(a868,a868),x95611),f332(f253(a868),x95612))),f332(f332(f6(a868,a868),x95613),f332(f253(a868),x95612))),f332(f332(f6(a868,a868),f332(f332(f18(a868,a868,a868),f332(f332(f8(a868,f875(a868,a868),a868),f22(a868)),x95611)),x95613)),f332(f253(a868),x95612)))+~P24(f332(f332(f246(a868),f332(x95613,f364(x95612,x95611,x95613))),f332(x95611,f364(x95612,x95611,x95613)))) % 165.28/165.04 [9865]E(f332(f252(f874(x98651,x98652)),f332(f271(x98651,x98652,a862),f332(f332(f7(x98651,f875(x98652,f872(x98652)),f875(x98652,a862)),f332(f332(f8(f875(f872(x98652),a862),f875(f875(x98652,f872(x98652)),f875(x98652,a862)),x98651),f8(f872(x98652),a862,x98652)),f332(f332(f8(f872(x98652),f875(f872(x98652),a862),x98651),a329),f332(f180(x98651,x98652),x98653)))),f208(x98652)))),f332(f174(f874(x98651,x98652)),x98653))+~P24(f332(f138(x98651),f332(f332(f155(f874(x98651,x98652),x98651),f266(x98651,x98652)),x98653))) % 165.28/165.04 [5626]~P67(x56261)+E(f332(f332(f22(x56261),f332(f332(f81(x56261),x56262),x56263)),x56263),x56262) % 165.28/165.04 [5627]~P67(x56271)+E(f332(f332(f81(x56271),f332(f332(f22(x56271),x56272),x56273)),x56273),x56272) % 165.28/165.04 [5848]~P67(x58481)+E(f332(f332(f81(x58481),x58482),f332(f332(f81(x58481),f332(f80(x58481),x58482)),x58483)),x58483) % 165.28/165.04 [5932]~P79(x59321)+E(f332(f332(f82(x59321),f332(f332(f257(x59321),x59322),x59323)),x59322),f332(f332(f257(x59321),x59322),f332(a115,x59323))) % 165.28/165.04 [5933]~P113(x59331)+E(f332(f332(f82(x59331),f332(f332(f257(x59331),x59332),x59333)),x59332),f332(f332(f257(x59331),x59332),f332(a115,x59333))) % 165.28/165.04 [6147]~P118(x61471)+E(f332(f76(x61471),f332(f332(f257(x61471),f332(f80(x61471),x61472)),x61473)),f332(f76(x61471),f332(f332(f257(x61471),x61472),x61473))) % 165.28/165.04 [6207]~P79(x62071)+E(f332(f332(f82(x62071),f332(f332(f257(x62071),x62072),x62073)),x62072),f332(f332(f82(x62071),x62072),f332(f332(f257(x62071),x62072),x62073))) % 165.28/165.04 [6260]E(f332(f332(f22(a102),f332(f332(f81(a102),x62601),x62602)),x62603),f282(x62601,x62602,x62603))+~P24(f332(f332(f247(a102),x62602),x62603)) % 165.28/165.04 [6281]~E(f332(f332(f139(x62811),x62813),x62812),f116(x62811))+P24(f332(f332(f246(a868),f332(f197(f869(x62811)),x62812)),x62813)) % 165.28/165.04 [6416]E(f332(f332(f82(a868),f332(f106(a868),x64161)),f332(f332(f82(a868),f332(f106(a868),x64162)),x64163)),f2(a868))+~P24(f332(f332(f247(a1),x64161),a84)) % 165.28/165.04 [6432]~P60(x64321)+E(f332(f332(f257(x64321),f332(f332(f290(x64321),f79(x64321)),x64322)),x64323),f332(f332(f290(x64321),f79(x64321)),f332(f332(f257(x64321),x64322),x64323))) % 165.28/165.04 [6510]E(f332(f332(f22(a868),f332(f332(f81(a868),x65101),x65102)),x65103),f332(f332(f22(a868),x65101),f332(f332(f22(a868),x65103),x65102)))+~P24(f332(f332(f246(a868),x65102),x65103)) % 165.28/165.04 [6512]E(f332(f332(f22(a868),f332(f332(f81(a868),x65121),x65122)),x65123),f332(f332(f81(a868),x65121),f332(f332(f22(a868),x65122),x65123)))+~P24(f332(f332(f246(a868),x65123),x65122)) % 165.28/165.04 [6547]~P26(x65471)+P24(f332(f332(f246(x65471),f332(f332(f104(x65471),x65472),x65473)),x65473)) % 165.28/165.04 [6548]~P100(x65481)+P24(f332(f332(f246(x65481),f332(f332(f104(x65481),x65482),x65483)),x65483)) % 165.28/165.04 [6549]~P26(x65491)+P24(f332(f332(f246(x65491),f332(f332(f104(x65491),x65492),x65493)),x65492)) % 165.28/165.04 [6550]~P100(x65501)+P24(f332(f332(f246(x65501),f332(f332(f104(x65501),x65502),x65503)),x65502)) % 165.28/165.04 [6551]~P106(x65511)+P24(f332(f332(f246(x65511),f332(f332(f244(x65511),x65512),x65513)),x65513)) % 165.28/165.04 [6552]~P106(x65521)+P24(f332(f332(f246(x65521),f332(f332(f244(x65521),x65522),x65523)),x65522)) % 165.28/165.04 [6565]E(f332(f332(f39(a1),f332(f332(f39(a1),x65651),x65652)),x65653),f332(f332(f39(a1),x65651),f332(f332(f82(a1),x65652),x65653)))+~P24(f332(f332(f247(a1),f2(a1)),x65653)) % 165.28/165.04 [6616]~P113(x66161)+E(f332(f332(f81(x66161),f332(f332(f82(x66161),x66162),x66163)),x66163),f332(f332(f82(x66161),f332(f332(f81(x66161),x66162),f79(x66161))),x66163)) % 165.28/165.04 [6617]~P92(x66171)+E(f332(f332(f82(x66171),f332(f80(x66171),f332(f106(x66171),x66172))),x66173),f332(f332(f82(x66171),f332(f106(x66171),f332(f80(a1),x66172))),x66173)) % 165.28/165.04 [6689]~P80(x66891)+E(f332(f167(x66891),f332(f332(f155(x66892,x66891),f332(f16(x66891,x66892),f2(x66891))),x66893)),f2(x66891)) % 165.28/165.04 [6705]E(f332(f332(f81(a868),f332(f106(a868),x67051)),f332(f332(f81(a868),f332(f106(a868),x67052)),x67053)),f332(f332(f81(a868),f332(f106(a868),x67052)),x67053))+~P24(f332(a201,f332(f106(a1),x67051))) % 165.28/165.04 [6719]~P30(x67191)+E(f40(x67191,f332(f332(f310(x67191),x67192),f332(f332(f310(x67191),x67193),f196(f875(x67191,a862))))),f332(f332(f113(x67191),x67192),x67193)) % 165.28/165.04 [6720]~P30(x67201)+E(f41(x67201,f332(f332(f310(x67201),x67202),f332(f332(f310(x67201),x67203),f196(f875(x67201,a862))))),f332(f332(f104(x67201),x67202),x67203)) % 165.28/165.04 [6743]E(f332(f332(f177(x67431),x67432),x67433),x67433)+~P24(f332(f332(f246(a868),f332(f197(f869(x67431)),x67433)),x67432)) % 165.28/165.04 [6756]E(f332(f332(f139(x67561),x67562),x67563),f116(x67561))+~P24(f332(f332(f246(a868),f332(f197(f869(x67561)),x67563)),x67562)) % 165.28/165.04 [6767]E(f332(f332(f81(a868),f332(f332(f22(a868),x67671),x67672)),x67673),f332(f332(f22(a868),f332(f332(f81(a868),x67671),x67673)),x67672))+~P24(f332(f332(f246(a868),x67672),x67671)) % 165.28/165.04 [6781]~P24(f332(f332(f247(a868),x67811),x67813))+P24(f332(f332(f247(a868),f332(f332(f22(a868),x67811),x67812)),x67813)) % 165.28/165.04 [6809]~P106(x68091)+E(f172(x68091,x68092,f332(f332(f149(x68091,x68091,f5(x68091)),x68092),x68093)),x68093) % 165.28/165.04 [6898]E(f332(f332(f22(a868),f332(f332(f81(a868),x68981),x68982)),f332(a115,x68983)),f332(f332(f22(a868),x68981),f332(a115,f332(f332(f22(a868),x68983),x68982))))+~P24(f332(f332(f246(a868),x68982),x68983)) % 165.28/165.04 [6899]~P118(x68991)+P24(f332(f332(f246(x68991),f2(x68991)),f332(f332(f257(x68991),f332(f76(x68991),x68992)),x68993))) % 165.28/165.04 [6944]P20(x69441,x69442,x69443)+~P24(f332(f332(f246(f875(f867(x69441),a862)),x69443),x69442)) % 165.28/165.04 [6987]~P24(f332(f62(x69871),x69872))+P24(f332(f62(x69871),f332(f332(f22(f875(x69871,a862)),x69872),x69873))) % 165.28/165.04 [6988]~P24(f332(f62(x69881),x69883))+P24(f332(f62(x69881),f332(f332(f104(f875(x69881,a862)),x69882),x69883))) % 165.28/165.04 [6989]~P24(f332(f62(x69891),x69892))+P24(f332(f62(x69891),f332(f332(f104(f875(x69891,a862)),x69892),x69893))) % 165.28/165.04 [7128]~P41(x71281,x71283)+P41(x71281,f332(f332(f104(f875(f874(x71281,x71281),a862)),x71282),x71283)) % 165.28/165.04 [7129]~P41(x71291,x71292)+P41(x71291,f332(f332(f104(f875(f874(x71291,x71291),a862)),x71292),x71293)) % 165.28/165.04 [7244]~P26(x72441)+E(f10(x72441,f332(f174(x72441),f332(f332(f152(x72441),x72442),x72443))),f332(f143(x72441,x72441,f113(x72441),x72442),x72443)) % 165.28/165.04 [7245]~P26(x72451)+E(f11(x72451,f332(f174(x72451),f332(f332(f152(x72451),x72452),x72453))),f332(f143(x72451,x72451,f104(x72451),x72452),x72453)) % 165.28/165.04 [7246]~P106(x72461)+E(f14(x72461,f332(f174(x72461),f332(f332(f152(x72461),x72462),x72463))),f332(f143(x72461,x72461,f245(x72461),x72462),x72463)) % 165.28/165.04 [7247]~P106(x72471)+E(f15(x72471,f332(f174(x72471),f332(f332(f152(x72471),x72472),x72473))),f332(f143(x72471,x72471,f244(x72471),x72472),x72473)) % 165.28/165.04 [7307]~P24(f332(f62(x73071),x73072))+P24(f332(f332(f246(a868),f332(f38(x73071),x73072)),f332(f38(x73071),f332(f332(f310(x73071),x73073),x73072)))) % 165.28/165.04 [7315]E(f332(f332(f113(f875(a868,a862)),f332(f302(a868,x73151),x73152)),f332(f302(a868,x73152),f332(f332(f81(a868),x73152),x73153))),f332(f302(a868,x73151),f332(f332(f81(a868),x73152),x73153)))+~P24(f332(f332(f246(a868),x73151),x73152)) % 165.28/165.04 [7325]P24(f332(f332(f246(a868),x73251),x73252))+~P24(f332(f332(f246(a868),f332(f332(f81(a868),x73253),x73251)),x73252)) % 165.28/165.04 [7326]P24(f332(f332(f246(a868),x73261),x73262))+~P24(f332(f332(f246(a868),f332(f332(f81(a868),x73261),x73263)),x73262)) % 165.28/165.04 [7327]P24(f332(f332(f247(a868),x73271),x73272))+~P24(f332(f332(f247(a868),f332(f332(f81(a868),x73271),x73273)),x73272)) % 165.28/165.04 [7366]~P106(x73661)+E(f12(x73661,f244(x73661),f332(f174(x73661),f332(f332(f152(x73661),x73662),x73663))),f332(f143(x73661,x73661,f244(x73661),x73662),x73663)) % 165.28/165.04 [7367]~P106(x73671)+E(f13(x73671,f245(x73671),f332(f174(x73671),f332(f332(f152(x73671),x73672),x73673))),f332(f143(x73671,x73671,f245(x73671),x73672),x73673)) % 165.28/165.04 [7371]~E(x73712,f196(f875(f874(x73711,x73711),a862)))+P24(f332(f332(f246(f875(f874(x73711,x73711),a862)),x73712),x73713)) % 165.28/165.04 [7481]E(f332(f332(f113(f875(x74811,a862)),x74812),f332(f332(f22(f875(x74811,a862)),x74813),x74812)),x74813)+~P24(f332(f332(f246(f875(x74811,a862)),x74812),x74813)) % 165.28/165.04 [7482]~P24(f332(f332(f246(a868),x74821),f332(f332(f81(a868),x74823),x74822)))+P24(f332(f332(f246(a868),f332(f332(f22(a868),x74821),x74822)),x74823)) % 165.28/165.04 [7483]~P24(f332(f332(f247(a868),x74831),f332(f332(f22(a868),x74833),x74832)))+P24(f332(f332(f247(a868),f332(f332(f81(a868),x74831),x74832)),x74833)) % 165.28/165.04 [7540]E(x75401,f116(x75402))+E(f332(f142(x75402),f332(f332(f332(f191(f869(x75402),f869(x75402)),x75403),f169(x75402)),x75401)),f332(f332(f166(x75402),x75401),f45(a868,x75403,f332(f197(f869(x75402)),x75401)))) % 165.28/165.04 [7549]E(f332(f332(f310(x75491),x75492),f332(f332(f22(f875(x75491,a862)),x75493),f332(f332(f310(x75491),x75492),f196(f875(x75491,a862))))),x75493)+~P24(f332(f332(f334(x75491),x75492),x75493)) % 165.28/165.04 [7710]P24(f332(f332(f246(a868),x77101),f332(f332(f81(a868),x77102),x77103)))+~P24(f332(f332(f246(a868),f332(f332(f22(a868),x77101),x77103)),x77102)) % 165.28/165.04 [7711]P24(f332(f332(f247(a868),x77111),f332(f332(f22(a868),x77112),x77113)))+~P24(f332(f332(f247(a868),f332(f332(f81(a868),x77111),x77113)),x77112)) % 165.28/165.04 [7734]P24(f332(f62(x77341),x77342))+~P24(f332(f62(x77341),f332(f332(f113(f875(x77341,a862)),x77343),x77342))) % 165.28/165.04 [7735]P24(f332(f62(x77351),x77352))+~P24(f332(f62(x77351),f332(f332(f113(f875(x77351,a862)),x77352),x77353))) % 165.28/165.04 [7808]~P49(x78081,x78083)+P24(f332(f332(f334(f874(x78081,x78081)),f332(f332(f267(x78081,x78081),x78082),x78082)),x78083)) % 165.28/165.04 [7941]E(f332(f332(f166(a868),f140(a868,f332(f302(a868,x79411),x79412))),x79413),f332(f332(f81(a868),x79411),x79413))+~P24(f332(f332(f247(a868),f332(f332(f81(a868),x79411),x79413)),x79412)) % 165.28/165.04 [8007]E(f332(f332(f177(a868),x80071),f140(a868,f332(f302(a868,x80072),x80073))),f140(a868,f332(f302(a868,x80072),f332(f332(f81(a868),x80072),x80071))))+~P24(f332(f332(f246(a868),f332(f332(f81(a868),x80072),x80071)),x80073)) % 165.28/165.04 [8060]~P92(x80601)+E(f332(f332(f257(x80601),x80602),f332(f106(a868),f332(f332(f81(a1),x80603),x80603))),f332(f332(f87(x80601,x80601),f332(f332(f257(x80601),x80602),f332(f106(a868),x80603))),f332(f332(f18(x80601,x80601,x80601),f82(x80601)),f5(x80601)))) % 165.28/165.04 [8325]E(f332(f332(f135(x83251),f332(f332(f177(x83251),x83252),x83253)),f332(f332(f152(x83251),f332(f332(f166(x83251),x83253),x83252)),f332(f332(f139(x83251),f332(a115,x83252)),x83253))),x83253)+~P24(f332(f332(f247(a868),x83252),f332(f197(f869(x83251)),x83253))) % 165.28/165.04 [8332]P24(f332(f332(f246(f875(x83321,a862)),f320(x83321,x83322)),f320(x83321,x83323)))+~P24(f332(f332(f246(f875(x83321,f875(x83321,a862))),x83323),x83322)) % 165.28/165.04 [8334]~P54(x83341,x83342,x83343)+P54(x83341,x83342,f332(f332(f22(f875(f874(x83341,x83341),a862)),x83343),f308(x83341,f196(f875(f874(x83341,x83341),a862))))) % 165.28/165.04 [8351]P24(f332(f332(f246(f875(x83511,a862)),f321(x83511,x83512)),f321(x83511,x83513)))+~P24(f332(f332(f246(f875(f874(x83511,x83511),a862)),x83513),x83512)) % 165.28/165.04 [8358]~P121(x83581)+P24(f332(f332(f246(x83581),f2(x83581)),f332(f332(f81(x83581),f332(f332(f82(x83581),x83582),x83582)),f332(f332(f82(x83581),x83583),x83583)))) % 165.28/165.04 [8390]P24(f332(f332(f246(f875(x83901,a862)),f332(f285(x83901),x83902)),f332(f285(x83901),x83903)))+~P24(f332(f332(f246(f875(f874(x83901,x83901),a862)),x83902),x83903)) % 165.28/165.04 [8420]~P45(x84201,x84202)+~P24(f332(f332(f334(f874(x84201,x84201)),f332(f332(f267(x84201,x84201),x84203),x84203)),x84202)) % 165.28/165.04 [8422]~P41(x84221,x84222)+~P24(f332(f332(f334(f874(x84221,x84221)),f332(f332(f267(x84221,x84221),x84223),x84223)),x84222)) % 165.28/165.04 [8477]P24(f332(f332(f246(f875(x84771,a862)),f40(f875(x84771,a862),x84772)),f40(f875(x84771,a862),x84773)))+~P24(f332(f332(f246(f875(f875(x84771,a862),a862)),x84772),x84773)) % 165.28/165.04 [8478]P24(f332(f332(f246(f875(x84781,a862)),f41(f875(x84781,a862),x84782)),f41(f875(x84781,a862),x84783)))+~P24(f332(f332(f246(f875(f875(x84781,a862),a862)),x84783),x84782)) % 165.28/165.04 [8530]~P6(x85301,x85303,x85302)+P24(f332(f332(f246(f875(f874(x85301,x85301),a862)),x85302),f332(f332(f269(x85301,x85301),x85303),f332(f16(f875(x85301,a862),x85301),x85303)))) % 165.28/165.04 [8531]~P43(x85311,x85313,x85312)+P24(f332(f332(f246(f875(f874(x85311,x85311),a862)),x85312),f332(f332(f269(x85311,x85311),x85313),f332(f16(f875(x85311,a862),x85311),x85313)))) % 165.28/165.04 [8577]~P85(x85771)+P24(f332(f332(f246(x85771),f332(f332(f22(x85771),f332(f76(x85771),x85772)),f332(f76(x85771),x85773))),f332(f76(x85771),f332(f332(f22(x85771),x85773),x85772)))) % 165.28/165.04 [8578]~P85(x85781)+P24(f332(f332(f246(x85781),f332(f332(f22(x85781),f332(f76(x85781),x85782)),f332(f76(x85781),x85783))),f332(f76(x85781),f332(f332(f22(x85781),x85782),x85783)))) % 165.28/165.04 [8607]P24(f332(f332(f246(f875(f874(x86071,x86071),a862)),f308(x86071,x86072)),f308(x86071,x86073)))+~P24(f332(f332(f246(f875(f874(x86071,x86071),a862)),x86072),x86073)) % 165.28/165.04 [8763]P54(x87631,x87632,x87633)+~P54(x87631,x87632,f332(f332(f22(f875(f874(x87631,x87631),a862)),x87633),f308(x87631,f196(f875(f874(x87631,x87631),a862))))) % 165.28/165.04 [8781]P24(f332(f332(f246(f875(f874(f869(x87811),f869(x87811)),a862)),f159(x87811,x87812)),f159(x87811,x87813)))+~P24(f332(f332(f246(f875(f874(x87811,x87811),a862)),x87812),x87813)) % 165.28/165.04 [8782]P24(f332(f332(f246(f875(f874(f869(x87821),f869(x87821)),a862)),f158(x87821,x87822)),f158(x87821,x87823)))+~P24(f332(f332(f246(f875(f874(x87821,x87821),a862)),x87822),x87823)) % 165.28/165.04 [8801]~P43(x88011,x88013,x88012)+P24(f332(f332(f246(f875(f874(x88011,x88011),a862)),x88012),f332(f332(f289(x88011,x88011,x88011),f332(f287(x88011,x88011),x88012)),x88012))) % 165.28/165.04 [8850]~P24(f332(f138(x88501),x88502))+E(f332(f137(x88501,f332(f332(f7(x88501,f875(x88501,a862),a862),f334(x88501)),f332(f174(x88501),f178(x88501,x88502,x88503)))),x88502),f178(x88501,x88502,x88503)) % 165.28/165.04 [8907]E(x89071,x89072)+~P24(f332(f332(f334(f874(x89073,x89073)),f332(f332(f267(x89073,x89073),x89071),x89072)),f308(x89073,f196(f875(f874(x89073,x89073),a862))))) % 165.28/165.04 [8989]P24(f332(f332(f334(x89891),x89892),f321(x89891,x89893)))+P24(f332(f332(f334(f874(x89891,x89891)),f332(f332(f267(x89891,x89891),f660(x89893,x89892,x89891)),x89892)),x89893)) % 165.28/165.04 [8990]P24(f332(f332(f334(x89901),x89902),f321(x89901,x89903)))+P24(f332(f332(f334(f874(x89901,x89901)),f332(f332(f267(x89901,x89901),f710(x89903,x89902,x89901)),x89902)),x89903)) % 165.28/165.04 [8991]P24(f332(f332(f334(x89911),x89912),f321(x89911,x89913)))+P24(f332(f332(f334(f874(x89911,x89911)),f332(f332(f267(x89911,x89911),f719(x89913,x89912,x89911)),x89912)),x89913)) % 165.28/165.04 [9077]~P24(f332(f332(f334(f869(x90771)),x90773),f162(x90771,x90772)))+P24(f332(f161(x90771,f332(f332(f7(x90771,f875(x90771,a862),a862),f334(x90771)),x90772)),x90773)) % 165.28/165.04 [9098]P24(f332(x90983,x90982))+E(f332(f252(x90981),f332(f332(f18(x90981,a862,a862),f332(f332(f8(a862,f875(a862,a862),x90981),a330),f332(a329,x90982))),x90983)),f196(f875(x90981,a862))) % 165.28/165.04 [9116]~P85(x91161)+P24(f332(f332(f246(x91161),f332(f76(x91161),f332(f332(f22(x91161),f332(f76(x91161),x91162)),f332(f76(x91161),x91163)))),f332(f76(x91161),f332(f332(f22(x91161),x91162),x91163)))) % 165.28/165.04 [9130]~P24(f332(x91303,x91302))+E(f332(f252(x91301),f332(f332(f18(x91301,a862,a862),f332(f332(f8(a862,f875(a862,a862),x91301),a330),f332(a329,x91302))),x91303)),f332(f332(f310(x91301),x91302),f196(f875(x91301,a862)))) % 165.28/165.04 [9137]~P24(f332(f332(f334(f875(x91371,a862)),x91373),f332(f309(x91371),x91372)))+P24(f332(f260(x91371,f332(f332(f7(x91371,f875(x91371,a862),a862),f334(x91371)),x91372)),x91373)) % 165.28/165.04 [9170]P41(x91701,x91702)+P24(f332(f332(f334(f874(x91701,x91701)),f332(f332(f267(x91701,x91701),f332(f673(x91702,x91701),f332(a115,x91703))),f332(f673(x91702,x91701),x91703))),x91702)) % 165.28/165.04 [9301]P24(f332(f332(f334(f869(x93011)),x93012),f162(x93011,x93013)))+~P24(f332(f161(x93011,f332(f332(f7(x93011,f875(x93011,a862),a862),f334(x93011)),x93013)),x93012)) % 165.28/165.04 [9313]P24(f332(f332(f334(f875(x93131,a862)),x93132),f332(f309(x93131),x93133)))+~P24(f332(f260(x93131,f332(f332(f7(x93131,f875(x93131,a862),a862),f334(x93131)),x93133)),x93132)) % 165.28/165.04 [9368]P24(f332(f332(f334(x93681),f332(f278(x93681,x93682),x93683)),f332(f174(x93681),f332(f332(f155(f874(a102,x93681),x93681),f270(a102,x93681)),x93682))))+~P24(f332(f332(f247(a102),x93683),f332(f167(a102),f332(f332(f155(f874(a102,x93681),a102),f266(a102,x93681)),x93682)))) % 165.28/165.04 [9415]P24(f332(f332(f246(f875(f874(f869(x94151),f869(x94151)),a862)),f159(x94151,x94152)),f332(f332(f269(f869(x94151),f869(x94151)),f162(x94151,x94153)),f332(f16(f875(f869(x94151),a862),f869(x94151)),f162(x94151,x94153)))))+~P24(f332(f332(f246(f875(f874(x94151,x94151),a862)),x94152),f332(f332(f269(x94151,x94151),x94153),f332(f16(f875(x94151,a862),x94151),x94153)))) % 165.28/165.04 [9435]P24(f332(f332(f334(x94351),f332(f266(x94351,f874(a102,a102)),f332(f276(x94351,x94352),x94353))),f332(f174(x94351),f332(f332(f155(f874(a102,x94351),x94351),f270(a102,x94351)),x94352))))+~P24(f332(f332(f247(a102),f2(a102)),f332(f167(a102),f332(f332(f155(f874(a102,x94351),a102),f266(a102,x94351)),x94352)))) % 165.28/165.04 [9449]~P24(f332(f332(f246(f875(f874(x94491,x94491),a862)),x94492),f332(f332(f269(x94491,x94491),x94493),f332(f16(f875(x94491,a862),x94491),x94493))))+P24(f332(f332(f246(f875(f874(x94491,x94491),a862)),f332(f332(f289(x94491,x94491,x94491),x94492),f308(x94491,x94492))),f332(f332(f269(x94491,x94491),x94493),f332(f16(f875(x94491,a862),x94491),x94493)))) % 165.28/165.04 [9753]~P41(x97531,x97532)+~P24(f332(f332(f334(f874(x97531,x97531)),f332(f332(f267(x97531,x97531),f332(x97533,f332(a115,f671(x97532,x97531,x97533)))),f332(x97533,f671(x97532,x97531,x97533)))),x97532)) % 165.28/165.04 [9754]~P41(x97541,x97542)+~P24(f332(f332(f334(f874(x97541,x97541)),f332(f332(f267(x97541,x97541),f332(x97543,f332(a115,f725(x97543,x97542,x97541)))),f332(x97543,f725(x97543,x97542,x97541)))),x97542)) % 165.28/165.04 [10005]P24(f332(f332(f246(f875(f874(f875(x100051,a862),f875(x100051,a862)),a862)),f332(f332(f289(f875(x100051,a862),f875(x100051,a862),f875(x100051,a862)),f325(x100051,x100052)),f332(f332(f113(f875(f874(f875(x100051,a862),f875(x100051,a862)),a862)),f325(x100051,x100053)),f332(f332(f310(f874(f875(x100051,a862),f875(x100051,a862))),f332(f332(f267(f875(x100051,a862),f875(x100051,a862)),f196(f875(x100051,a862))),f196(f875(x100051,a862)))),f196(f875(f874(f875(x100051,a862),f875(x100051,a862)),a862)))))),f325(x100051,x100052)))+~P24(f332(f332(f246(f875(f874(x100051,x100051),a862)),f332(f332(f289(x100051,x100051,x100051),x100052),x100053)),x100052)) % 165.28/165.04 [10006]P24(f332(f332(f246(f875(f874(f875(x100061,a862),f875(x100061,a862)),a862)),f332(f332(f289(f875(x100061,a862),f875(x100061,a862),f875(x100061,a862)),f323(x100061,x100062)),f332(f332(f113(f875(f874(f875(x100061,a862),f875(x100061,a862)),a862)),f323(x100061,x100063)),f332(f332(f310(f874(f875(x100061,a862),f875(x100061,a862))),f332(f332(f267(f875(x100061,a862),f875(x100061,a862)),f196(f875(x100061,a862))),f196(f875(x100061,a862)))),f196(f875(f874(f875(x100061,a862),f875(x100061,a862)),a862)))))),f323(x100061,x100062)))+~P24(f332(f332(f246(f875(f874(x100061,x100061),a862)),f332(f332(f289(x100061,x100061,x100061),x100062),x100063)),x100062)) % 165.28/165.04 [7243]~P24(f332(f332(f246(a868),x72432),x72431))+E(f332(f332(f22(a868),f332(a115,f332(f332(f22(a868),x72431),x72432))),x72433),f332(f332(f22(a868),f332(a115,x72431)),f332(f332(f81(a868),x72432),x72433))) % 165.28/165.04 [7282]~P28(x72821)+E(f332(f332(f81(x72821),f45(x72821,x72822,x72823)),f332(f332(f82(x72821),f332(f332(f39(x72821),x72822),x72823)),x72823)),x72822) % 165.28/165.04 [7487]E(f332(f332(f82(a868),f332(f106(a868),x74871)),f332(f332(f82(a868),f332(f106(a868),x74872)),x74873)),f332(f332(f82(a868),f332(f106(a868),f332(f332(f82(a1),x74871),x74872))),x74873))+P24(f332(f332(f247(a1),x74871),a84)) % 165.28/165.04 [7950]~P24(f332(f332(f246(a868),x79503),x79502))+P24(f332(f332(f246(a868),x79501),f332(f332(f22(a868),f332(f332(f81(a868),x79502),x79501)),x79503))) % 165.28/165.04 [8147]~P24(f332(f332(f246(a868),x81471),x81472))+E(f332(f332(f135(a868),f140(a868,f332(f302(a868,x81471),x81472))),f140(a868,f332(f302(a868,x81472),f332(f332(f81(a868),x81472),x81473)))),f140(a868,f332(f302(a868,x81471),f332(f332(f81(a868),x81472),x81473)))) % 165.28/165.04 [8399]~P24(f332(f62(x83991),x83992))+E(f332(a115,f332(f38(x83991),f332(f332(f22(f875(x83991,a862)),x83992),f332(f332(f310(x83991),x83993),f196(f875(x83991,a862)))))),f332(f38(x83991),f332(f332(f310(x83991),x83993),x83992))) % 165.28/165.04 [8440]~P24(f332(f62(x84401),x84402))+E(f332(f332(f81(a868),f79(a868)),f332(f38(x84401),f332(f332(f22(f875(x84401,a862)),x84402),f332(f332(f310(x84401),x84403),f196(f875(x84401,a862)))))),f332(f38(x84401),f332(f332(f310(x84401),x84403),x84402))) % 165.28/165.04 [8616]E(f332(f332(f22(a868),f332(f38(x86161),x86162)),f332(f38(x86161),f332(f332(f104(f875(x86161,a862)),x86162),x86163))),f332(f38(x86161),f332(f332(f22(f875(x86161,a862)),x86162),x86163)))+~P24(f332(f62(x86161),f332(f332(f104(f875(x86161,a862)),x86162),x86163))) % 165.28/165.04 [8846]~P31(f332(x88462,f371(x88462,x88463,x88461)))+E(f332(f103(a1),f332(f332(f6(x88461,a868),f332(f332(f8(a1,a868,x88461),a107),x88462)),x88463)),f332(f332(f6(x88461,a1),x88462),x88463)) % 165.28/165.04 [8847]~P31(f332(x88472,f372(x88472,x88473,x88471)))+E(f332(f103(a1),f332(f332(f9(x88471,a868),f332(f332(f8(a1,a868,x88471),a107),x88472)),x88473)),f332(f332(f9(x88471,a1),x88472),x88473)) % 165.28/165.04 [8892]~P24(f332(f62(x88921),x88923))+P24(f332(f332(f246(a868),f332(f332(f22(a868),f332(f38(x88921),x88922)),f332(f38(x88921),x88923))),f332(f38(x88921),f332(f332(f22(f875(x88921,a862)),x88922),x88923)))) % 165.28/165.04 [8915]P24(f332(f332(f334(x89151),f371(x89152,x89153,x89151)),x89153))+E(f332(f103(a1),f332(f332(f6(x89151,a868),f332(f332(f8(a1,a868,x89151),a107),x89152)),x89153)),f332(f332(f6(x89151,a1),x89152),x89153)) % 165.28/165.04 [8916]P24(f332(f332(f334(x89161),f372(x89162,x89163,x89161)),x89163))+E(f332(f103(a1),f332(f332(f9(x89161,a868),f332(f332(f8(a1,a868,x89161),a107),x89162)),x89163)),f332(f332(f9(x89161,a1),x89162),x89163)) % 165.28/165.04 [8981]E(f86(x89811,f332(f332(f7(x89811,f875(x89811,a862),a862),f334(x89811)),f332(f332(f22(f875(x89811,a862)),x89812),f332(f332(f310(x89811),x89813),f196(f875(x89811,a862)))))),f259(x89811,x89813,x89812))+P24(f332(f332(f246(f875(x89811,a862)),x89812),f332(f332(f310(x89811),x89813),f196(f875(x89811,a862))))) % 165.28/165.04 [9314]E(f332(f332(f155(f869(x93141),x93141),f332(f332(f7(f869(x93141),a868,x93141),f166(x93141)),x93142)),f332(f137(f869(x93141),f332(f332(f8(a868,a862,f869(x93141)),f332(f247(a868),x93142)),f197(f869(x93141)))),x93143)),f332(f332(f166(f869(x93141)),f182(x93141,x93143)),x93142))+~P24(f332(f332(f247(a868),x93142),f332(f197(f869(f869(x93141))),f182(x93141,x93143)))) % 165.28/165.04 [9385]E(f332(f137(x93851,x93852),x93853),f179(x93851,x93852,x93853))+P24(f332(f332(f334(x93851),f632(x93853,x93852,x93851)),f332(f174(x93851),f332(f332(f139(x93851),f332(f197(f869(x93851)),f179(x93851,x93852,x93853))),x93853)))) % 165.28/165.04 [9520]E(f332(f332(f139(x95201),f332(f197(f869(x95201)),f179(x95201,x95202,x95203))),x95203),f116(x95201))+~P24(f332(x95202,f332(f142(x95201),f332(f332(f139(x95201),f332(f197(f869(x95201)),f179(x95201,x95202,x95203))),x95203)))) % 165.28/165.04 [9613]~P24(f332(f332(f334(f874(x96131,x96131)),x96132),f308(x96131,x96133)))+P24(f332(f332(f334(f874(x96131,x96131)),x96132),f332(f332(f42(a868,f875(f874(x96131,x96131),a862)),f255(f875(a868,a862))),f332(f332(f7(a868,f875(f874(x96131,x96131),a862),f875(f874(x96131,x96131),a862)),f191(f874(x96131,x96131),a862)),x96133)))) % 165.28/165.04 [9670]~P24(f332(f332(f246(f875(x96701,a862)),f332(f332(f42(a868,f875(x96701,a862)),f332(f302(a868,f2(a868)),f478(x96703,x96702,x96701))),x96702)),x96703))+P24(f332(f332(f246(f875(x96701,a862)),f332(f332(f42(a868,f875(x96701,a862)),f255(f875(a868,a862))),x96702)),x96703)) % 165.28/165.04 [9728]~P24(f332(f332(f247(a1),f2(a1)),x97283))+P24(f332(f332(f247(a1),x97281),f332(f332(f81(a1),x97282),f332(f332(f82(a1),f332(f332(f81(a1),f332(f76(a1),f332(f332(f22(a1),x97282),x97281))),f79(a1))),x97283)))) % 165.28/165.04 [9740]~P41(x97401,f332(f332(f113(f875(f874(x97401,x97401),a862)),x97402),x97403))+P41(x97401,f332(f332(f113(f875(f874(x97401,x97401),a862)),f332(f332(f113(f875(f874(x97401,x97401),a862)),f332(f332(f289(x97401,x97401,x97401),x97402),x97402)),f332(f332(f289(x97401,x97401,x97401),x97403),x97402))),x97403)) % 165.28/165.04 [9821]P41(x98211,f332(f332(f113(f875(f874(x98211,x98211),a862)),x98212),x98213))+~P41(x98211,f332(f332(f113(f875(f874(x98211,x98211),a862)),f332(f332(f113(f875(f874(x98211,x98211),a862)),f332(f332(f289(x98211,x98211,x98211),x98212),x98212)),f332(f332(f289(x98211,x98211,x98211),x98213),x98212))),x98213)) % 165.28/165.04 [9388]~P138(x93881)+E(f332(f105(x93881),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x93882),x93883)),f196(f875(f874(a868,a868),a862)))))),f332(f332(f22(x93881),f332(f103(x93881),x93882)),f332(f103(x93881),x93883))) % 165.28/165.04 [9467]P24(f332(x94673,x94672))+E(f332(f252(x94671),f332(f332(f18(x94671,a862,a862),f332(f332(f8(a862,f875(a862,a862),x94671),a330),f332(f332(f7(x94671,x94671,a862),a329),x94672))),x94673)),f196(f875(x94671,a862))) % 165.28/165.04 [9469]~P24(f332(x94693,x94692))+E(f332(f252(x94691),f332(f332(f18(x94691,a862,a862),f332(f332(f8(a862,f875(a862,a862),x94691),a330),f332(f332(f7(x94691,x94691,a862),a329),x94692))),x94693)),f332(f332(f310(x94691),x94692),f196(f875(x94691,a862)))) % 165.28/165.04 [9706]E(x97061,x97062)+P24(f332(f332(f256(x97063,x97063,f332(f332(f8(f875(x97063,a862),f875(x97063,a862),x97063),f332(f8(a862,a862,x97063),a327)),a329)),x97061),x97062)) % 165.28/165.04 [9798]~E(x97981,x97982)+~P24(f332(f332(f256(x97983,x97983,f332(f332(f8(f875(x97983,a862),f875(x97983,a862),x97983),f332(f8(a862,a862,x97983),a327)),a329)),x97981),x97982)) % 165.28/165.04 [9813]~P24(f332(f62(x98131),x98133))+E(f332(f332(f65(x98131,f875(x98131,a862),f332(f332(f8(f875(x98131,a862),f875(f875(x98131,a862),f875(x98131,a862)),x98131),f332(f7(f875(x98131,a862),f875(x98131,a862),f875(x98131,a862)),f22(f875(x98131,a862)))),f332(f332(f7(x98131,f875(x98131,a862),f875(x98131,a862)),f310(x98131)),f196(f875(x98131,a862))))),x98132),x98133),f332(f332(f22(f875(x98131,a862)),x98132),x98133)) % 165.28/165.04 [9845]~P24(f332(f332(f247(a1),f2(a1)),x98453))+P24(f332(f332(f247(a1),f332(f332(f22(a1),x98451),f332(f332(f82(a1),f332(f332(f81(a1),f332(f76(a1),f332(f332(f22(a1),x98451),x98452))),f79(a1))),x98453))),x98452)) % 165.28/165.04 [10066]~P24(f332(f332(f334(x100661),x100663),f321(x100661,x100662)))+P24(f332(f320(x100661,f332(f332(f7(x100661,f875(f874(x100661,x100661),a862),f875(x100661,a862)),f332(f332(f8(f875(x100661,f875(f875(f874(x100661,x100661),a862),a862)),f875(f875(f874(x100661,x100661),a862),f875(x100661,a862)),x100661),f7(x100661,f875(f874(x100661,x100661),a862),a862)),f332(f332(f8(f875(x100661,f874(x100661,x100661)),f875(x100661,f875(f875(f874(x100661,x100661),a862),a862)),x100661),f332(f8(f874(x100661,x100661),f875(f875(f874(x100661,x100661),a862),a862),x100661),f334(f874(x100661,x100661)))),f267(x100661,x100661)))),x100662)),x100663)) % 165.28/165.04 [10078]P24(f332(f332(f334(x100781),x100782),f321(x100781,x100783)))+~P24(f332(f320(x100781,f332(f332(f7(x100781,f875(f874(x100781,x100781),a862),f875(x100781,a862)),f332(f332(f8(f875(x100781,f875(f875(f874(x100781,x100781),a862),a862)),f875(f875(f874(x100781,x100781),a862),f875(x100781,a862)),x100781),f7(x100781,f875(f874(x100781,x100781),a862),a862)),f332(f332(f8(f875(x100781,f874(x100781,x100781)),f875(x100781,f875(f875(f874(x100781,x100781),a862),a862)),x100781),f332(f8(f874(x100781,x100781),f875(f875(f874(x100781,x100781),a862),a862),x100781),f334(f874(x100781,x100781)))),f267(x100781,x100781)))),x100783)),x100782)) % 165.28/165.04 [9668]~P24(f332(f62(x96681),f332(f252(x96681),x96683)))+P24(f332(f62(x96681),f332(f252(x96681),f332(f332(f18(x96681,a862,a862),f332(f332(f8(a862,f875(a862,a862),x96681),a330),x96682)),x96683)))) % 165.28/165.04 [9669]~P24(f332(f62(x96691),f332(f252(x96691),x96692)))+P24(f332(f62(x96691),f332(f252(x96691),f332(f332(f18(x96691,a862,a862),f332(f332(f8(a862,f875(a862,a862),x96691),a330),x96692)),x96693)))) % 165.28/165.04 [9772]P24(f332(f62(x97721),f332(f252(x97721),x97722)))+~P24(f332(f62(x97721),f332(f252(x97721),f332(f332(f18(x97721,a862,a862),f332(f332(f8(a862,f875(a862,a862),x97721),a331),x97723)),x97722)))) % 165.28/165.04 [9773]P24(f332(f62(x97731),f332(f252(x97731),x97732)))+~P24(f332(f62(x97731),f332(f252(x97731),f332(f332(f18(x97731,a862,a862),f332(f332(f8(a862,f875(a862,a862),x97731),a331),x97732)),x97733)))) % 165.28/165.04 [10053]~P24(f332(f62(x100531),x100532))+P24(f332(f62(f869(x100531)),f332(f252(f869(x100531)),f332(f332(f18(f869(x100531),a862,a862),f332(f332(f8(a862,f875(a862,a862),f869(x100531)),a330),f332(f332(f7(f869(x100531),f875(x100531,a862),a862),f332(f332(f8(f875(x100531,a862),f875(f875(x100531,a862),a862),f869(x100531)),f246(f875(x100531,a862))),f174(x100531))),x100532))),f332(f332(f7(f869(x100531),a868,a862),f332(f332(f8(a868,f875(a868,a862),f869(x100531)),a329),f197(f869(x100531)))),x100533))))) % 165.28/165.04 [10054]~P24(f332(f62(x100541),x100542))+P24(f332(f62(f869(x100541)),f332(f252(f869(x100541)),f332(f332(f18(f869(x100541),a862,a862),f332(f332(f8(a862,f875(a862,a862),f869(x100541)),a330),f332(f332(f7(f869(x100541),f875(x100541,a862),a862),f332(f332(f8(f875(x100541,a862),f875(f875(x100541,a862),a862),f869(x100541)),f246(f875(x100541,a862))),f174(x100541))),x100542))),f332(f332(f7(f869(x100541),a868,a862),f332(f332(f8(a868,f875(a868,a862),f869(x100541)),f246(a868)),f197(f869(x100541)))),x100543))))) % 165.28/165.04 [9787]~P113(x97871)+E(f332(f332(f257(x97871),x97872),f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x97873)),f332(f332(f82(x97871),f332(f332(f257(x97871),x97872),x97873)),f332(f332(f257(x97871),x97872),x97873))) % 165.28/165.04 [9826]~P79(x98261)+E(f332(f332(f257(x98261),f332(f332(f257(x98261),x98262),x98263)),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(f332(f257(x98261),x98262),f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x98263))) % 165.28/165.04 [9872]~P138(x98721)+E(f332(f332(f257(x98721),f332(f80(x98721),x98722)),f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x98723)),f332(f332(f257(x98721),x98722),f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x98723))) % 165.28/165.04 [10012]~P118(x100121)+P24(f332(f332(f246(x100121),f2(x100121)),f332(f332(f81(x100121),f332(f332(f257(x100121),x100122),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x100121),x100123),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))))) % 165.28/165.04 [9882]~P113(x98821)+E(f332(f332(f257(x98821),x98822),f332(a115,f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x98823))),f332(f332(f82(x98821),x98822),f332(f332(f82(x98821),f332(f332(f257(x98821),x98822),x98823)),f332(f332(f257(x98821),x98822),x98823)))) % 165.28/165.04 [9931]~P79(x99311)+E(f332(f332(f82(x99311),x99312),f332(f332(f257(x99311),f332(f332(f257(x99311),x99312),x99313)),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x99311),x99312),f332(a115,f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x99313)))) % 165.28/165.04 [9970]~P118(x99701)+P24(f332(f332(f246(x99701),f2(x99701)),f332(f332(f257(x99701),x99702),f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x99703)))) % 165.28/165.04 [10034]~P92(x100341)+E(f332(f332(f22(x100341),f332(f332(f81(x100341),f332(f332(f257(x100341),x100342),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x100341),x100343),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))),f332(f332(f82(x100341),f332(f332(f82(x100341),f332(f106(x100341),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x100342)),x100343)),f332(f332(f257(x100341),f332(f332(f22(x100341),x100342),x100343)),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))) % 165.28/165.04 [10035]~P92(x100351)+E(f332(f332(f81(x100351),f332(f332(f81(x100351),f332(f332(f257(x100351),x100352),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x100351),x100353),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))),f332(f332(f82(x100351),f332(f332(f82(x100351),f332(f106(x100351),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x100352)),x100353)),f332(f332(f257(x100351),f332(f332(f81(x100351),x100352),x100353)),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))) % 165.28/165.04 [4664]E(x46641,x46642)+~E(f34(x46643,x46641),f34(x46644,x46642)) % 165.28/165.04 [4665]E(x46651,x46652)+~E(f34(x46651,x46653),f34(x46652,x46654)) % 165.28/165.04 [4666]E(x46661,x46662)+~E(f33(x46663,x46661),f33(x46664,x46662)) % 165.28/165.04 [4667]E(x46671,x46672)+~E(f33(x46671,x46673),f33(x46672,x46674)) % 165.28/165.04 [7752]P21(x77521,x77522,x77523,x77524)+~E(f652(x77524,x77523,x77522,x77521),f669(x77524,x77523,x77522,x77521)) % 165.28/165.04 [8039]P38(x80391,x80392,x80393,x80394,f116(x80392))+~E(x80394,f116(x80391)) % 165.28/165.04 [8040]P38(x80401,x80402,x80403,f116(x80401),x80404)+~E(x80404,f116(x80402)) % 165.28/165.04 [8252]~P21(x82521,f872(x82522),x82524,f186(x82521,x82522,x82524))+P21(x82521,f872(x82522),f187(x82521,x82522,x82523,x82524),f186(x82521,x82522,x82524)) % 165.28/165.04 [8454]~P21(x84541,f872(x84542),f187(x84541,x84542,x84544,x84543),f186(x84541,x84542,x84543))+P21(x84541,f872(x84542),x84543,f186(x84541,x84542,x84543)) % 165.28/165.04 [8567]~P38(x85672,x85673,x85674,x85671,f116(x85673))+E(x85671,f116(x85672)) % 165.28/165.04 [8568]~P38(x85683,x85682,x85684,f116(x85683),x85681)+E(x85681,f116(x85682)) % 165.28/165.04 [5043]~P13(x50433,x50431,x50434)+E(f332(f332(x50431,x50432),x50432),x50432) % 165.28/165.04 [5302]P24(f332(x53022,x53024))+E(f332(f137(x53021,x53022),f171(x53021,x53023,x53024)),f116(x53021)) % 165.28/165.04 [5338]~E(x53384,f196(f875(x53381,a862)))+E(f332(f311(x53381,x53382,x53383),x53384),f196(f875(x53382,a862))) % 165.28/165.04 [5578]~P24(f332(x55782,x55784))+E(f332(f137(x55781,x55782),f171(x55781,x55783,x55784)),f171(x55781,x55783,x55784)) % 165.28/165.04 [5607]~E(f332(f311(x56072,x56073,x56074),x56071),f196(f875(x56073,a862)))+E(x56071,f196(f875(x56072,a862))) % 165.28/165.04 [5891]~P106(x58912)+E(f332(f332(f149(x58911,x58912,x58913),x58914),f116(x58911)),f332(f332(f152(x58911),x58914),f116(x58911))) % 165.28/165.04 [5928]E(f332(x59281,x59282),f209(x59283))+P24(f332(f332(f334(x59284),x59282),f186(x59284,x59283,x59281))) % 165.28/165.04 [6254]~E(x62541,f196(f875(x62542,a862)))+~P24(f332(f63(x62542,x62543,x62541),x62544)) % 165.28/165.04 [6275]~P57(x62751,x62753,x62754,x62752)+P24(f332(f62(x62751),x62752)) % 165.28/165.04 [6276]~P57(x62761,x62763,x62762,x62764)+P24(f332(f62(x62761),x62762)) % 165.28/165.04 [6282]~P57(x62822,x62823,x62824,x62821)+~E(x62821,f196(f875(x62822,a862))) % 165.28/165.04 [6313]~P107(x63131)+E(f332(f332(f104(f875(x63131,a862)),f332(f302(x63131,x63132),x63133)),f303(x63131,x63133,x63134)),f196(f875(x63131,a862))) % 165.28/165.04 [6340]~P24(f332(f332(x63403,x63404),x63402))+P24(f332(f332(f334(x63401),x63402),f293(x63401,x63403,x63404))) % 165.28/165.04 [6341]~P24(f332(f332(x63413,x63414),x63412))+P24(f332(f332(f334(x63411),x63412),f294(x63411,x63413,x63414))) % 165.28/165.04 [6342]~P24(f332(f332(x63423,x63422),x63424))+P24(f332(f332(f334(x63421),x63422),f295(x63421,x63423,x63424))) % 165.28/165.04 [6343]~P24(f332(f332(x63433,x63432),x63434))+P24(f332(f332(f334(x63431),x63432),f298(x63431,x63433,x63434))) % 165.28/165.04 [6484]~P107(x64841)+E(f332(f332(f104(f875(x64841,a862)),f306(x64841,x64842,x64843)),f303(x64841,x64843,x64844)),f196(f875(x64841,a862))) % 165.28/165.04 [6485]~P107(x64851)+E(f332(f332(f104(f875(x64851,a862)),f305(x64851,x64852,x64853)),f306(x64851,x64853,x64854)),f196(f875(x64851,a862))) % 165.28/165.04 [6486]~P107(x64861)+E(f332(f332(f104(f875(x64861,a862)),f305(x64861,x64862,x64863)),f305(x64861,x64863,x64864)),f196(f875(x64861,a862))) % 165.28/165.04 [6487]~P107(x64871)+E(f332(f332(f104(f875(x64871,a862)),f303(x64871,x64872,x64873)),f306(x64871,x64873,x64874)),f196(f875(x64871,a862))) % 165.28/165.04 [6488]~P107(x64881)+E(f332(f332(f104(f875(x64881,a862)),f303(x64881,x64882,x64883)),f305(x64881,x64883,x64884)),f196(f875(x64881,a862))) % 165.28/165.04 [6526]P24(f332(f332(x65261,x65262),f681(x65262,x65261)))+~P24(f332(f261(x65263,x65264,x65261),x65262)) % 165.28/165.04 [6574]~E(f332(x65741,x65742),f209(x65743))+~P24(f332(f332(f334(x65744),x65742),f186(x65744,x65743,x65741))) % 165.28/165.04 [6603]~P106(x66032)+E(f332(f174(x66031),f151(x66031,x66032,x66033,x66034)),f332(f174(x66031),x66034)) % 165.28/165.04 [6654]~P142(x66541)+E(f198(x66541,x66542,f332(a115,x66543),x66544),f198(x66541,x66542,x66543,f332(x66542,x66544))) % 165.28/165.04 [6714]~P24(f332(f332(f334(x67144),x67143),f293(x67144,x67141,x67142)))+P24(f332(f332(x67141,x67142),x67143)) % 165.28/165.04 [6715]~P24(f332(f332(f334(x67154),x67153),f294(x67154,x67151,x67152)))+P24(f332(f332(x67151,x67152),x67153)) % 165.28/165.04 [6716]~P24(f332(f332(f334(x67164),x67162),f295(x67164,x67161,x67163)))+P24(f332(f332(x67161,x67162),x67163)) % 165.28/165.04 [6717]~P24(f332(f332(f334(x67174),x67172),f298(x67174,x67171,x67173)))+P24(f332(f332(x67171,x67172),x67173)) % 165.28/165.04 [6794]E(f332(f38(f876(x67941,x67942)),f319(x67941,x67942,x67943,x67944)),f2(a868))+P24(f332(f62(x67942),x67944)) % 165.28/165.04 [6795]E(f332(f38(f876(x67951,x67952)),f319(x67951,x67952,x67953,x67954)),f2(a868))+P24(f332(f62(x67951),x67953)) % 165.28/165.04 [6996]~P11(x69964,x69961,x69962)+E(f332(f74(x69961,x69961,x69961,f332(x69962,x69963)),f332(x69962,x69963)),f332(x69962,x69963)) % 165.28/165.04 [7872]~E(x78722,x78723)+P24(f332(f332(f334(f874(x78721,x78721)),f332(f332(f267(x78721,x78721),x78722),x78723)),f308(x78721,x78724))) % 165.28/165.04 [7900]~P21(x79001,x79002,x79003,f255(f875(x79001,a862)))+E(f332(f78(x79001,x79002,f255(f875(x79001,a862)),x79003),f332(x79003,x79004)),x79004) % 165.28/165.04 [7990]~P24(f332(f332(f334(f869(x79901)),f332(f332(f152(x79901),x79904),x79902)),f162(x79901,x79903)))+P24(f332(f332(f334(f869(x79901)),x79902),f162(x79901,x79903))) % 165.28/165.04 [7991]~P24(f332(f332(f334(f869(x79911)),f332(f332(f135(x79911),x79914),x79912)),f162(x79911,x79913)))+P24(f332(f332(f334(f869(x79911)),x79912),f162(x79911,x79913))) % 165.28/165.04 [7992]~P24(f332(f332(f334(f869(x79921)),f332(f332(f135(x79921),x79922),x79924)),f162(x79921,x79923)))+P24(f332(f332(f334(f869(x79921)),x79922),f162(x79921,x79923))) % 165.28/165.04 [8003]~P106(x80031)+P32(x80031,f332(f332(f155(x80032,x80031),x80033),f151(x80032,x80031,x80033,x80034))) % 165.28/165.04 [8100]P21(x81004,x81003,x81001,x81002)+E(f332(x81001,f652(x81002,x81001,x81003,x81004)),f332(x81001,f669(x81002,x81001,x81003,x81004))) % 165.28/165.04 [8112]E(f187(x81121,x81122,x81123,x81124),f187(x81121,x81122,x81124,x81123))+~E(f332(f332(f104(f875(x81121,a862)),f186(x81121,x81122,x81123)),f186(x81121,x81122,x81124)),f196(f875(x81121,a862))) % 165.28/165.04 [8215]~P21(x82152,x82151,x82154,x82153)+P21(x82151,x82152,f78(x82152,x82151,x82153,x82154),f332(f311(x82152,x82151,x82154),x82153)) % 165.28/165.04 [8349]P41(f874(x83492,x83494),f284(x83492,x83494,x83491,x83493))+P24(f332(x83491,f672(x83492,x83493,x83494,x83491))) % 165.28/165.04 [8461]E(x84611,x84612)+~P24(f332(f332(f334(f874(x84613,x84613)),f332(f332(f267(x84613,x84613),x84611),x84612)),f264(x84613,x84614))) % 165.28/165.04 [8522]~P24(f332(f62(f876(x85223,x85221)),f319(x85223,x85221,x85224,x85222)))+P24(f332(f62(x85221),x85222)) % 165.28/165.04 [8523]~P24(f332(f62(f876(x85231,x85233)),f319(x85231,x85233,x85232,x85234)))+P24(f332(f62(x85231),x85232)) % 165.28/165.04 [8700]P41(f874(x87001,x87002),f284(x87001,x87002,x87003,x87004))+~P41(x87002,f332(x87004,f672(x87001,x87004,x87002,x87003))) % 165.28/165.04 [9239]E(f332(f332(f160(x92391,x92392),f555(x92393,x92394,x92392,x92391)),f556(x92393,x92394,x92392,x92391)),x92394)+~P24(f332(f332(f334(f874(f869(x92391),f869(x92391))),f332(f332(f267(f869(x92391),f869(x92391)),x92392),x92394)),f158(x92391,x92393))) % 165.28/165.04 [9244]~P24(f332(f332(f334(f874(f869(x92441),f869(x92441))),f332(f332(f267(f869(x92441),f869(x92441)),x92442),x92443)),f146(x92441,x92444)))+P24(f332(f332(f334(f874(f869(x92441),f869(x92441))),f332(f332(f267(f869(x92441),f869(x92441)),x92442),x92443)),f148(x92441,x92444))) % 165.28/165.04 [9347]P24(f332(f62(x93471),x93472))+~P24(f332(f332(f334(f874(f875(x93471,a862),f875(x93471,a862))),f332(f332(f267(f875(x93471,a862),f875(x93471,a862)),x93473),x93472)),f323(x93471,x93474))) % 165.28/165.04 [9348]P24(f332(f62(x93481),x93482))+~P24(f332(f332(f334(f874(f875(x93481,a862),f875(x93481,a862))),f332(f332(f267(f875(x93481,a862),f875(x93481,a862)),x93482),x93483)),f323(x93481,x93484))) % 165.28/165.04 [9351]~E(x93511,f196(f875(x93512,a862)))+~P24(f332(f332(f334(f874(f875(x93512,a862),f875(x93512,a862))),f332(f332(f267(f875(x93512,a862),f875(x93512,a862)),x93513),x93511)),f323(x93512,x93514))) % 165.28/165.04 [9981]P9(x99811,x99812,x99813,x99814)+~P24(f332(f332(f271(x99811,x99811,a862),f332(f332(f7(x99811,f875(x99811,x99812),f875(x99811,a862)),f332(f332(f8(f875(x99812,a862),f875(f875(x99811,x99812),f875(x99811,a862)),x99811),f8(x99812,a862,x99811)),f332(f332(f8(x99812,f875(x99812,a862),x99811),a329),x99814))),x99814)),f546(x99814,x99813,x99812,x99811))) % 165.28/165.04 [4942]~E(x49424,f209(x49421))+E(f332(f332(f210(x49421,x49422),x49423),x49424),f209(x49422)) % 165.28/165.04 [4943]~E(x49434,f116(x49431))+E(f332(f332(f155(x49431,x49432),x49433),x49434),f116(x49432)) % 165.28/165.04 [4944]~E(x49442,f116(x49441))+E(f332(f332(f160(x49441,x49442),x49443),x49444),f116(x49441)) % 165.28/165.04 [5182]E(x51821,f209(x51822))+~E(f332(f332(f210(x51822,x51823),x51824),x51821),f209(x51823)) % 165.28/165.04 [5183]E(x51831,f116(x51832))+~E(f332(f332(f155(x51832,x51833),x51834),x51831),f116(x51833)) % 165.28/165.04 [5184]E(x51841,f116(x51842))+~E(f332(f332(f160(x51842,x51841),x51843),x51844),f116(x51842)) % 165.28/165.04 [5217]E(x52171,x52172)+~E(f332(f332(f135(x52173),x52174),x52171),f332(f332(f135(x52173),x52174),x52172)) % 165.28/165.04 [5218]E(x52181,x52182)+~E(f332(f332(f135(x52183),x52181),x52184),f332(f332(f135(x52183),x52182),x52184)) % 165.28/165.04 [5375]P24(f332(x53753,x53752))+E(f172(x53751,x53752,f332(f137(x53751,x53753),x53754)),f332(f137(x53751,x53753),x53754)) % 165.28/165.04 [5378]~P24(f332(x53782,x53783))+P37(x53781,x53782,f332(f332(f152(x53781),x53783),x53784)) % 165.28/165.04 [5387]E(x53871,x53872)+~E(f140(a868,f332(f302(a868,x53871),x53873)),f332(f332(f152(a868),x53872),x53874)) % 165.28/165.04 [5435]~P22(x54352,x54353)+P22(x54351,f332(f332(f75(x54352,x54351),x54353),x54354)) % 165.28/165.04 [5436]~P41(x54362,x54363)+P41(x54361,f332(f332(f288(x54362,x54361),x54363),x54364)) % 165.28/165.04 [5562]~P37(x55621,x55622,x55624)+P37(x55621,x55622,f332(f332(f152(x55621),x55623),x55624)) % 165.28/165.04 [5563]~P37(x55631,x55632,x55634)+P37(x55631,x55632,f332(f332(f135(x55631),x55633),x55634)) % 165.28/165.04 [5564]~P37(x55641,x55642,x55643)+P37(x55641,x55642,f332(f332(f135(x55641),x55643),x55644)) % 165.28/165.04 [5650]~E(x56501,f116(x56502))+~E(f332(f332(f135(x56502),x56503),f332(f332(f152(x56502),x56504),f116(x56502))),x56501) % 165.28/165.04 [5675]~P35(x56753,x56751,f332(f332(f152(x56753),x56752),x56754))+P24(f332(x56751,x56752)) % 165.28/165.04 [5685]E(f117(x56851,x56852),x56853)+~E(f332(f332(f135(x56851),x56853),f332(f332(f152(x56851),x56854),f116(x56851))),x56852) % 165.28/165.04 [5686]E(f145(x56861,x56862),x56863)+~E(f332(f332(f135(x56861),x56864),f332(f332(f152(x56861),x56863),f116(x56861))),x56862) % 165.28/165.04 [5796]~E(f140(a868,f332(f302(a868,x57961),x57962)),f332(f332(f152(a868),x57963),x57964))+P24(f332(f332(f247(a868),x57961),x57962)) % 165.28/165.04 [5804]P35(x58041,x58042,x58043)+~P35(x58041,x58042,f332(f332(f152(x58041),x58044),x58043)) % 165.28/165.04 [5805]P35(x58051,x58052,x58053)+~P35(x58051,x58052,f332(f332(f135(x58051),x58054),x58053)) % 165.28/165.04 [5806]P35(x58061,x58062,x58063)+~P35(x58061,x58062,f332(f332(f135(x58061),x58063),x58064)) % 165.28/165.04 [5995]E(x59951,f332(f332(f135(x59952),f332(f170(x59952),x59953)),f332(f332(f152(x59952),x59954),f116(x59952))))+~E(f332(f170(x59952),x59951),f332(f332(f152(x59952),x59954),x59953)) % 165.28/165.04 [6174]~P107(x61741)+E(f332(f332(f104(f875(x61741,a862)),f332(f302(x61741,x61742),x61743)),f332(f302(x61741,x61743),x61744)),f196(f875(x61741,a862))) % 165.28/165.04 [6185]E(f332(f332(f166(x61851),f171(x61851,x61852,x61853)),x61854),x61853)+~P24(f332(f332(f247(a868),x61854),x61852)) % 165.28/165.04 [6212]~P74(x62121)+E(f332(f167(x62121),f332(f332(f155(a1,x62121),x62122),f181(x62123,x62124))),f332(f332(f6(a1,x62121),x62122),f332(f174(a1),f181(x62123,x62124)))) % 165.28/165.04 [6213]~P74(x62131)+E(f332(f332(f6(a1,x62131),x62132),f332(f174(a1),f181(x62133,x62134))),f332(f167(x62131),f332(f332(f155(a1,x62131),x62132),f181(x62133,x62134)))) % 165.28/165.04 [6355]~E(x63552,f332(f332(f135(x63551),f332(f170(x63551),x63554)),f332(f332(f152(x63551),x63553),f116(x63551))))+E(f332(f170(x63551),x63552),f332(f332(f152(x63551),x63553),x63554)) % 165.28/165.04 [6371]~P15(x63712,x63713,x63714,x63711)+E(f332(x63711,f196(f875(x63712,a862))),f35(x63713)) % 165.28/165.04 [6397]~P107(x63971)+E(f332(f332(f104(f875(x63971,a862)),f306(x63971,x63972,x63973)),f332(f302(x63971,x63973),x63974)),f196(f875(x63971,a862))) % 165.28/165.04 [6604]E(x66041,f196(f875(x66042,a862)))+~E(f319(x66043,x66042,x66044,x66041),f196(f875(f876(x66043,x66042),a862))) % 165.28/165.04 [6605]E(x66051,f196(f875(x66052,a862)))+~E(f319(x66052,x66053,x66051,x66054),f196(f875(f876(x66052,x66053),a862))) % 165.28/165.04 [6673]~P106(x66732)+E(f332(f197(f869(x66731)),f151(x66731,x66732,x66733,x66734)),f332(f197(f869(x66731)),x66734)) % 165.28/165.04 [6685]~P24(f332(f262(x66853,x66854,x66851),x66852))+P24(f332(f332(x66851,f667(x66852,x66851)),x66852)) % 165.28/165.04 [6725]~P24(f332(f62(x67252),x67254))+P24(f332(f62(x67251),f332(f311(x67252,x67251,x67253),x67254))) % 165.28/165.04 [6956]~P21(x69562,x69561,x69563,x69564)+E(f332(f38(x69561),f332(f311(x69562,x69561,x69563),x69564)),f332(f38(x69562),x69564)) % 165.28/165.04 [6975]E(f332(f311(x69751,x69752,x69753),f332(f312(x69751,x69752,x69753),x69754)),x69754)+~E(f332(f311(x69751,x69752,x69753),f255(f875(x69751,a862))),f255(f875(x69752,a862))) % 165.28/165.04 [7380]~P21(x73801,x73802,x73803,f255(f875(x73801,a862)))+E(f332(f312(x73801,x73802,x73803),f332(f311(x73801,x73802,x73803),x73804)),x73804) % 165.28/165.04 [7668]E(x76681,x76682)+~P24(f332(f332(f334(x76683),x76681),f332(f174(x76683),f171(x76683,x76684,x76682)))) % 165.28/165.04 [7677]~E(x76771,f2(a868))+~P24(f332(f332(f334(x76772),x76773),f332(f174(x76772),f171(x76772,x76771,x76774)))) % 165.28/165.04 [7713]P24(f332(x77131,x77132))+~P24(f332(f332(f334(x77133),x77132),f332(f174(x77133),f179(x77133,x77131,x77134)))) % 165.28/165.04 [7819]~P24(f332(f332(f334(f869(x78191)),f332(f332(f152(x78191),x78192),x78194)),f162(x78191,x78193)))+P24(f332(f332(f334(x78191),x78192),x78193)) % 165.28/165.04 [7946]~P24(f332(f332(f334(x79461),x79462),f332(f174(x79461),f172(x79461,x79464,x79463))))+P24(f332(f332(f334(x79461),x79462),f332(f174(x79461),x79463))) % 165.28/165.04 [7948]~P24(f332(f332(f334(x79481),x79482),f332(f174(x79481),f178(x79481,x79483,x79484))))+P24(f332(f332(f334(x79481),x79482),f332(f174(x79481),x79483))) % 165.28/165.04 [7949]~P24(f332(f332(f334(x79491),x79492),f332(f174(x79491),f179(x79491,x79494,x79493))))+P24(f332(f332(f334(x79491),x79492),f332(f174(x79491),x79493))) % 165.28/165.04 [7959]E(f332(f197(f869(x79591)),x79592),x79593)+~P24(f332(f332(f334(f869(x79591)),x79592),f332(f174(f869(x79591)),f55(x79591,x79593,x79594)))) % 165.28/165.04 [8051]P24(f332(x80513,x80512))+E(f332(f137(x80511,f332(f332(f8(a862,a862,x80511),a327),f332(a329,x80512))),f332(f137(x80511,x80513),x80514)),f332(f137(x80511,x80513),x80514)) % 165.28/165.04 [8164]E(f332(f332(f166(x81641),f179(x81641,x81642,x81643)),x81644),f332(f332(f166(x81641),x81643),x81644))+~P24(f332(f332(f247(a868),x81644),f332(f197(f869(x81641)),f179(x81641,x81642,x81643)))) % 165.28/165.04 [8250]~P74(x82501)+E(f332(f332(f6(a868,x82501),f332(f332(f8(a868,x82501,a868),x82502),a115)),f332(f302(a868,x82503),x82504)),f332(f332(f6(a868,x82501),x82502),f332(f302(a868,f332(a115,x82503)),f332(a115,x82504)))) % 165.28/165.04 [8259]~P74(x82591)+E(f332(f332(f6(a868,x82591),f332(f332(f8(a868,x82591,a868),x82592),a115)),f303(a868,x82593,x82594)),f332(f332(f6(a868,x82591),x82592),f303(a868,f332(a115,x82593),f332(a115,x82594)))) % 165.28/165.04 [8384]~P21(x83841,x83843,x83844,f255(f875(x83841,a862)))+P21(x83841,f875(x83842,x83843),f332(f332(f8(x83843,f875(x83842,x83843),x83841),f16(x83843,x83842)),x83844),f255(f875(x83841,a862))) % 165.28/165.04 [8466]~P21(x84662,x84661,x84664,x84663)+E(f332(f311(x84661,x84662,f78(x84662,x84661,x84663,x84664)),f332(f311(x84662,x84661,x84664),x84663)),x84663) % 165.28/165.04 [8524]~P24(f332(f332(f334(f874(x85241,x85241)),f332(f332(f267(x85241,x85241),x85242),x85244)),f264(x85241,x85243)))+P24(f332(f332(f334(x85241),x85242),x85243)) % 165.28/165.04 [8612]E(f332(f332(f332(f73(x86121,f872(x86122)),f332(f16(f872(x86122),x86121),f209(x86122))),x86123),f332(f208(x86122),f582(x86123,x86124,x86122,x86121))),x86124)+~E(f186(x86121,x86122,x86124),f332(f332(f310(x86121),x86123),f196(f875(x86121,a862)))) % 165.28/165.04 [8735]~E(f332(f332(f6(x87351,a868),x87354),x87353),f332(a115,x87352))+P24(f332(f332(f334(x87351),f475(x87352,x87353,x87354,x87351)),x87353)) % 165.28/165.04 [8755]~E(f332(f332(f6(x87554,a868),x87551),x87553),f332(a115,x87552))+P24(f332(f332(f247(a868),f2(a868)),f332(x87551,f475(x87552,x87553,x87551,x87554)))) % 165.28/165.04 [8766]~P24(f332(f62(x87662),x87664))+P24(f332(f332(f246(a868),f332(f38(x87661),f332(f311(x87662,x87661,x87663),x87664))),f332(f38(x87662),x87664))) % 165.28/165.04 [8767]E(f332(f332(f267(x87671,x87672),f776(x87673,x87674,x87672,x87671)),f777(x87673,x87674,x87672,x87671)),x87674)+~P24(f332(f332(f334(f874(x87671,x87672)),x87674),f332(f287(x87672,x87671),x87673))) % 165.28/165.04 [8775]P21(x87751,x87752,x87753,x87754)+P24(f332(f332(f334(x87751),f652(x87754,x87753,x87752,x87751)),x87754)) % 165.28/165.04 [8776]P21(x87761,x87762,x87763,x87764)+P24(f332(f332(f334(x87761),f669(x87764,x87763,x87762,x87761)),x87764)) % 165.28/165.04 [8837]P9(x88371,x88372,x88373,x88374)+P24(f332(f332(f334(f874(x88371,x88371)),f546(x88374,x88373,x88372,x88371)),x88373)) % 165.28/165.04 [8896]P24(f332(x88961,x88962))+~P24(f332(x88961,f332(f332(f267(x88963,x88964),f497(x88964,x88963,x88961)),f498(x88964,x88963,x88961)))) % 165.28/165.04 [8912]E(f332(f197(f869(x89121)),x89122),f332(f197(f869(x89121)),x89123))+~P24(f332(f332(f334(f874(f869(x89121),f869(x89121))),f332(f332(f267(f869(x89121),f869(x89121)),x89122),x89123)),f159(x89121,x89124))) % 165.28/165.04 [8913]E(f332(f197(f869(x89131)),x89132),f332(f197(f869(x89131)),x89133))+~P24(f332(f332(f334(f874(f869(x89131),f869(x89131))),f332(f332(f267(f869(x89131),f869(x89131)),x89132),x89133)),f146(x89131,x89134))) % 165.28/165.04 [8914]E(f332(f197(f869(x89141)),x89142),f332(f197(f869(x89141)),x89143))+~P24(f332(f332(f334(f874(f869(x89141),f869(x89141))),f332(f332(f267(f869(x89141),f869(x89141)),x89142),x89143)),f158(x89141,x89144))) % 165.28/165.04 [8985]P24(f332(f332(f246(a868),f156(x89851,x89852,x89853)),f156(x89851,x89854,x89853)))+P24(f332(f332(f334(x89851),f560(x89854,x89852,x89853,x89851)),f332(f174(x89851),x89853))) % 165.28/165.04 [8988]E(f332(f197(f869(x89881)),x89882),f332(f197(f869(x89881)),x89883))+~P24(f332(f332(f334(f874(f869(x89881),f869(x89881))),f332(f332(f267(f869(x89881),f869(x89881)),x89882),x89883)),f308(f869(x89881),f158(x89881,x89884)))) % 165.28/165.04 [9214]~P21(x92141,x92142,x92143,x92144)+~P24(f332(f332(f247(a868),f332(f38(x92142),f332(f311(x92141,x92142,x92143),x92144))),f332(f38(x92141),x92144))) % 165.28/165.04 [9255]~P24(f332(f332(f334(f874(f869(x92551),f869(x92551))),f332(f332(f267(f869(x92551),f869(x92551)),x92552),x92553)),f158(x92551,x92554)))+P24(f332(f332(f334(f874(f869(x92551),f869(x92551))),f332(f332(f267(f869(x92551),f869(x92551)),x92552),x92553)),f159(x92551,f308(x92551,x92554)))) % 165.28/165.04 [9259]~P24(f332(f332(f334(f874(f869(x92591),f869(x92591))),f332(f332(f267(f869(x92591),f869(x92591)),x92592),x92593)),f159(x92591,x92594)))+P24(f332(f332(f334(f874(f869(x92591),f869(x92591))),f332(f332(f267(f869(x92591),f869(x92591)),x92592),x92593)),f308(f869(x92591),f158(x92591,x92594)))) % 165.28/165.04 [9276]P24(f332(f332(f334(f874(x92761,x92761)),f332(f332(f267(x92761,x92761),x92762),x92763)),f308(x92761,x92764)))+~P24(f332(f332(f334(f874(x92761,x92761)),f332(f332(f267(x92761,x92761),x92762),x92763)),f332(f332(f289(x92761,x92761,x92761),x92764),f308(x92761,x92764)))) % 165.28/165.04 [9450]E(f332(f332(f135(x94501),f587(x94502,x94503,x94504,x94501)),f332(f332(f152(x94501),f588(x94502,x94503,x94504,x94501)),f590(x94502,x94503,x94504,x94501))),x94504)+~P24(f332(f332(f334(f874(f869(x94501),f869(x94501))),f332(f332(f267(f869(x94501),f869(x94501)),x94504),x94503)),f158(x94501,x94502))) % 165.28/165.04 [9451]E(f332(f332(f135(x94511),f587(x94512,x94513,x94514,x94511)),f332(f332(f152(x94511),f589(x94512,x94513,x94514,x94511)),f590(x94512,x94513,x94514,x94511))),x94513)+~P24(f332(f332(f334(f874(f869(x94511),f869(x94511))),f332(f332(f267(f869(x94511),f869(x94511)),x94514),x94513)),f158(x94511,x94512))) % 165.28/165.04 [9527]P24(f332(f332(f334(f874(x95271,x95271)),f332(f332(f267(x95271,x95271),x95272),f754(x95273,x95274,x95272,x95271))),f308(x95271,x95273)))+~P24(f332(f332(f334(f874(x95271,x95271)),f332(f332(f267(x95271,x95271),x95272),x95274)),f332(f332(f289(x95271,x95271,x95271),x95273),f308(x95271,x95273)))) % 165.28/165.04 [9596]P24(f332(f332(f246(a868),f156(x95961,x95962,x95963)),f156(x95961,x95964,x95963)))+~P24(f332(f332(f247(a868),f332(x95962,f560(x95964,x95962,x95963,x95961))),f332(x95964,f560(x95964,x95962,x95963,x95961)))) % 165.28/165.04 [9664]P24(f332(f332(f334(f874(x96641,x96641)),f332(f332(f267(x96641,x96641),f753(x96642,x96643,x96644,x96641)),x96643)),f308(x96641,x96642)))+~P24(f332(f332(f334(f874(x96641,x96641)),f332(f332(f267(x96641,x96641),x96644),x96643)),f332(f332(f289(x96641,x96641,x96641),x96642),f308(x96641,x96642)))) % 165.28/165.04 [5198]~E(x51982,x51983)+E(f172(x51981,x51982,f332(f332(f152(x51981),x51983),x51984)),x51984) % 165.28/165.04 [5330]P24(f332(x53302,x53303))+E(f179(x53301,x53302,f332(f332(f152(x53301),x53303),x53304)),f116(x53301)) % 165.28/165.04 [5399]~P82(x53992)+E(f332(f332(f80(f875(x53991,x53992)),x53993),x53994),f332(f80(x53992),f332(x53993,x53994))) % 165.28/165.04 [5411]~E(x54112,f2(a868))+E(f332(f332(f139(x54111),x54112),f332(f332(f152(x54111),x54113),x54114)),f332(f332(f152(x54111),x54113),x54114)) % 165.28/165.04 [5412]P24(f332(x54122,x54123))+E(f332(f137(x54121,x54122),f332(f332(f152(x54121),x54123),x54124)),f332(f137(x54121,x54122),x54124)) % 165.28/165.04 [5545]~E(x55452,x55454)+P24(f332(f332(f332(f310(x55451),x55452),x55453),x55454)) % 165.28/165.04 [5553]E(x55531,f116(x55532))+E(f145(x55533,f332(f332(f155(x55532,x55533),x55534),x55531)),f332(x55534,f145(x55532,x55531))) % 165.28/165.04 [5567]~E(x55671,f64(x55672,x55674))+E(f332(x55671,f332(f332(f310(x55672),x55673),f196(f875(x55672,a862)))),x55673) % 165.28/165.04 [5602]E(x56021,f116(x56022))+E(f332(f142(x56023),f332(f332(f155(x56022,x56023),x56024),x56021)),f332(x56024,f332(f142(x56022),x56021))) % 165.28/165.04 [5705]~P24(f332(x57053,x57054))+P24(f332(f332(f332(f310(x57051),x57052),x57053),x57054)) % 165.28/165.04 [5821]~P14(x58212,x58214,x58211)+E(f332(x58211,f332(f332(f310(x58212),x58213),f196(f875(x58212,a862)))),x58213) % 165.28/165.04 [5845]~E(x58452,x58453)+P24(f332(f332(f334(x58451),x58452),f332(f332(f310(x58451),x58453),x58454))) % 165.28/165.04 [5849]~P26(x58491)+E(f332(f332(f113(x58491),x58492),f332(f332(f113(x58491),x58493),x58494)),f332(f332(f113(x58491),x58493),f332(f332(f113(x58491),x58492),x58494))) % 165.28/165.04 [5851]~P99(x58511)+E(f332(f332(f113(x58511),x58512),f332(f332(f113(x58511),x58513),x58514)),f332(f332(f113(x58511),x58513),f332(f332(f113(x58511),x58512),x58514))) % 165.28/165.04 [5852]~P26(x58521)+E(f332(f332(f104(x58521),x58522),f332(f332(f104(x58521),x58523),x58524)),f332(f332(f104(x58521),x58523),f332(f332(f104(x58521),x58522),x58524))) % 165.28/165.04 [5854]~P100(x58541)+E(f332(f332(f104(x58541),x58542),f332(f332(f104(x58541),x58543),x58544)),f332(f332(f104(x58541),x58543),f332(f332(f104(x58541),x58542),x58544))) % 165.28/165.04 [5855]~P113(x58551)+E(f332(f332(f81(x58551),x58552),f332(f332(f81(x58551),x58553),x58554)),f332(f332(f81(x58551),x58553),f332(f332(f81(x58551),x58552),x58554))) % 165.28/165.04 [5856]~P113(x58561)+E(f332(f332(f82(x58561),x58562),f332(f332(f82(x58561),x58563),x58564)),f332(f332(f82(x58561),x58563),f332(f332(f82(x58561),x58562),x58564))) % 165.28/165.04 [5858]~P106(x58581)+E(f332(f332(f244(x58581),x58582),f332(f332(f244(x58581),x58583),x58584)),f332(f332(f244(x58581),x58583),f332(f332(f244(x58581),x58582),x58584))) % 165.28/165.04 [5860]~P106(x58601)+E(f332(f332(f245(x58601),x58602),f332(f332(f245(x58601),x58603),x58604)),f332(f332(f245(x58601),x58603),f332(f332(f245(x58601),x58602),x58604))) % 165.28/165.04 [5865]E(x58651,x58652)+E(f172(x58653,x58651,f332(f332(f152(x58653),x58652),x58654)),f332(f332(f152(x58653),x58652),f172(x58653,x58651,x58654))) % 165.28/165.04 [5878]~P24(f332(x58782,x58783))+E(f332(f137(x58781,x58782),f332(f332(f152(x58781),x58783),x58784)),f332(f332(f152(x58781),x58783),f332(f137(x58781,x58782),x58784))) % 165.28/165.04 [6015]~P24(f332(x60152,x60153))+E(f179(x60151,x60152,f332(f332(f152(x60151),x60153),x60154)),f332(f332(f152(x60151),x60153),f179(x60151,x60152,x60154))) % 165.28/165.04 [6066]P20(x60661,x60662,x60663)+~P20(x60661,x60662,f332(f332(f310(f867(x60661)),x60664),x60663)) % 165.28/165.04 [6079]E(x60791,f196(f875(x60792,a862)))+E(f332(f332(f42(x60792,f875(x60793,a862)),x60791),f332(f16(f875(x60793,a862),x60792),x60794)),x60794) % 165.28/165.04 [6080]E(x60801,f196(f875(x60802,a862)))+E(f332(f332(f43(x60802,f875(x60803,a862)),x60801),f332(f16(f875(x60803,a862),x60802),x60804)),x60804) % 165.28/165.04 [6089]~E(x60894,f196(f875(x60892,a862)))+E(f332(f332(f269(x60891,x60892),x60893),f332(f16(f875(x60892,a862),x60891),x60894)),f196(f875(f874(x60891,x60892),a862))) % 165.28/165.04 [6090]~E(x60903,f196(f875(x60901,a862)))+E(f332(f332(f269(x60901,x60902),x60903),f332(f16(f875(x60902,a862),x60901),x60904)),f196(f875(f874(x60901,x60902),a862))) % 165.28/165.04 [6138]E(x61381,f2(a868))+E(f332(f332(f139(x61382),x61381),f332(f332(f152(x61382),x61383),x61384)),f332(f332(f139(x61382),f332(f332(f22(a868),x61381),f79(a868))),x61384)) % 165.28/165.04 [6168]E(x61681,f196(f875(x61682,a862)))+E(f332(f311(x61682,x61683,f332(f16(x61683,x61682),x61684)),x61681),f332(f332(f310(x61683),x61684),f196(f875(x61683,a862)))) % 165.28/165.04 [6171]E(f332(f312(x61711,x61712,f332(f16(x61712,x61711),x61713)),x61714),f196(f875(x61711,a862)))+P24(f332(f332(f334(x61712),x61713),x61714)) % 165.28/165.04 [6238]~E(x62383,f196(f875(x62381,a862)))+E(f332(f332(f42(x62381,f875(x62382,a862)),x62383),f332(f16(f875(x62382,a862),x62381),x62384)),f196(f875(x62382,a862))) % 165.28/165.04 [6239]~E(x62393,f196(f875(x62391,a862)))+E(f332(f332(f43(x62391,f875(x62392,a862)),x62393),f332(f16(f875(x62392,a862),x62391),x62394)),f255(f875(x62392,a862))) % 165.28/165.04 [6241]~P28(x62411)+E(f45(x62411,f332(f332(f82(x62411),x62412),x62413),f332(f332(f82(x62411),x62412),x62414)),f332(f332(f82(x62411),x62412),f45(x62411,x62413,x62414))) % 165.28/165.04 [6407]E(f332(f312(x64071,x64072,f332(f16(x64072,x64071),x64073)),x64074),f255(f875(x64071,a862)))+~P24(f332(f332(f334(x64072),x64073),x64074)) % 165.28/165.04 [6430]~P24(f332(f332(f334(x64301),x64302),x64304))+P24(f332(f332(f334(x64301),x64302),f332(f332(f310(x64301),x64303),x64304))) % 165.28/165.04 [6435]P24(f332(x64351,x64352))+~P24(f332(f161(x64353,x64351),f332(f332(f152(x64353),x64352),x64354))) % 165.28/165.04 [6444]~E(x64443,f332(f332(f22(a868),f332(f197(f869(x64441)),x64442)),f79(a868)))+E(f117(x64441,f332(f332(f160(x64441,x64442),x64443),x64444)),f117(x64441,x64442)) % 165.28/165.04 [6463]~P106(x64631)+E(f332(f332(f104(f875(x64631,a862)),f332(f301(x64631),x64632)),f303(x64631,x64633,x64634)),f303(x64631,x64633,f332(f332(f244(x64631),x64632),x64634))) % 165.28/165.04 [6464]~P106(x64641)+E(f332(f332(f104(f875(x64641,a862)),f332(f254(x64641),x64642)),f303(x64641,x64643,x64644)),f303(x64641,f332(f332(f245(x64641),x64642),x64643),x64644)) % 165.28/165.04 [6479]E(f332(f332(f104(f875(x64791,a862)),x64792),f332(f332(f310(x64791),x64793),x64794)),f332(f332(f104(f875(x64791,a862)),x64792),x64794))+P24(f332(f332(f334(x64791),x64793),x64792)) % 165.28/165.04 [6491]E(f172(x64911,x64912,f332(f332(f135(x64911),x64913),x64914)),f332(f332(f135(x64911),x64913),f172(x64911,x64912,x64914)))+P24(f332(f332(f334(x64911),x64912),f332(f174(x64911),x64913))) % 165.28/165.04 [6495]~P79(x64951)+E(f332(f332(f82(x64951),f332(f332(f257(x64951),x64952),x64953)),f332(f332(f257(x64951),x64952),x64954)),f332(f332(f257(x64951),x64952),f332(f332(f81(a868),x64953),x64954))) % 165.28/165.04 [6496]~P113(x64961)+E(f332(f332(f82(x64961),f332(f332(f257(x64961),x64962),x64963)),f332(f332(f257(x64961),x64962),x64964)),f332(f332(f257(x64961),x64962),f332(f332(f81(a868),x64963),x64964))) % 165.28/165.04 [6533]~P97(x65331)+E(f332(f332(f104(x65331),f332(f332(f113(x65331),x65332),x65333)),f332(f332(f113(x65331),x65332),x65334)),f332(f332(f113(x65331),x65332),f332(f332(f104(x65331),x65333),x65334))) % 165.28/165.04 [6534]~P97(x65341)+E(f332(f332(f113(x65341),f332(f332(f104(x65341),x65342),x65343)),f332(f332(f104(x65341),x65342),x65344)),f332(f332(f104(x65341),x65342),f332(f332(f113(x65341),x65343),x65344))) % 165.28/165.04 [6535]~P113(x65351)+E(f332(f332(f81(x65351),f332(f332(f82(x65351),x65352),x65353)),f332(f332(f82(x65351),x65352),x65354)),f332(f332(f82(x65351),x65352),f332(f332(f81(x65351),x65353),x65354))) % 165.28/165.04 [6536]~P106(x65361)+E(f332(f332(f245(x65361),f332(f332(f244(x65361),x65362),x65363)),f332(f332(f244(x65361),x65362),x65364)),f332(f332(f244(x65361),x65362),f332(f332(f245(x65361),x65363),x65364))) % 165.28/165.04 [6537]~P106(x65371)+E(f332(f332(f244(x65371),f332(f332(f245(x65371),x65372),x65373)),f332(f332(f245(x65371),x65372),x65374)),f332(f332(f245(x65371),x65372),f332(f332(f244(x65371),x65373),x65374))) % 165.28/165.04 [6568]~P28(x65681)+E(f45(x65681,f332(f332(f82(x65681),x65682),x65683),f332(f332(f82(x65681),x65684),x65683)),f332(f332(f82(x65681),f45(x65681,x65682,x65684)),x65683)) % 165.28/165.04 [6571]~E(f332(f197(f869(x65711)),x65713),f332(f197(f869(x65712)),x65714))+E(f332(f332(f155(f874(x65711,x65712),x65712),f270(x65711,x65712)),f332(f332(f184(x65711,x65712),x65713),x65714)),x65714) % 165.28/165.04 [6572]~E(f332(f197(f869(x65721)),x65723),f332(f197(f869(x65722)),x65724))+E(f332(f332(f155(f874(x65721,x65722),x65721),f266(x65721,x65722)),f332(f332(f184(x65721,x65722),x65723),x65724)),x65723) % 165.28/165.04 [6578]P24(f332(f161(x65781,x65782),x65783))+~P24(f332(f161(x65781,x65782),f332(f332(f152(x65781),x65784),x65783))) % 165.28/165.04 [6579]P24(f332(f161(x65791,x65792),x65793))+~P24(f332(f161(x65791,x65792),f332(f332(f135(x65791),x65794),x65793))) % 165.28/165.04 [6580]P24(f332(f161(x65801,x65802),x65803))+~P24(f332(f161(x65801,x65802),f332(f332(f135(x65801),x65803),x65804))) % 165.28/165.04 [6585]~P29(x65851)+E(f45(x65851,f332(f332(f22(x65851),x65852),f45(x65851,x65853,x65854)),x65854),f45(x65851,f332(f332(f22(x65851),x65852),x65853),x65854)) % 165.28/165.04 [6587]~P28(x65871)+E(f45(x65871,f332(f332(f82(x65871),x65872),f45(x65871,x65873,x65874)),x65874),f45(x65871,f332(f332(f82(x65871),x65872),x65873),x65874)) % 165.28/165.04 [6588]~P28(x65881)+E(f45(x65881,f332(f332(f81(x65881),x65882),f45(x65881,x65883,x65884)),x65884),f45(x65881,f332(f332(f81(x65881),x65882),x65883),x65884)) % 165.28/165.04 [6667]~P106(x66671)+E(f332(f332(f104(f875(x66671,a862)),f303(x66671,x66672,x66673)),f332(f301(x66671),x66674)),f303(x66671,x66672,f332(f332(f244(x66671),x66673),x66674))) % 165.28/165.04 [6668]~P106(x66681)+E(f332(f332(f104(f875(x66681,a862)),f303(x66681,x66682,x66683)),f332(f254(x66681),x66684)),f303(x66681,f332(f332(f245(x66681),x66682),x66684),x66683)) % 165.28/165.04 [6671]~E(f332(f197(f869(x66711)),x66713),f332(f197(f869(x66712)),x66714))+E(f332(f332(f184(x66711,x66712),f332(f170(x66711),x66713)),f332(f170(x66712),x66714)),f332(f170(f874(x66711,x66712)),f332(f332(f184(x66711,x66712),x66713),x66714))) % 165.28/165.04 [6681]E(x66811,f332(f332(f22(a868),f332(f197(f869(x66812)),x66813)),f79(a868)))+E(f117(x66812,f332(f332(f160(x66812,x66813),x66811),x66814)),f332(f332(f160(x66812,f117(x66812,x66813)),x66811),x66814)) % 165.28/165.04 [6696]~P24(f332(f138(x66962),x66964))+P24(f332(f138(f874(x66961,x66962)),f332(f332(f184(x66961,x66962),x66963),x66964))) % 165.28/165.04 [6697]~P24(f332(f138(x66971),x66973))+P24(f332(f138(f874(x66971,x66972)),f332(f332(f184(x66971,x66972),x66973),x66974))) % 165.28/165.04 [6959]E(f332(f332(f39(a868),x69591),x69592),x69593)+~P24(f332(f48(x69591,x69592),f332(f332(f267(a868,a868),x69593),x69594))) % 165.28/165.04 [6983]E(f45(a868,x69831,x69832),x69833)+~P24(f332(f48(x69831,x69832),f332(f332(f267(a868,a868),x69834),x69833))) % 165.28/165.04 [6986]P24(f332(f138(x69861),x69862))+~P24(f332(f138(x69863),f332(f332(f155(x69861,x69863),x69864),x69862))) % 165.28/165.04 [6994]~P20(x69941,x69942,f332(f332(f310(f867(x69941)),x69943),x69944))+P20(x69941,x69942,f332(f332(f310(f867(x69941)),x69943),f196(f875(f867(x69941),a862)))) % 165.28/165.04 [7070]E(f172(x70701,x70702,f332(f332(f135(x70701),x70703),x70704)),f332(f332(f135(x70701),f172(x70701,x70702,x70703)),x70704))+~P24(f332(f332(f334(x70701),x70702),f332(f174(x70701),x70703))) % 165.28/165.04 [7160]~P29(x71601)+E(f45(x71601,f332(f332(f22(x71601),f45(x71601,x71602,x71603)),x71604),x71603),f45(x71601,f332(f332(f22(x71601),x71602),x71604),x71603)) % 165.28/165.04 [7163]~P28(x71631)+E(f45(x71631,f332(f332(f81(x71631),f45(x71631,x71632,x71633)),x71634),x71633),f45(x71631,f332(f332(f81(x71631),x71632),x71634),x71633)) % 165.28/165.04 [7164]~P28(x71641)+E(f45(x71641,f332(f332(f82(x71641),f45(x71641,x71642,x71643)),x71644),x71643),f45(x71641,f332(f332(f82(x71641),x71642),x71644),x71643)) % 165.28/165.04 [7351]~E(x73511,f332(f332(f152(x73512),x73513),x73514))+~P24(f332(f332(f246(a868),f332(f197(f869(x73512)),x73511)),f332(f197(f869(x73512)),x73514))) % 165.28/165.04 [7427]~E(f332(f180(x74271,x74272),x74273),f332(f180(x74271,x74272),x74274))+E(f332(f311(f874(x74271,x74272),x74271,f266(x74271,x74272)),f332(f174(f874(x74271,x74272)),x74273)),f332(f311(f874(x74271,x74272),x74271,f266(x74271,x74272)),f332(f174(f874(x74271,x74272)),x74274))) % 165.28/165.04 [7561]P21(x75611,x75612,x75613,f332(f174(x75611),x75614))+~P24(f332(f138(x75612),f332(f332(f155(x75611,x75612),x75613),x75614))) % 165.28/165.04 [7635]~P24(f332(f332(f246(f875(x76351,a862)),x76352),x76354))+P24(f332(f332(f246(f875(x76351,a862)),x76352),f332(f332(f310(x76351),x76353),x76354))) % 165.28/165.04 [7669]~P29(x76691)+E(f45(x76691,f332(f332(f22(x76691),f45(x76691,x76692,x76693)),f45(x76691,x76694,x76693)),x76693),f45(x76691,f332(f332(f22(x76691),x76692),x76694),x76693)) % 165.28/165.04 [7670]~P28(x76701)+E(f45(x76701,f332(f332(f81(x76701),f45(x76701,x76702,x76703)),f45(x76701,x76704,x76703)),x76703),f45(x76701,f332(f332(f81(x76701),x76702),x76704),x76703)) % 165.28/165.04 [7671]~P28(x76711)+E(f45(x76711,f332(f332(f82(x76711),f45(x76711,x76712,x76713)),f45(x76711,x76714,x76713)),x76713),f45(x76711,f332(f332(f82(x76711),x76712),x76714),x76713)) % 165.28/165.04 [7776]~E(f332(x77764,f452(x77764,x77763,x77761,x77762)),f196(f875(x77762,a862)))+E(f332(f332(f42(x77761,f875(x77762,a862)),x77763),x77764),f196(f875(x77762,a862))) % 165.28/165.04 [7777]~E(f332(x77774,f597(x77774,x77773,x77771,x77772)),f255(f875(x77772,a862)))+E(f332(f332(f43(x77771,f875(x77772,a862)),x77773),x77774),f255(f875(x77772,a862))) % 165.28/165.04 [7778]~E(f332(x77784,f453(x77784,x77783,x77782,x77781)),f196(f875(x77782,a862)))+E(f332(f332(f42(x77781,f875(x77782,a862)),x77783),x77784),f196(f875(x77782,a862))) % 165.28/165.04 [7779]~E(f332(x77794,f598(x77794,x77793,x77792,x77791)),f255(f875(x77792,a862)))+E(f332(f332(f43(x77791,f875(x77792,a862)),x77793),x77794),f255(f875(x77792,a862))) % 165.28/165.04 [8165]P24(f332(x81651,x81652))+~P24(f332(f332(f334(x81653),x81652),f332(f332(f104(f875(x81653,a862)),x81654),f332(f252(x81653),x81651)))) % 165.28/165.04 [8204]~P24(f332(f332(f246(f875(x82041,a862)),x82043),x82044))+P24(f332(f332(f246(f875(x82041,a862)),f332(f332(f310(x82041),x82042),x82043)),f332(f332(f310(x82041),x82042),x82044))) % 165.28/165.04 [8376]P24(f332(x83762,x83763))+E(f332(f332(f139(x83761),f332(f197(f869(x83761)),f179(x83761,x83762,f332(f332(f152(x83761),x83763),x83764)))),f332(f332(f152(x83761),x83763),x83764)),f332(f332(f152(x83761),x83763),x83764)) % 165.28/165.04 [8480]~P24(f332(f332(f247(a868),f332(x84804,x84802)),f332(x84804,x84803)))+P24(f332(f332(f334(f874(x84801,x84801)),f332(f332(f267(x84801,x84801),x84802),x84803)),f332(f332(f288(a868,x84801),a251),x84804))) % 165.28/165.04 [8570]~P24(f332(x85702,f701(x85704,x85702,x85703,x85701)))+E(f179(x85701,x85702,f332(f332(f135(x85701),x85703),x85704)),f332(f332(f135(x85701),x85703),f179(x85701,x85702,x85704))) % 165.28/165.04 [8640]P21(f869(x86401),f869(x86402),f332(f155(x86401,x86402),x86403),x86404)+~P21(x86401,x86402,x86403,f40(f875(x86401,a862),f332(f311(f869(x86401),f875(x86401,a862),f174(x86401)),x86404))) % 165.28/165.04 [8707]~P24(f332(x87072,x87073))+E(f332(f332(f139(x87071),f332(f197(f869(x87071)),f179(x87071,x87072,f332(f332(f152(x87071),x87073),x87074)))),f332(f332(f152(x87071),x87073),x87074)),f332(f332(f139(x87071),f332(f197(f869(x87071)),f179(x87071,x87072,x87074))),x87074)) % 165.28/165.04 [8746]~E(x87462,x87463)+E(f332(f137(x87461,f332(f332(f8(a862,a862,x87461),a327),f332(a329,x87462))),f332(f332(f152(x87461),x87463),x87464)),f332(f137(x87461,f332(f332(f8(a862,a862,x87461),a327),f332(a329,x87462))),x87464)) % 165.28/165.04 [8756]E(f332(f332(f42(x87561,f875(x87562,a862)),x87563),x87564),f196(f875(x87562,a862)))+P24(f332(f332(f334(x87561),f452(x87564,x87563,x87561,x87562)),x87563)) % 165.28/165.04 [8757]E(f332(f332(f43(x87571,f875(x87572,a862)),x87573),x87574),f255(f875(x87572,a862)))+P24(f332(f332(f334(x87571),f597(x87574,x87573,x87571,x87572)),x87573)) % 165.28/165.04 [8758]E(f332(f332(f42(x87581,f875(x87582,a862)),x87583),x87584),f196(f875(x87582,a862)))+P24(f332(f332(f334(x87581),f453(x87584,x87583,x87582,x87581)),x87583)) % 165.28/165.04 [8759]E(f332(f332(f43(x87591,f875(x87592,a862)),x87593),x87594),f255(f875(x87592,a862)))+P24(f332(f332(f334(x87591),f598(x87594,x87593,x87592,x87591)),x87593)) % 165.28/165.04 [8795]P24(f332(f332(f247(a868),f332(x87951,x87952)),f332(x87951,x87953)))+~P24(f332(f332(f334(f874(x87954,x87954)),f332(f332(f267(x87954,x87954),x87952),x87953)),f332(f332(f288(a868,x87954),a251),x87951))) % 165.28/165.04 [8816]E(f179(x88161,x88162,f332(f332(f135(x88161),x88163),x88164)),f332(f332(f135(x88161),x88163),f179(x88161,x88162,x88164)))+P24(f332(f332(f334(x88161),f701(x88164,x88162,x88163,x88161)),f332(f174(x88161),x88163))) % 165.28/165.04 [8974]P24(f332(f332(f334(x89741),f476(x89742,x89743,x89744,x89741)),x89743))+~P24(f332(f332(f334(f875(x89741,a862)),x89744),f332(f332(f61(x89741),x89743),x89742))) % 165.28/165.04 [8977]E(x89771,x89772)+~P24(f332(f332(f334(f874(x89773,x89773)),f332(f332(f267(x89773,x89773),x89771),x89772)),f332(f332(f191(f874(x89773,x89773),a862),f2(a868)),x89774))) % 165.28/165.04 [9055]E(f332(f286(x90551,x90551,x90552),f332(f332(f310(x90551),f476(x90552,x90553,x90554,x90551)),f196(f875(x90551,a862)))),x90554)+~P24(f332(f332(f334(f875(x90551,a862)),x90554),f332(f332(f61(x90551),x90553),x90552))) % 165.28/165.04 [9061]~P24(f332(f332(f334(f874(x90611,x90611)),f332(f332(f267(x90611,x90611),x90613),x90612)),f308(x90611,x90614)))+P24(f332(f332(f334(f874(x90611,x90611)),f332(f332(f267(x90611,x90611),x90612),x90613)),f308(x90611,f332(f287(x90611,x90611),x90614)))) % 165.28/165.04 [9073]~P28(x90731)+E(f332(f332(f81(x90731),f332(f332(f81(x90731),f332(f332(f82(x90731),x90732),f332(f332(f39(x90731),x90733),x90732))),f45(x90731,x90733,x90732))),x90734),f332(f332(f81(x90731),x90733),x90734)) % 165.28/165.04 [9083]~P24(f332(f332(f334(x90831),x90833),x90834))+P24(f332(f332(f334(f875(x90831,a862)),f332(f286(x90831,x90831,x90832),f332(f332(f310(x90831),x90833),f196(f875(x90831,a862))))),f332(f332(f61(x90831),x90834),x90832))) % 165.28/165.04 [9094]P24(f332(f332(f334(f874(x90941,x90941)),f332(f332(f267(x90941,x90941),x90942),x90943)),f308(x90941,x90944)))+~P24(f332(f332(f334(f874(x90941,x90941)),f332(f332(f267(x90941,x90941),x90943),x90942)),f308(x90941,f332(f287(x90941,x90941),x90944)))) % 165.28/165.04 [9177]E(f332(f332(f160(x91771,f332(f170(x91771),x91772)),f332(f332(f22(a868),f332(f332(f22(a868),f332(f197(f869(x91771)),x91772)),x91773)),f79(a868))),x91774),f332(f170(x91771),f332(f332(f160(x91771,x91772),x91773),x91774)))+~P24(f332(f332(f247(a868),x91773),f332(f197(f869(x91771)),x91772))) % 165.28/165.04 [9180]~P24(f332(x91802,f695(x91804,x91802,x91803,x91801)))+E(f332(f332(f139(x91801),f332(f197(f869(x91801)),f179(x91801,x91802,f332(f332(f135(x91801),x91803),x91804)))),f332(f332(f135(x91801),x91803),x91804)),f332(f332(f139(x91801),f332(f197(f869(x91801)),f179(x91801,x91802,x91804))),x91804)) % 165.28/165.04 [9220]~P21(x92202,x92201,x92203,f255(f875(x92202,a862)))+P24(f332(f332(f246(f875(x92201,a862)),f332(f311(x92202,x92201,x92203),f332(f80(f875(x92202,a862)),x92204))),f332(f80(f875(x92201,a862)),f332(f311(x92202,x92201,x92203),x92204)))) % 165.28/165.04 [9230]~P30(x92301)+E(f332(f143(x92301,x92302,f332(f7(x92302,x92301,x92301),f332(f332(f8(x92301,f875(x92301,x92301),x92302),f113(x92301)),x92303)),f196(x92301)),x92304),f332(f332(f42(x92302,x92301),f332(f174(x92302),x92304)),x92303)) % 165.28/165.04 [9231]~P30(x92311)+E(f332(f143(x92311,x92312,f332(f7(x92312,x92311,x92311),f332(f332(f8(x92311,f875(x92311,x92311),x92312),f104(x92311)),x92313)),f255(x92311)),x92314),f332(f332(f43(x92312,x92311),f332(f174(x92312),x92314)),x92313)) % 165.28/165.04 [9241]E(f332(f332(f139(x92411),f332(f197(f869(x92411)),f179(x92411,x92412,f332(f332(f135(x92411),x92413),x92414)))),f332(f332(f135(x92411),x92413),x92414)),f332(f332(f139(x92411),f332(f197(f869(x92411)),f179(x92411,x92412,x92414))),x92414))+P24(f332(f332(f334(x92411),f695(x92414,x92412,x92413,x92411)),f332(f174(x92411),x92413))) % 165.28/165.04 [9308]~P24(f332(f332(f334(f874(f869(x93084),f869(x93084))),f332(f332(f267(f869(x93084),f869(x93084)),x93083),x93082)),f158(x93084,x93081)))+P24(f332(f332(f247(a868),f555(x93081,x93082,x93083,x93084)),f332(f197(f869(x93084)),x93083))) % 165.28/165.04 [9309]~P28(x93091)+E(f332(f332(f81(x93091),f332(f332(f81(x93091),f332(f332(f82(x93091),f332(f332(f39(x93091),x93092),x93093)),x93093)),f45(x93091,x93092,x93093))),x93094),f332(f332(f81(x93091),x93092),x93094)) % 165.28/165.04 [9335]~P24(f332(f332(f334(f874(f869(x93351),f869(x93351))),f332(f332(f267(f869(x93351),f869(x93351)),x93352),x93353)),f332(f287(f869(x93351),f869(x93351)),f158(x93351,x93354))))+P24(f332(f332(f334(f874(f869(x93351),f869(x93351))),f332(f332(f267(f869(x93351),f869(x93351)),x93352),x93353)),f158(x93351,f332(f287(x93351,x93351),x93354)))) % 165.28/165.04 [9336]P24(f332(f332(f334(f874(f869(x93361),f869(x93361))),f332(f332(f267(f869(x93361),f869(x93361)),x93362),x93363)),f332(f287(f869(x93361),f869(x93361)),f158(x93361,x93364))))+~P24(f332(f332(f334(f874(f869(x93361),f869(x93361))),f332(f332(f267(f869(x93361),f869(x93361)),x93362),x93363)),f158(x93361,f332(f287(x93361,x93361),x93364)))) % 165.28/165.04 [9370]~P24(f332(f332(f334(x93701),x93703),f332(f265(x93701,x93702),x93704)))+P24(f332(f332(f334(f874(x93701,x93702)),f332(f332(f267(x93701,x93702),x93703),f680(x93704,x93702,x93703,x93701))),x93704)) % 165.28/165.04 [9371]~P24(f332(f332(f334(x93711),x93713),f332(f265(x93711,x93712),x93714)))+P24(f332(f332(f334(f874(x93711,x93712)),f332(f332(f267(x93711,x93712),x93713),f682(x93714,x93712,x93713,x93711))),x93714)) % 165.28/165.04 [9475]~P24(f332(f62(f872(x94751)),f332(f311(x94752,f872(x94751),x94753),f255(f875(x94752,a862)))))+P24(f332(f62(f872(x94751)),f332(f311(x94752,f872(x94751),f187(x94752,x94751,x94753,f332(f180(x94752,x94751),x94754))),f255(f875(x94752,a862))))) % 165.28/165.04 [9522]~P24(f332(f332(f334(f874(x95221,x95221)),f332(f332(f267(x95221,x95221),x95222),x95224)),f332(f332(f289(x95221,x95221,x95221),x95223),f308(x95221,x95223))))+P24(f332(f332(f334(f874(x95221,x95221)),f332(f332(f267(x95221,x95221),x95222),f753(x95223,x95224,x95222,x95221))),x95223)) % 165.28/165.04 [9691]~P24(f332(f332(f334(f874(x96912,x96911)),x96914),f332(f287(x96911,x96912),x96913)))+P24(f332(f332(f334(f874(x96911,x96912)),f332(f332(f267(x96911,x96912),f777(x96913,x96914,x96911,x96912)),f776(x96913,x96914,x96911,x96912))),x96913)) % 165.28/165.04 [9719]~P24(f332(f332(f334(f874(f869(x97191),f869(x97191))),f332(f332(f267(f869(x97191),f869(x97191)),x97194),x97193)),f158(x97191,x97192)))+P24(f332(f332(f334(f874(x97191,x97191)),f332(f332(f267(x97191,x97191),f588(x97192,x97193,x97194,x97191)),f589(x97192,x97193,x97194,x97191))),x97192)) % 165.28/165.04 [9815]~P24(f332(f332(f334(f874(f869(x98151),f869(x98151))),f332(f332(f267(f869(x98151),f869(x98151)),x98152),x98154)),f158(x98151,x98153)))+P24(f332(f332(f334(f874(x98151,x98151)),f332(f332(f267(x98151,x98151),f332(f332(f166(x98151),x98152),f555(x98153,x98154,x98152,x98151))),f556(x98153,x98154,x98152,x98151))),x98153)) % 165.28/165.04 [9837]~P24(f332(f62(x98372),x98374))+E(f332(f332(f332(f66(f875(x98371,a862),x98372,f113(f875(x98371,a862))),f332(f332(f7(x98372,f875(x98371,a862),f875(x98371,a862)),f332(f332(f8(x98371,f875(f875(x98371,a862),f875(x98371,a862)),x98372),f310(x98371)),x98373)),f196(f875(x98371,a862)))),f196(f875(x98371,a862))),x98374),f332(f311(x98372,x98371,x98373),x98374)) % 165.28/165.04 [9932]~P21(x99321,x99322,x99323,f255(f875(x99321,a862)))+P24(f332(f332(f246(f875(x99321,a862)),f332(f312(x99321,x99322,x99323),f332(f332(f310(x99322),x99324),f196(f875(x99322,a862))))),f332(f332(f310(x99321),f86(x99321,f332(f332(f7(x99321,x99322,a862),f332(f332(f8(x99322,f875(x99322,a862),x99321),a329),x99323)),x99324))),f196(f875(x99321,a862))))) % 165.28/165.04 [5611]~E(f332(f332(f135(x56111),x56112),x56114),x56113)+E(f332(f332(f177(x56111),f332(f197(f869(x56111)),x56112)),x56113),x56112) % 165.28/165.04 [5612]~E(f332(f332(f135(x56122),x56123),x56121),x56124)+E(x56121,f332(f332(f139(x56122),f332(f197(f869(x56122)),x56123)),x56124)) % 165.28/165.04 [5623]~E(x56234,f2(a868))+E(f332(f332(f166(x56231),f332(f332(f152(x56231),x56232),x56233)),x56234),x56232) % 165.28/165.04 [6151]~P113(x61511)+E(f332(f332(f257(x61511),f332(f332(f257(x61511),x61512),x61513)),x61514),f332(f332(f257(x61511),x61512),f332(f332(f82(a868),x61513),x61514))) % 165.28/165.04 [6152]~P79(x61521)+E(f332(f332(f257(x61521),f332(f332(f257(x61521),x61522),x61523)),x61524),f332(f332(f257(x61521),x61522),f332(f332(f82(a868),x61523),x61524))) % 165.28/165.04 [6169]E(x61691,f2(a868))+E(f332(f332(f166(x61692),f332(f332(f152(x61692),x61693),x61694)),x61691),f332(f332(f166(x61692),x61694),f332(f332(f22(a868),x61691),f79(a868)))) % 165.28/165.04 [6196]~P116(x61961)+E(f332(f332(f290(x61961),f332(f332(f82(x61961),x61962),x61963)),x61964),f332(f332(f82(x61961),x61962),f332(f332(f290(x61961),x61963),x61964))) % 165.28/165.04 [6197]~P26(x61971)+E(f332(f332(f113(x61971),f332(f332(f113(x61971),x61972),x61973)),x61974),f332(f332(f113(x61971),x61972),f332(f332(f113(x61971),x61973),x61974))) % 165.28/165.04 [6199]~P99(x61991)+E(f332(f332(f113(x61991),f332(f332(f113(x61991),x61992),x61993)),x61994),f332(f332(f113(x61991),x61992),f332(f332(f113(x61991),x61993),x61994))) % 165.28/165.04 [6200]~P26(x62001)+E(f332(f332(f104(x62001),f332(f332(f104(x62001),x62002),x62003)),x62004),f332(f332(f104(x62001),x62002),f332(f332(f104(x62001),x62003),x62004))) % 165.28/165.04 [6202]~P100(x62021)+E(f332(f332(f104(x62021),f332(f332(f104(x62021),x62022),x62023)),x62024),f332(f332(f104(x62021),x62022),f332(f332(f104(x62021),x62023),x62024))) % 165.28/165.04 [6203]~P70(x62031)+E(f332(f332(f81(x62031),f332(f332(f81(x62031),x62032),x62033)),x62034),f332(f332(f81(x62031),x62032),f332(f332(f81(x62031),x62033),x62034))) % 165.28/165.04 [6204]~P113(x62041)+E(f332(f332(f81(x62041),f332(f332(f81(x62041),x62042),x62043)),x62044),f332(f332(f81(x62041),x62042),f332(f332(f81(x62041),x62043),x62044))) % 165.28/165.04 [6205]~P113(x62051)+E(f332(f332(f82(x62051),f332(f332(f82(x62051),x62052),x62053)),x62054),f332(f332(f82(x62051),x62052),f332(f332(f82(x62051),x62053),x62054))) % 165.28/165.04 [6206]~P71(x62061)+E(f332(f332(f82(x62061),f332(f332(f82(x62061),x62062),x62063)),x62064),f332(f332(f82(x62061),x62062),f332(f332(f82(x62061),x62063),x62064))) % 165.28/165.04 [6209]~P106(x62091)+E(f332(f332(f244(x62091),f332(f332(f244(x62091),x62092),x62093)),x62094),f332(f332(f244(x62091),x62092),f332(f332(f244(x62091),x62093),x62094))) % 165.28/165.04 [6211]~P106(x62111)+E(f332(f332(f245(x62111),f332(f332(f245(x62111),x62112),x62113)),x62114),f332(f332(f245(x62111),x62112),f332(f332(f245(x62111),x62113),x62114))) % 165.28/165.04 [6222]~P28(x62221)+E(f45(x62221,f332(f332(f81(x62221),x62222),f332(f332(f82(x62221),x62223),x62224)),x62224),f45(x62221,x62222,x62224)) % 165.28/165.04 [6223]~P28(x62231)+E(f45(x62231,f332(f332(f81(x62231),x62232),f332(f332(f82(x62231),x62233),x62234)),x62233),f45(x62231,x62232,x62233)) % 165.28/165.04 [6356]E(f332(f332(f166(x63561),f332(f332(f177(x63561),x63562),x63563)),x63564),f332(f332(f166(x63561),x63563),x63564))+~P24(f332(f332(f247(a868),x63564),x63562)) % 165.28/165.04 [6531]~P113(x65311)+E(f332(f332(f81(x65311),f332(f332(f81(x65311),x65312),x65313)),x65314),f332(f332(f81(x65311),f332(f332(f81(x65311),x65312),x65314)),x65313)) % 165.28/165.04 [6532]~P113(x65321)+E(f332(f332(f82(x65321),f332(f332(f82(x65321),x65322),x65323)),x65324),f332(f332(f82(x65321),f332(f332(f82(x65321),x65322),x65324)),x65323)) % 165.28/165.04 [6591]~P142(x65912)+E(f332(f332(f6(x65911,x65912),f332(f16(x65912,x65911),x65913)),x65914),f332(f332(f82(x65912),f332(f103(x65912),f332(f38(x65911),x65914))),x65913)) % 165.28/165.04 [6759]E(f332(f332(f104(f875(x67591,a862)),f332(f332(f310(x67591),x67592),x67593)),x67594),f332(f332(f104(f875(x67591,a862)),x67593),x67594))+P24(f332(f332(f334(x67591),x67592),x67594)) % 165.28/165.04 [6829]~P97(x68291)+E(f332(f332(f104(x68291),f332(f332(f113(x68291),x68292),x68293)),f332(f332(f113(x68291),x68294),x68293)),f332(f332(f113(x68291),f332(f332(f104(x68291),x68292),x68294)),x68293)) % 165.28/165.04 [6830]~P77(x68301)+E(f332(f332(f244(x68301),f332(f332(f22(x68301),x68302),x68303)),f332(f332(f22(x68301),x68304),x68303)),f332(f332(f22(x68301),f332(f332(f244(x68301),x68302),x68304)),x68303)) % 165.28/165.04 [6831]~P77(x68311)+E(f332(f332(f245(x68311),f332(f332(f22(x68311),x68312),x68313)),f332(f332(f22(x68311),x68314),x68313)),f332(f332(f22(x68311),f332(f332(f245(x68311),x68312),x68314)),x68313)) % 165.28/165.04 [6832]~P97(x68321)+E(f332(f332(f113(x68321),f332(f332(f104(x68321),x68322),x68323)),f332(f332(f104(x68321),x68324),x68323)),f332(f332(f104(x68321),f332(f332(f113(x68321),x68322),x68324)),x68323)) % 165.28/165.04 [6833]~P83(x68331)+E(f332(f332(f244(x68331),f332(f332(f81(x68331),x68332),x68333)),f332(f332(f81(x68331),x68334),x68333)),f332(f332(f81(x68331),f332(f332(f244(x68331),x68332),x68334)),x68333)) % 165.28/165.04 [6834]~P83(x68341)+E(f332(f332(f245(x68341),f332(f332(f81(x68341),x68342),x68343)),f332(f332(f81(x68341),x68344),x68343)),f332(f332(f81(x68341),f332(f332(f245(x68341),x68342),x68344)),x68343)) % 165.28/165.04 [6836]~P114(x68361)+E(f332(f332(f81(x68361),f332(f332(f82(x68361),x68362),x68363)),f332(f332(f82(x68361),x68364),x68363)),f332(f332(f82(x68361),f332(f332(f81(x68361),x68362),x68364)),x68363)) % 165.28/165.04 [6837]~P73(x68371)+E(f332(f332(f82(x68371),f332(f332(f257(x68371),x68372),x68373)),f332(f332(f257(x68371),x68374),x68373)),f332(f332(f257(x68371),f332(f332(f82(x68371),x68372),x68374)),x68373)) % 165.28/165.04 [6838]~P113(x68381)+E(f332(f332(f82(x68381),f332(f332(f257(x68381),x68382),x68383)),f332(f332(f257(x68381),x68384),x68383)),f332(f332(f257(x68381),f332(f332(f82(x68381),x68382),x68384)),x68383)) % 165.28/165.04 [6839]~P60(x68391)+E(f332(f332(f290(x68391),f332(f332(f257(x68391),x68392),x68393)),f332(f332(f257(x68391),x68394),x68393)),f332(f332(f257(x68391),f332(f332(f290(x68391),x68392),x68394)),x68393)) % 165.28/165.04 [6840]~P116(x68401)+E(f332(f332(f22(x68401),f332(f332(f290(x68401),x68402),x68403)),f332(f332(f290(x68401),x68404),x68403)),f332(f332(f290(x68401),f332(f332(f22(x68401),x68402),x68404)),x68403)) % 165.28/165.04 [6841]~P116(x68411)+E(f332(f332(f81(x68411),f332(f332(f290(x68411),x68412),x68413)),f332(f332(f290(x68411),x68414),x68413)),f332(f332(f290(x68411),f332(f332(f81(x68411),x68412),x68414)),x68413)) % 165.28/165.04 [6842]~P106(x68421)+E(f332(f332(f245(x68421),f332(f332(f244(x68421),x68422),x68423)),f332(f332(f244(x68421),x68424),x68423)),f332(f332(f244(x68421),f332(f332(f245(x68421),x68422),x68424)),x68423)) % 165.28/165.04 [6843]~P106(x68431)+E(f332(f332(f244(x68431),f332(f332(f245(x68431),x68432),x68433)),f332(f332(f245(x68431),x68434),x68433)),f332(f332(f245(x68431),f332(f332(f244(x68431),x68432),x68434)),x68433)) % 165.28/165.04 [6844]~P113(x68441)+E(f332(f332(f81(x68441),f332(f332(f82(x68441),x68442),x68443)),f332(f332(f82(x68441),x68444),x68443)),f332(f332(f82(x68441),f332(f332(f81(x68441),x68442),x68444)),x68443)) % 165.28/165.04 [6876]E(f332(f332(f160(x68761,x68762),x68763),x68764),x68762)+~P24(f332(f332(f246(a868),f332(f197(f869(x68761)),x68762)),x68763)) % 165.28/165.04 [6901]~P24(f332(x69013,x69014))+P24(f332(f332(f332(f113(f875(x69011,a862)),x69012),x69013),x69014)) % 165.28/165.04 [6903]~P24(f332(x69032,x69034))+P24(f332(f332(f332(f113(f875(x69031,a862)),x69032),x69033),x69034)) % 165.28/165.04 [6922]E(f332(f332(f166(x69221),f332(f332(f135(x69221),x69222),x69223)),x69224),f332(f332(f166(x69221),x69222),x69224))+~P24(f332(f332(f247(a868),x69224),f332(f197(f869(x69221)),x69222))) % 165.28/165.04 [6932]E(f332(f332(f22(f875(x69321,a862)),f332(f332(f310(x69321),x69322),x69323)),x69324),f332(f332(f22(f875(x69321,a862)),x69323),x69324))+~P24(f332(f332(f334(x69321),x69322),x69324)) % 165.28/165.04 [6973]~E(f140(a868,f332(f302(a868,x69731),x69732)),f332(f332(f152(a868),x69734),x69733))+E(f140(a868,f332(f302(a868,f332(f332(f81(a868),x69731),f79(a868))),x69732)),x69733) % 165.28/165.04 [7044]E(x70441,f2(a868))+E(f332(f332(f152(x70442),x70443),f332(f332(f177(x70442),f332(f332(f22(a868),x70441),f79(a868))),x70444)),f332(f332(f177(x70442),x70441),f332(f332(f152(x70442),x70443),x70444))) % 165.28/165.04 [7144]E(f332(f332(f166(x71441),x71442),f332(f332(f22(a868),x71443),f332(f197(f869(x71441)),x71444))),f332(f332(f166(x71441),f332(f332(f135(x71441),x71444),x71442)),x71443))+P24(f332(f332(f247(a868),x71443),f332(f197(f869(x71441)),x71444))) % 165.28/165.04 [7174]E(f332(f332(f104(f875(x71741,a862)),x71742),f332(f332(f310(x71741),x71743),x71744)),f332(f332(f310(x71741),x71743),f332(f332(f104(f875(x71741,a862)),x71742),x71744)))+~P24(f332(f332(f334(x71741),x71743),x71742)) % 165.28/165.04 [7209]E(f332(f332(f166(x72091),f332(f332(f160(x72091,x72092),x72093),x72094)),x72093),x72094)+~P24(f332(f332(f247(a868),x72093),f332(f197(f869(x72091)),x72092))) % 165.28/165.04 [7230]E(x72301,f196(f875(x72302,a862)))+E(f332(f311(f874(x72303,x72302),x72303,f266(x72303,x72302)),f332(f332(f269(x72303,x72302),x72304),f332(f16(f875(x72302,a862),x72303),x72301))),x72304) % 165.28/165.04 [7231]E(x72311,f196(f875(x72312,a862)))+E(f332(f311(f874(x72312,x72313),x72313,f270(x72312,x72313)),f332(f332(f269(x72312,x72313),x72311),f332(f16(f875(x72313,a862),x72312),x72314))),x72314) % 165.28/165.04 [7298]E(f332(f332(f22(f875(x72981,a862)),f332(f332(f310(x72981),x72982),x72983)),x72984),f332(f332(f310(x72981),x72982),f332(f332(f22(f875(x72981,a862)),x72983),x72984)))+P24(f332(f332(f334(x72981),x72982),x72984)) % 165.28/165.04 [7335]~E(x73354,f196(f875(x73352,a862)))+E(f332(f311(f874(x73351,x73352),x73351,f266(x73351,x73352)),f332(f332(f269(x73351,x73352),x73353),f332(f16(f875(x73352,a862),x73351),x73354))),f196(f875(x73351,a862))) % 165.28/165.04 [7336]~E(x73363,f196(f875(x73361,a862)))+E(f332(f311(f874(x73361,x73362),x73362,f270(x73361,x73362)),f332(f332(f269(x73361,x73362),x73363),f332(f16(f875(x73362,a862),x73361),x73364))),f196(f875(x73362,a862))) % 165.28/165.04 [7392]~P24(f332(f332(f334(x73921),x73922),x73924))+P24(f332(f332(f334(x73921),x73922),f332(f332(f113(f875(x73921,a862)),x73923),x73924))) % 165.28/165.04 [7395]~P24(f332(f332(f334(x73951),x73952),x73953))+P24(f332(f332(f334(x73951),x73952),f332(f332(f113(f875(x73951,a862)),x73953),x73954))) % 165.28/165.04 [7414]E(f332(f332(f104(f875(x74141,a862)),f332(f332(f310(x74141),x74142),x74143)),x74144),f332(f332(f310(x74141),x74142),f332(f332(f104(f875(x74141,a862)),x74143),x74144)))+~P24(f332(f332(f334(x74141),x74142),x74144)) % 165.28/165.04 [7692]P24(f332(x76921,x76922))+~P24(f332(f332(f332(f104(f875(x76923,a862)),x76924),x76921),x76922)) % 165.28/165.04 [7693]P24(f332(x76931,x76932))+~P24(f332(f332(f332(f104(f875(x76933,a862)),x76931),x76934),x76932)) % 165.28/165.04 [7696]E(f332(f332(f6(x76961,a868),x76962),f332(f332(f22(f875(x76961,a862)),x76963),f332(f332(f310(x76961),x76964),f196(f875(x76961,a862))))),f332(f332(f6(x76961,a868),x76962),x76963))+P24(f332(f332(f334(x76961),x76964),x76963)) % 165.28/165.04 [7701]~P74(x77011)+E(f332(f167(x77011),f332(f332(f155(a868,x77011),x77012),f140(a868,f332(f302(a868,x77013),x77014)))),f332(f332(f6(a868,x77011),x77012),f332(f174(a868),f140(a868,f332(f302(a868,x77013),x77014))))) % 165.28/165.04 [7702]~P74(x77021)+E(f332(f332(f6(a868,x77021),x77022),f332(f174(a868),f140(a868,f332(f302(a868,x77023),x77024)))),f332(f167(x77021),f332(f332(f155(a868,x77021),x77022),f140(a868,f332(f302(a868,x77023),x77024))))) % 165.28/165.04 [7812]~E(x78123,x78124)+P24(f332(f63(x78121,x78122,f332(f332(f310(x78121),x78123),f196(f875(x78121,a862)))),x78124)) % 165.28/165.04 [7908]P24(f332(f332(f334(x79081),x79082),f332(f174(x79081),x79083)))+~P24(f332(f332(f334(x79081),x79082),f332(f174(x79081),f332(f332(f177(x79081),x79084),x79083)))) % 165.28/165.04 [7909]P24(f332(f332(f334(x79091),x79092),f332(f174(x79091),x79093)))+~P24(f332(f332(f334(x79091),x79092),f332(f174(x79091),f332(f332(f139(x79091),x79094),x79093)))) % 165.28/165.04 [7980]P24(f332(f332(f334(x79801),x79802),x79803))+~P24(f332(f332(f334(x79801),x79802),f332(f332(f22(f875(x79801,a862)),x79803),x79804))) % 165.28/165.04 [7982]P24(f332(f332(f334(x79821),x79822),x79823))+~P24(f332(f332(f334(x79821),x79822),f332(f332(f104(f875(x79821,a862)),x79824),x79823))) % 165.28/165.04 [7985]P24(f332(f332(f334(x79851),x79852),x79853))+~P24(f332(f332(f334(x79851),x79852),f332(f332(f104(f875(x79851,a862)),x79853),x79854))) % 165.28/165.04 [8000]E(f332(f332(f135(x80001),f332(f332(f177(x80001),x80002),x80003)),f332(f332(f152(x80001),x80004),f332(f332(f139(x80001),f332(a115,x80002)),x80003))),f332(f332(f160(x80001,x80003),x80002),x80004))+~P24(f332(f332(f247(a868),x80002),f332(f197(f869(x80001)),x80003))) % 165.28/165.04 [8023]P24(f332(f332(f334(x80231),x80232),x80233))+~P24(f332(f332(f246(f875(x80231,a862)),f332(f332(f310(x80231),x80232),x80234)),x80233)) % 165.28/165.04 [8056]~P24(f332(f332(f334(x80561),x80562),x80563))+~P24(f332(f332(f334(x80561),x80562),f332(f332(f22(f875(x80561,a862)),x80564),x80563))) % 165.28/165.04 [8088]~P24(f332(f332(f247(a868),x80884),f332(f197(f869(x80881)),x80883)))+P24(f332(f332(f334(x80881),x80882),f332(f174(x80881),f332(f332(f160(x80881,x80883),x80884),x80882)))) % 165.28/165.04 [8142]E(f332(f332(f166(x81421),f332(f332(f139(x81421),x81422),x81423)),x81424),f332(f332(f166(x81421),x81423),f332(f332(f81(a868),x81422),x81424)))+~P24(f332(f332(f246(a868),f332(f332(f81(a868),x81422),x81424)),f332(f197(f869(x81421)),x81423))) % 165.28/165.04 [8152]~P142(x81522)+E(f332(f332(f6(x81521,x81522),f332(f332(f8(a868,x81522,x81521),f103(x81522)),x81523)),x81524),f332(f103(x81522),f332(f332(f6(x81521,a868),x81523),x81524))) % 165.28/165.04 [8153]~P138(x81532)+E(f332(f332(f6(x81531,x81532),f332(f332(f8(a1,x81532,x81531),f105(x81532)),x81533)),x81534),f332(f105(x81532),f332(f332(f6(x81531,a1),x81533),x81534))) % 165.28/165.04 [8206]~P63(x82062)+E(f332(f332(f9(x82061,x82062),f332(f332(f8(x82062,x82062,x82061),f76(x82062)),x82063)),x82064),f332(f76(x82062),f332(f332(f9(x82061,x82062),x82063),x82064))) % 165.28/165.04 [8207]~P66(x82072)+E(f332(f332(f6(x82071,x82072),f332(f332(f8(x82072,x82072,x82071),f80(x82072)),x82073)),x82074),f332(f80(x82072),f332(f332(f6(x82071,x82072),x82073),x82074))) % 165.28/165.04 [8209]E(f332(f332(f6(x82091,a868),x82092),f332(f332(f22(f875(x82091,a862)),x82093),f332(f332(f310(x82091),x82094),f196(f875(x82091,a862))))),f332(f332(f22(a868),f332(f332(f6(x82091,a868),x82092),x82093)),f332(x82092,x82094)))+~P24(f332(f332(f334(x82091),x82094),x82093)) % 165.28/165.04 [8229]P24(f332(f332(f246(f875(x82291,a862)),x82292),x82293))+~P24(f332(f332(f246(f875(x82291,a862)),f332(f332(f310(x82291),x82294),x82292)),x82293)) % 165.28/165.04 [8429]E(f332(f332(f180(x84291,x84292),x84293),x84294),f209(x84292))+P24(f332(f332(f334(x84291),x84294),f332(f311(f874(x84291,x84292),x84291,f266(x84291,x84292)),f332(f174(f874(x84291,x84292)),x84293)))) % 165.28/165.04 [8430]P41(x84301,x84302)+~P41(x84301,f332(f332(f310(f874(x84301,x84301)),f332(f332(f267(x84301,x84301),x84303),x84304)),x84302)) % 165.28/165.04 [8431]P56(x84311,x84312)+~P56(x84311,f332(f332(f310(f874(x84311,x84311)),f332(f332(f267(x84311,x84311),x84313),x84314)),x84312)) % 165.28/165.04 [8437]~P106(x84371)+E(f332(f332(f149(x84371,x84371,f5(x84371)),x84372),f332(f332(f149(x84371,x84371,f5(x84371)),x84373),x84374)),f332(f332(f149(x84371,x84371,f5(x84371)),x84373),f332(f332(f149(x84371,x84371,f5(x84371)),x84372),x84374))) % 165.28/165.04 [8447]E(x84471,x84472)+~P24(f332(f63(x84473,x84474,f332(f332(f310(x84473),x84471),f196(f875(x84473,a862)))),x84472)) % 165.28/165.04 [8457]E(f332(f332(f135(x84571),f332(f332(f177(x84571),x84572),x84573)),f332(f332(f177(x84571),x84574),f332(f332(f139(x84571),x84572),x84573))),f332(f332(f177(x84571),f332(f332(f81(a868),x84572),x84574)),x84573))+~P24(f332(f332(f246(a868),f332(f332(f81(a868),x84572),x84574)),f332(f197(f869(x84571)),x84573))) % 165.28/165.04 [8494]P24(f332(f62(x84941),x84942))+~E(x84942,f332(f311(a868,x84941,x84943),f332(f252(a868),f332(f332(f7(a868,a868,a862),f247(a868)),x84944)))) % 165.28/165.04 [8514]~P89(x85141)+E(f332(f143(x85141,x85141,f81(x85141),f332(f332(f81(x85141),x85142),x85143)),x85144),f332(f332(f81(x85141),x85142),f332(f143(x85141,x85141,f81(x85141),x85143),x85144))) % 165.28/165.04 [8548]P24(f332(f332(f246(f875(x85481,a862)),f332(f265(x85481,x85482),x85483)),f332(f265(x85481,x85482),x85484)))+~P24(f332(f332(f246(f875(f874(x85481,x85482),a862)),x85483),x85484)) % 165.28/165.04 [8561]~P24(f332(f332(f246(a868),x85612),x85614))+P24(f332(f332(f246(f875(x85611,a862)),f332(f174(x85611),f332(f332(f177(x85611),x85612),x85613))),f332(f174(x85611),f332(f332(f177(x85611),x85614),x85613)))) % 165.28/165.04 [8562]~P24(f332(f332(f246(a868),x85624),x85622))+P24(f332(f332(f246(f875(x85621,a862)),f332(f174(x85621),f332(f332(f139(x85621),x85622),x85623))),f332(f174(x85621),f332(f332(f139(x85621),x85624),x85623)))) % 165.28/165.04 [8614]~P24(f332(f62(x86141),f332(f332(f22(f875(x86141,a862)),x86142),x86144)))+P24(f332(f62(x86141),f332(f332(f22(f875(x86141,a862)),x86142),f332(f332(f310(x86141),x86143),x86144)))) % 165.28/165.04 [8651]P24(f332(f332(f334(f874(x86511,x86511)),x86512),f308(x86511,x86513)))+~P24(f332(f332(f334(f874(x86511,x86511)),x86512),f332(f332(f191(f874(x86511,x86511),a862),x86514),x86513))) % 165.28/165.04 [8728]~P24(f332(f62(x87281),f332(f332(f22(f875(x87281,a862)),x87282),f332(f332(f310(x87281),x87284),x87283))))+P24(f332(f62(x87281),f332(f332(f22(f875(x87281,a862)),x87282),x87283))) % 165.28/165.04 [8874]~E(f332(f332(f180(x88741,x88742),x88743),x88744),f209(x88742))+~P24(f332(f332(f334(x88741),x88744),f332(f311(f874(x88741,x88742),x88741,f266(x88741,x88742)),f332(f174(f874(x88741,x88742)),x88743)))) % 165.28/165.04 [8934]~P26(x89341)+P24(f332(f332(f246(x89341),f332(f332(f113(x89341),x89342),f332(f332(f104(x89341),x89343),x89344))),f332(f332(f104(x89341),f332(f332(f113(x89341),x89342),x89343)),f332(f332(f113(x89341),x89342),x89344)))) % 165.28/165.04 [8935]~P106(x89351)+P24(f332(f332(f246(x89351),f332(f332(f245(x89351),x89352),f332(f332(f244(x89351),x89353),x89354))),f332(f332(f244(x89351),f332(f332(f245(x89351),x89352),x89353)),f332(f332(f245(x89351),x89352),x89354)))) % 165.28/165.04 [9079]E(x90791,x90792)+~P24(f332(f332(f334(f874(x90793,x90793)),f332(f332(f267(x90793,x90793),x90791),x90792)),f332(f174(f874(x90793,x90793)),f332(f332(f184(x90793,x90793),x90794),x90794)))) % 165.28/165.04 [9109]~P24(f332(f332(f334(f874(x91091,x91091)),f332(f332(f267(x91091,x91091),x91093),x91092)),f308(x91091,x91094)))+~P41(x91091,f332(f332(f310(f874(x91091,x91091)),f332(f332(f267(x91091,x91091),x91092),x91093)),x91094)) % 165.28/165.04 [9110]~P24(f332(f332(f334(f874(x91101,x91101)),f332(f332(f267(x91101,x91101),x91103),x91102)),f308(x91101,x91104)))+~P56(x91101,f332(f332(f310(f874(x91101,x91101)),f332(f332(f267(x91101,x91101),x91102),x91103)),x91104)) % 165.28/165.04 [9115]E(x91151,x91152)+E(f332(f137(x91153,f332(f332(f8(a862,a862,x91153),a327),f332(a329,x91151))),f332(f332(f152(x91153),x91152),x91154)),f332(f332(f152(x91153),x91152),f332(f137(x91153,f332(f332(f8(a862,a862,x91153),a327),f332(a329,x91151))),x91154))) % 165.28/165.04 [9159]~P26(x91591)+P24(f332(f332(f246(x91591),f332(f332(f113(x91591),f332(f332(f104(x91591),x91592),x91593)),f332(f332(f104(x91591),x91592),x91594))),f332(f332(f104(x91591),x91592),f332(f332(f113(x91591),x91593),x91594)))) % 165.28/165.04 [9160]~P106(x91601)+P24(f332(f332(f246(x91601),f332(f332(f245(x91601),f332(f332(f244(x91601),x91602),x91603)),f332(f332(f244(x91601),x91602),x91604))),f332(f332(f244(x91601),x91602),f332(f332(f245(x91601),x91603),x91604)))) % 165.28/165.04 [9226]~E(f332(f311(x92262,x92261,x92263),f255(f875(x92262,a862))),f255(f875(x92261,a862)))+P24(f332(f332(f246(f875(x92261,a862)),f332(f80(f875(x92261,a862)),f332(f311(x92262,x92261,x92263),x92264))),f332(f311(x92262,x92261,x92263),f332(f80(f875(x92262,a862)),x92264)))) % 165.28/165.04 [9536]P24(f332(f332(f334(f874(x95361,x95361)),f332(f332(f267(x95361,x95361),x95362),x95363)),f332(f287(x95361,x95361),f332(f332(f289(x95361,x95361,x95361),x95364),f308(x95361,x95364)))))+~P24(f332(f332(f334(f874(x95361,x95361)),f332(f332(f267(x95361,x95361),x95362),x95363)),f332(f332(f289(x95361,x95361,x95361),f332(f287(x95361,x95361),x95364)),f308(x95361,f332(f287(x95361,x95361),x95364))))) % 165.28/165.04 [9537]~P24(f332(f332(f334(f874(x95371,x95371)),f332(f332(f267(x95371,x95371),x95372),x95373)),f332(f287(x95371,x95371),f332(f332(f289(x95371,x95371,x95371),x95374),f308(x95371,x95374)))))+P24(f332(f332(f334(f874(x95371,x95371)),f332(f332(f267(x95371,x95371),x95372),x95373)),f332(f332(f289(x95371,x95371,x95371),f332(f287(x95371,x95371),x95374)),f308(x95371,f332(f287(x95371,x95371),x95374))))) % 165.28/165.04 [9558]~P24(f332(f332(f334(x95582),x95584),f332(f263(x95581,x95582),x95583)))+P24(f332(f332(f334(f874(x95581,x95582)),f332(f332(f267(x95581,x95582),f677(x95583,x95581,x95584,x95582)),x95584)),x95583)) % 165.28/165.04 [9559]~P24(f332(f332(f334(x95592),x95594),f332(f263(x95591,x95592),x95593)))+P24(f332(f332(f334(f874(x95591,x95592)),f332(f332(f267(x95591,x95592),f678(x95593,x95591,x95594,x95592)),x95594)),x95593)) % 165.28/165.04 [9584]~P24(f332(f332(f334(x95841),x95844),f332(f332(f113(f875(x95841,a862)),x95842),x95843)))+P24(f332(f332(f332(f113(f875(x95841,a862)),f332(f332(f7(x95841,f875(x95841,a862),a862),f334(x95841)),x95842)),f332(f332(f7(x95841,f875(x95841,a862),a862),f334(x95841)),x95843)),x95844)) % 165.28/165.04 [9585]~P24(f332(f332(f334(x95851),x95854),f332(f332(f104(f875(x95851,a862)),x95852),x95853)))+P24(f332(f332(f332(f104(f875(x95851,a862)),f332(f332(f7(x95851,f875(x95851,a862),a862),f334(x95851)),x95852)),f332(f332(f7(x95851,f875(x95851,a862),a862),f334(x95851)),x95853)),x95854)) % 165.28/165.04 [9662]~P24(f332(f332(f334(f874(x96621,x96621)),f332(f332(f267(x96621,x96621),x96624),x96623)),f332(f332(f289(x96621,x96621,x96621),x96622),f308(x96621,x96622))))+P24(f332(f332(f334(f874(x96621,x96621)),f332(f332(f267(x96621,x96621),f754(x96622,x96623,x96624,x96621)),x96623)),x96622)) % 165.28/165.04 [9707]P24(f332(f332(f334(x97071),x97072),f332(f332(f113(f875(x97071,a862)),x97073),x97074)))+~P24(f332(f332(f332(f113(f875(x97071,a862)),f332(f332(f7(x97071,f875(x97071,a862),a862),f334(x97071)),x97073)),f332(f332(f7(x97071,f875(x97071,a862),a862),f334(x97071)),x97074)),x97072)) % 165.28/165.04 [9708]P24(f332(f332(f334(x97081),x97082),f332(f332(f104(f875(x97081,a862)),x97083),x97084)))+~P24(f332(f332(f332(f104(f875(x97081,a862)),f332(f332(f7(x97081,f875(x97081,a862),a862),f334(x97081)),x97083)),f332(f332(f7(x97081,f875(x97081,a862),a862),f334(x97081)),x97084)),x97082)) % 165.28/165.04 [9986]P36(x99861,f332(f332(f7(x99861,f875(f874(x99861,x99861),a862),f875(x99861,a862)),f332(f332(f8(f875(x99861,f875(f875(f874(x99861,x99861),a862),a862)),f875(f875(f874(x99861,x99861),a862),f875(x99861,a862)),x99861),f7(x99861,f875(f874(x99861,x99861),a862),a862)),f332(f332(f8(f875(x99861,f874(x99861,x99861)),f875(x99861,f875(f875(f874(x99861,x99861),a862),a862)),x99861),f332(f8(f874(x99861,x99861),f875(f875(f874(x99861,x99861),a862),a862),x99861),f334(f874(x99861,x99861)))),f267(x99861,x99861)))),x99862),x99863,x99864)+~P24(f332(f332(f334(f874(f869(x99861),f869(x99861))),f332(f332(f267(f869(x99861),f869(x99861)),x99863),x99864)),f159(x99861,x99862))) % 165.28/165.04 [9990]P57(x99901,f332(f332(f7(x99901,f875(f874(x99901,x99901),a862),f875(x99901,a862)),f332(f332(f8(f875(x99901,f875(f875(f874(x99901,x99901),a862),a862)),f875(f875(f874(x99901,x99901),a862),f875(x99901,a862)),x99901),f7(x99901,f875(f874(x99901,x99901),a862),a862)),f332(f332(f8(f875(x99901,f874(x99901,x99901)),f875(x99901,f875(f875(f874(x99901,x99901),a862),a862)),x99901),f332(f8(f874(x99901,x99901),f875(f875(f874(x99901,x99901),a862),a862),x99901),f334(f874(x99901,x99901)))),f267(x99901,x99901)))),x99902),x99903,x99904)+~P24(f332(f332(f334(f874(f875(x99901,a862),f875(x99901,a862))),f332(f332(f267(f875(x99901,a862),f875(x99901,a862)),x99903),x99904)),f323(x99901,x99902))) % 165.28/165.04 [10019]E(x100191,x100192)+~E(f332(f332(f7(x100193,f875(f874(x100193,x100194),a862),f875(x100194,a862)),f332(f332(f8(f875(x100194,f875(f875(f874(x100193,x100194),a862),a862)),f875(f875(f874(x100193,x100194),a862),f875(x100194,a862)),x100193),f7(x100194,f875(f874(x100193,x100194),a862),a862)),f332(f332(f8(f875(x100194,f874(x100193,x100194)),f875(x100194,f875(f875(f874(x100193,x100194),a862),a862)),x100193),f332(f8(f874(x100193,x100194),f875(f875(f874(x100193,x100194),a862),a862),x100194),f334(f874(x100193,x100194)))),f267(x100193,x100194)))),x100191),f332(f332(f7(x100193,f875(f874(x100193,x100194),a862),f875(x100194,a862)),f332(f332(f8(f875(x100194,f875(f875(f874(x100193,x100194),a862),a862)),f875(f875(f874(x100193,x100194),a862),f875(x100194,a862)),x100193),f7(x100194,f875(f874(x100193,x100194),a862),a862)),f332(f332(f8(f875(x100194,f874(x100193,x100194)),f875(x100194,f875(f875(f874(x100193,x100194),a862),a862)),x100193),f332(f8(f874(x100193,x100194),f875(f875(f874(x100193,x100194),a862),a862),x100194),f334(f874(x100193,x100194)))),f267(x100193,x100194)))),x100192)) % 165.28/165.04 [10022]~P36(x100221,f332(f332(f7(x100221,f875(f874(x100221,x100221),a862),f875(x100221,a862)),f332(f332(f8(f875(x100221,f875(f875(f874(x100221,x100221),a862),a862)),f875(f875(f874(x100221,x100221),a862),f875(x100221,a862)),x100221),f7(x100221,f875(f874(x100221,x100221),a862),a862)),f332(f332(f8(f875(x100221,f874(x100221,x100221)),f875(x100221,f875(f875(f874(x100221,x100221),a862),a862)),x100221),f332(f8(f874(x100221,x100221),f875(f875(f874(x100221,x100221),a862),a862),x100221),f334(f874(x100221,x100221)))),f267(x100221,x100221)))),x100224),x100222,x100223)+P24(f332(f332(f334(f874(f869(x100221),f869(x100221))),f332(f332(f267(f869(x100221),f869(x100221)),x100222),x100223)),f159(x100221,x100224))) % 165.28/165.04 [10023]~P57(x100231,f332(f332(f7(x100231,f875(f874(x100231,x100231),a862),f875(x100231,a862)),f332(f332(f8(f875(x100231,f875(f875(f874(x100231,x100231),a862),a862)),f875(f875(f874(x100231,x100231),a862),f875(x100231,a862)),x100231),f7(x100231,f875(f874(x100231,x100231),a862),a862)),f332(f332(f8(f875(x100231,f874(x100231,x100231)),f875(x100231,f875(f875(f874(x100231,x100231),a862),a862)),x100231),f332(f8(f874(x100231,x100231),f875(f875(f874(x100231,x100231),a862),a862),x100231),f334(f874(x100231,x100231)))),f267(x100231,x100231)))),x100234),x100232,x100233)+P24(f332(f332(f334(f874(f875(x100231,a862),f875(x100231,a862))),f332(f332(f267(f875(x100231,a862),f875(x100231,a862)),x100232),x100233)),f323(x100231,x100234))) % 165.28/165.04 [7465]~P92(x74651)+E(f332(f332(f81(x74651),f332(f106(x74651),x74652)),f332(f332(f22(x74651),f332(f106(x74651),x74653)),x74654)),f332(f332(f22(x74651),f332(f106(x74651),f332(f332(f81(a1),x74652),x74653))),x74654)) % 165.28/165.04 [7466]~P92(x74661)+E(f332(f332(f81(x74661),f332(f106(x74661),x74662)),f332(f332(f81(x74661),f332(f106(x74661),x74663)),x74664)),f332(f332(f81(x74661),f332(f106(x74661),f332(f332(f81(a1),x74662),x74663))),x74664)) % 165.28/165.04 [7467]~P92(x74671)+E(f332(f332(f82(x74671),f332(f106(x74671),x74672)),f332(f332(f82(x74671),f332(f106(x74671),x74673)),x74674)),f332(f332(f82(x74671),f332(f106(x74671),f332(f332(f82(a1),x74672),x74673))),x74674)) % 165.28/165.04 [7512]~P142(x75121)+E(f332(f167(x75121),f332(f332(f155(x75122,x75121),f332(f16(x75121,x75122),x75123)),x75124)),f332(f332(f82(x75121),f332(f103(x75121),f332(f197(f869(x75122)),x75124))),x75123)) % 165.28/165.04 [7748]E(f332(f278(x77481,f332(f332(f152(f874(a102,x77481)),x77482),x77483)),x77484),f332(f270(a102,x77481),x77482))+~P24(f332(f332(f247(a102),x77484),f332(f266(a102,x77481),x77482))) % 165.28/165.04 [7790]~P92(x77901)+E(f332(f332(f81(x77901),f332(f106(x77901),x77902)),f332(f332(f22(x77901),x77903),f332(f106(x77901),x77904))),f332(f332(f81(x77901),f332(f106(x77901),f332(f332(f81(a1),x77902),f332(f80(a1),x77904)))),x77903)) % 165.28/165.04 [7921]E(f332(f278(x79211,x79212),f332(f332(f22(a102),x79213),f332(f266(a102,x79211),x79214))),f332(f278(x79211,f332(f332(f152(f874(a102,x79211)),x79214),x79212)),x79213))+P24(f332(f332(f247(a102),x79213),f332(f266(a102,x79211),x79214))) % 165.28/165.04 [8353]~P24(f332(f332(f334(x83531),x83532),f332(f174(x83531),f117(x83531,x83534))))+P24(f332(f332(f334(x83531),x83532),f332(f174(x83531),f117(x83531,f332(f332(f135(x83531),x83533),x83534))))) % 165.28/165.04 [8354]~P24(f332(f332(f334(x83541),x83542),f332(f174(x83541),f117(x83541,x83543))))+P24(f332(f332(f334(x83541),x83542),f332(f174(x83541),f117(x83541,f332(f332(f135(x83541),x83543),x83544))))) % 165.28/165.04 [8371]E(f332(f332(f113(f875(x83711,a862)),f332(f332(f104(f875(x83711,a862)),x83712),x83713)),x83714),f332(f332(f104(f875(x83711,a862)),x83712),f332(f332(f113(f875(x83711,a862)),x83713),x83714)))+~P24(f332(f332(f246(f875(x83711,a862)),x83714),x83712)) % 165.28/165.04 [8664]~E(f332(f332(f113(f875(x86641,a862)),f332(f332(f104(f875(x86641,a862)),x86643),x86644)),x86642),f332(f332(f104(f875(x86641,a862)),x86643),f332(f332(f113(f875(x86641,a862)),x86644),x86642)))+P24(f332(f332(f246(f875(x86641,a862)),x86642),x86643)) % 165.28/165.04 [8939]~P24(f332(f332(f246(f875(x89391,a862)),x89392),f332(f332(f113(f875(x89391,a862)),x89393),x89394)))+P24(f332(f332(f246(f875(x89391,a862)),f332(f332(f22(f875(x89391,a862)),x89392),x89393)),x89394)) % 165.28/165.04 [9057]P24(f332(f332(f246(f875(x90571,a862)),x90572),f332(f332(f113(f875(x90571,a862)),x90573),x90574)))+~P24(f332(f332(f246(f875(x90571,a862)),f332(f332(f22(f875(x90571,a862)),x90572),x90573)),x90574)) % 165.28/165.04 [9140]~P85(x91401)+E(f332(f76(x91401),f332(f332(f6(x91402,x91401),f332(f332(f8(x91401,x91401,x91402),f76(x91401)),x91403)),x91404)),f332(f332(f6(x91402,x91401),f332(f332(f8(x91401,x91401,x91402),f76(x91401)),x91403)),x91404)) % 165.28/165.04 [9300]~P85(x93001)+P24(f332(f332(f246(x93001),f2(x93001)),f332(f332(f6(x93002,x93001),f332(f332(f8(x93001,x93001,x93002),f76(x93001)),x93003)),x93004))) % 165.28/165.04 [9304]~P66(x93041)+E(f332(f167(x93041),f332(f332(f155(x93042,x93041),f332(f74(x93041,x93041,x93042,f80(x93041)),x93043)),x93044)),f332(f80(x93041),f332(f167(x93041),f332(f332(f155(x93042,x93041),x93043),x93044)))) % 165.28/165.04 [9434]~P85(x94341)+P24(f332(f332(f246(x94341),f332(f76(x94341),f332(f332(f6(x94342,x94341),x94343),x94344))),f332(f332(f6(x94342,x94341),f332(f332(f8(x94341,x94341,x94342),f76(x94341)),x94343)),x94344))) % 165.28/165.04 [9461]~E(f332(f332(f81(a868),x94611),x94614),f332(f332(f81(a868),x94613),x94612))+P24(f332(f332(f334(f874(f874(a868,a868),f874(a868,a868))),f332(f332(f267(f874(a868,a868),f874(a868,a868)),f332(f332(f267(a868,a868),x94611),x94612)),f332(f332(f267(a868,a868),x94613),x94614))),a111)) % 165.28/165.04 [9462]~P24(f332(f332(f247(a868),x94621),x94623))+P24(f332(f332(f334(f874(f874(a868,a868),f874(a868,a868))),f332(f332(f267(f874(a868,a868),f874(a868,a868)),f332(f332(f267(a868,a868),x94621),x94622)),f332(f332(f267(a868,a868),x94623),x94624))),a36)) % 165.28/165.04 [9463]~P24(f332(f332(f247(a868),x94631),x94633))+P24(f332(f332(f334(f874(f874(a868,a868),f874(a868,a868))),f332(f332(f267(f874(a868,a868),f874(a868,a868)),f332(f332(f267(a868,a868),x94631),x94632)),f332(f332(f267(a868,a868),x94633),x94634))),a71)) % 165.28/165.04 [9609]E(f332(f332(f81(a868),x96091),x96092),f332(f332(f81(a868),x96093),x96094))+~P24(f332(f332(f334(f874(f874(a868,a868),f874(a868,a868))),f332(f332(f267(f874(a868,a868),f874(a868,a868)),f332(f332(f267(a868,a868),x96091),x96094)),f332(f332(f267(a868,a868),x96093),x96092))),a111)) % 165.28/165.04 [9636]E(f332(f332(f166(x96361),f332(f332(f139(x96361),f332(f197(f869(x96361)),f179(x96361,x96362,x96363))),x96363)),x96364),f332(f332(f166(x96361),x96363),f332(f332(f81(a868),x96364),f332(f197(f869(x96361)),f179(x96361,x96362,x96363)))))+~P24(f332(f332(f247(a868),x96364),f332(f197(f869(x96361)),f332(f332(f139(x96361),f332(f197(f869(x96361)),f179(x96361,x96362,x96363))),x96363)))) % 165.28/165.04 [9653]~P24(f332(f332(f334(x96532),x96534),f332(f332(f42(x96531,f875(x96532,a862)),f255(f875(x96531,a862))),x96533)))+P24(f332(f332(f332(f42(x96531,f875(x96532,a862)),f255(f875(x96531,a862))),f332(f332(f8(f875(x96532,a862),f875(x96532,a862),x96531),f332(f7(x96532,f875(x96532,a862),a862),f334(x96532))),x96533)),x96534)) % 165.28/165.04 [9654]~P24(f332(f332(f334(x96542),x96544),f332(f332(f43(x96541,f875(x96542,a862)),f255(f875(x96541,a862))),x96543)))+P24(f332(f332(f332(f43(x96541,f875(x96542,a862)),f255(f875(x96541,a862))),f332(f332(f8(f875(x96542,a862),f875(x96542,a862),x96541),f332(f7(x96542,f875(x96542,a862),a862),f334(x96542))),x96543)),x96544)) % 165.28/165.04 [9735]~P24(f332(f49(x97351,x97352),f332(f332(f267(a1,a1),x97354),x97353)))+P24(f332(f49(f332(f80(a1),x97351),x97352),f332(f332(f267(a1,a1),f332(f332(f332(f99(a1),f332(f332(a329,x97353),f2(a1))),f332(f80(a1),x97354)),f332(f332(f22(a1),f332(f80(a1),x97354)),f79(a1)))),f332(f332(f332(f99(a1),f332(f332(a329,x97353),f2(a1))),f2(a1)),f332(f332(f22(a1),x97352),x97353))))) % 165.28/165.04 [9745]P24(f332(f332(f334(x97451),x97452),f332(f332(f42(x97453,f875(x97451,a862)),f255(f875(x97453,a862))),x97454)))+~P24(f332(f332(f332(f42(x97453,f875(x97451,a862)),f255(f875(x97453,a862))),f332(f332(f8(f875(x97451,a862),f875(x97451,a862),x97453),f332(f7(x97451,f875(x97451,a862),a862),f334(x97451))),x97454)),x97452)) % 165.28/165.04 [9746]P24(f332(f332(f334(x97461),x97462),f332(f332(f43(x97463,f875(x97461,a862)),f255(f875(x97463,a862))),x97464)))+~P24(f332(f332(f332(f43(x97463,f875(x97461,a862)),f255(f875(x97463,a862))),f332(f332(f8(f875(x97461,a862),f875(x97461,a862),x97463),f332(f7(x97461,f875(x97461,a862),a862),f334(x97461))),x97464)),x97462)) % 165.28/165.04 [9758]E(f332(f332(f42(a868,f875(x97581,a862)),f255(f875(a868,a862))),x97582),f332(f332(f42(a868,f875(x97581,a862)),f255(f875(a868,a862))),x97583))+~E(f332(f332(f42(a868,f875(x97581,a862)),f332(f302(a868,f2(a868)),f479(x97582,x97584,x97583,x97581))),x97583),f332(f332(f42(a868,f875(x97581,a862)),f332(f302(a868,f2(a868)),f332(f332(f81(a868),f479(x97582,x97584,x97583,x97581)),x97584))),x97582)) % 165.28/165.04 [10076]~P24(f332(f332(f246(f875(f874(x100761,x100762),a862)),x100763),x100764))+P24(f332(f332(f246(f875(x100761,f875(x100762,a862))),f332(f332(f7(x100761,f875(f874(x100761,x100762),a862),f875(x100762,a862)),f332(f332(f8(f875(x100762,f875(f875(f874(x100761,x100762),a862),a862)),f875(f875(f874(x100761,x100762),a862),f875(x100762,a862)),x100761),f7(x100762,f875(f874(x100761,x100762),a862),a862)),f332(f332(f8(f875(x100762,f874(x100761,x100762)),f875(x100762,f875(f875(f874(x100761,x100762),a862),a862)),x100761),f332(f8(f874(x100761,x100762),f875(f875(f874(x100761,x100762),a862),a862),x100762),f334(f874(x100761,x100762)))),f267(x100761,x100762)))),x100763)),f332(f332(f7(x100761,f875(f874(x100761,x100762),a862),f875(x100762,a862)),f332(f332(f8(f875(x100762,f875(f875(f874(x100761,x100762),a862),a862)),f875(f875(f874(x100761,x100762),a862),f875(x100762,a862)),x100761),f7(x100762,f875(f874(x100761,x100762),a862),a862)),f332(f332(f8(f875(x100762,f874(x100761,x100762)),f875(x100762,f875(f875(f874(x100761,x100762),a862),a862)),x100761),f332(f8(f874(x100761,x100762),f875(f875(f874(x100761,x100762),a862),a862),x100762),f334(f874(x100761,x100762)))),f267(x100761,x100762)))),x100764))) % 165.28/165.04 [10093]P24(f332(f332(f246(f875(f874(x100931,x100932),a862)),x100933),x100934))+~P24(f332(f332(f246(f875(x100931,f875(x100932,a862))),f332(f332(f7(x100931,f875(f874(x100931,x100932),a862),f875(x100932,a862)),f332(f332(f8(f875(x100932,f875(f875(f874(x100931,x100932),a862),a862)),f875(f875(f874(x100931,x100932),a862),f875(x100932,a862)),x100931),f7(x100932,f875(f874(x100931,x100932),a862),a862)),f332(f332(f8(f875(x100932,f874(x100931,x100932)),f875(x100932,f875(f875(f874(x100931,x100932),a862),a862)),x100931),f332(f8(f874(x100931,x100932),f875(f875(f874(x100931,x100932),a862),a862),x100932),f334(f874(x100931,x100932)))),f267(x100931,x100932)))),x100933)),f332(f332(f7(x100931,f875(f874(x100931,x100932),a862),f875(x100932,a862)),f332(f332(f8(f875(x100932,f875(f875(f874(x100931,x100932),a862),a862)),f875(f875(f874(x100931,x100932),a862),f875(x100932,a862)),x100931),f7(x100932,f875(f874(x100931,x100932),a862),a862)),f332(f332(f8(f875(x100932,f874(x100931,x100932)),f875(x100932,f875(f875(f874(x100931,x100932),a862),a862)),x100931),f332(f8(f874(x100931,x100932),f875(f875(f874(x100931,x100932),a862),a862),x100932),f334(f874(x100931,x100932)))),f267(x100931,x100932)))),x100934))) % 165.28/165.05 [9183]~P24(f332(f332(f334(f874(x91831,x91831)),x91832),f308(x91831,x91834)))+P24(f332(f332(f334(f874(x91831,x91831)),x91832),f308(x91831,f332(f332(f113(f875(f874(x91831,x91831),a862)),x91833),x91834)))) % 165.28/165.05 [9184]~P24(f332(f332(f334(f874(x91841,x91841)),x91842),f308(x91841,x91843)))+P24(f332(f332(f334(f874(x91841,x91841)),x91842),f308(x91841,f332(f332(f113(f875(f874(x91841,x91841),a862)),x91843),x91844)))) % 165.28/165.05 [9528]~E(f332(f174(x95281),x95284),f186(x95281,x95282,x95283))+E(f332(f180(x95281,x95282),f332(f332(f155(x95281,f874(x95281,x95282)),f332(f332(f18(x95281,x95282,f874(x95281,x95282)),f267(x95281,x95282)),f332(f332(f8(f872(x95282),x95282,x95281),f243(x95282)),x95283))),x95284)),x95283) % 165.28/165.05 [9851]~P24(f332(f332(f246(a868),f332(f332(f81(a868),x98511),x98514)),f332(f332(f81(a868),x98513),x98512)))+P24(f332(f332(f246(a1),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x98511),x98512)),f196(f875(f874(a868,a868),a862)))))),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x98513),x98514)),f196(f875(f874(a868,a868),a862))))))) % 165.28/165.05 [9852]~P24(f332(f332(f247(a868),f332(f332(f81(a868),x98521),x98524)),f332(f332(f81(a868),x98523),x98522)))+P24(f332(f332(f247(a1),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x98521),x98522)),f196(f875(f874(a868,a868),a862)))))),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x98523),x98524)),f196(f875(f874(a868,a868),a862))))))) % 165.28/165.05 [9929]P24(f332(f332(f246(a868),f332(f332(f81(a868),x99291),x99292)),f332(f332(f81(a868),x99293),x99294)))+~P24(f332(f332(f246(a1),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x99291),x99294)),f196(f875(f874(a868,a868),a862)))))),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x99293),x99292)),f196(f875(f874(a868,a868),a862))))))) % 165.28/165.05 [9930]P24(f332(f332(f247(a868),f332(f332(f81(a868),x99301),x99302)),f332(f332(f81(a868),x99303),x99304)))+~P24(f332(f332(f247(a1),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x99301),x99304)),f196(f875(f874(a868,a868),a862)))))),f332(a90,f332(f286(f874(a868,a868),f874(a868,a868),a111),f332(f332(f310(f874(a868,a868)),f332(f332(f267(a868,a868),x99303),x99302)),f196(f875(f874(a868,a868),a862))))))) % 165.28/165.05 [9972]P24(f332(f332(f246(f875(x99721,a862)),f332(f332(f42(a868,f875(x99721,a862)),f255(f875(a868,a862))),x99722)),f332(f332(f42(a868,f875(x99721,a862)),f255(f875(a868,a862))),x99723)))+~P24(f332(f332(f246(f875(x99721,a862)),f332(f332(f42(a868,f875(x99721,a862)),f332(f302(a868,f2(a868)),f480(x99723,x99724,x99722,x99721))),x99722)),f332(f332(f42(a868,f875(x99721,a862)),f332(f302(a868,f2(a868)),f332(f332(f81(a868),f480(x99723,x99724,x99722,x99721)),x99724))),x99723))) % 165.28/165.05 [10067]~P24(f332(f332(f334(x100672),x100674),f332(f263(x100671,x100672),x100673)))+P24(f332(f262(x100671,x100672,f332(f332(f7(x100671,f875(f874(x100671,x100672),a862),f875(x100672,a862)),f332(f332(f8(f875(x100672,f875(f875(f874(x100671,x100672),a862),a862)),f875(f875(f874(x100671,x100672),a862),f875(x100672,a862)),x100671),f7(x100672,f875(f874(x100671,x100672),a862),a862)),f332(f332(f8(f875(x100672,f874(x100671,x100672)),f875(x100672,f875(f875(f874(x100671,x100672),a862),a862)),x100671),f332(f8(f874(x100671,x100672),f875(f875(f874(x100671,x100672),a862),a862),x100672),f334(f874(x100671,x100672)))),f267(x100671,x100672)))),x100673)),x100674)) % 165.28/165.05 [10068]~P24(f332(f332(f334(x100681),x100684),f332(f265(x100681,x100682),x100683)))+P24(f332(f261(x100681,x100682,f332(f332(f7(x100681,f875(f874(x100681,x100682),a862),f875(x100682,a862)),f332(f332(f8(f875(x100682,f875(f875(f874(x100681,x100682),a862),a862)),f875(f875(f874(x100681,x100682),a862),f875(x100682,a862)),x100681),f7(x100682,f875(f874(x100681,x100682),a862),a862)),f332(f332(f8(f875(x100682,f874(x100681,x100682)),f875(x100682,f875(f875(f874(x100681,x100682),a862),a862)),x100681),f332(f8(f874(x100681,x100682),f875(f875(f874(x100681,x100682),a862),a862),x100682),f334(f874(x100681,x100682)))),f267(x100681,x100682)))),x100683)),x100684)) % 165.28/165.05 [10079]P24(f332(f332(f334(x100791),x100792),f332(f263(x100793,x100791),x100794)))+~P24(f332(f262(x100793,x100791,f332(f332(f7(x100793,f875(f874(x100793,x100791),a862),f875(x100791,a862)),f332(f332(f8(f875(x100791,f875(f875(f874(x100793,x100791),a862),a862)),f875(f875(f874(x100793,x100791),a862),f875(x100791,a862)),x100793),f7(x100791,f875(f874(x100793,x100791),a862),a862)),f332(f332(f8(f875(x100791,f874(x100793,x100791)),f875(x100791,f875(f875(f874(x100793,x100791),a862),a862)),x100793),f332(f8(f874(x100793,x100791),f875(f875(f874(x100793,x100791),a862),a862),x100791),f334(f874(x100793,x100791)))),f267(x100793,x100791)))),x100794)),x100792)) % 165.28/165.05 [10080]P24(f332(f332(f334(x100801),x100802),f332(f265(x100801,x100803),x100804)))+~P24(f332(f261(x100801,x100803,f332(f332(f7(x100801,f875(f874(x100801,x100803),a862),f875(x100803,a862)),f332(f332(f8(f875(x100803,f875(f875(f874(x100801,x100803),a862),a862)),f875(f875(f874(x100801,x100803),a862),f875(x100803,a862)),x100801),f7(x100803,f875(f874(x100801,x100803),a862),a862)),f332(f332(f8(f875(x100803,f874(x100801,x100803)),f875(x100803,f875(f875(f874(x100801,x100803),a862),a862)),x100801),f332(f8(f874(x100801,x100803),f875(f875(f874(x100801,x100803),a862),a862),x100803),f334(f874(x100801,x100803)))),f267(x100801,x100803)))),x100804)),x100802)) % 165.28/165.05 [9768]P24(f332(f161(x97681,x97682),x97683))+~P24(f332(f161(x97681,f332(f332(f18(x97681,a862,a862),f332(f332(f8(a862,f875(a862,a862),x97681),a330),x97684)),x97682)),x97683)) % 165.28/165.05 [9769]P24(f332(f161(x97691,x97692),x97693))+~P24(f332(f161(x97691,f332(f332(f18(x97691,a862,a862),f332(f332(f8(a862,f875(a862,a862),x97691),a330),x97692)),x97694)),x97693)) % 165.28/165.05 [9853]~P113(x98531)+E(f332(f332(f82(x98531),f332(f332(f81(x98531),f79(x98531)),f79(x98531))),f332(f332(f6(a868,x98531),f332(f332(f8(x98531,x98531,a868),f332(f81(x98531),x98532)),f332(f332(f7(a868,x98531,x98531),f332(f332(f8(x98531,f875(x98531,x98531),a868),f82(x98531)),f103(x98531))),x98533))),f332(f253(a868),x98534))),f332(f332(f82(x98531),f332(f103(x98531),x98534)),f332(f332(f81(x98531),x98532),f332(f332(f81(x98531),x98532),f332(f332(f82(x98531),f332(f103(x98531),f332(f332(f22(a868),x98534),f79(a868)))),x98533))))) % 165.28/165.05 [9993]P24(f332(x99931,f675(x99932,x99933,x99934,x99931)))+P41(x99932,f332(f252(f874(x99932,x99932)),f332(f271(x99932,x99932,a862),f332(f332(f8(f875(x99932,a862),f875(x99932,a862),x99932),f332(f18(x99932,a862,a862),f332(f332(f8(a862,f875(a862,a862),x99932),a330),x99931))),f332(f332(f7(x99932,f875(x99932,x99932),f875(x99932,a862)),f332(f332(f8(f875(x99932,a862),f875(f875(x99932,x99932),f875(x99932,a862)),x99932),f8(x99932,a862,x99932)),a329)),x99933))))) % 165.28/165.05 [10007]~P24(f332(f332(f247(a868),f332(x100074,f332(x100073,f675(x100071,x100073,x100074,x100072)))),f332(x100074,f675(x100071,x100073,x100074,x100072))))+P41(x100071,f332(f252(f874(x100071,x100071)),f332(f271(x100071,x100071,a862),f332(f332(f8(f875(x100071,a862),f875(x100071,a862),x100071),f332(f18(x100071,a862,a862),f332(f332(f8(a862,f875(a862,a862),x100071),a330),x100072))),f332(f332(f7(x100071,f875(x100071,x100071),f875(x100071,a862)),f332(f332(f8(f875(x100071,a862),f875(f875(x100071,x100071),f875(x100071,a862)),x100071),f8(x100071,a862,x100071)),a329)),x100073))))) % 165.28/165.05 [10106]~P24(f332(f332(f334(f874(x101061,x101061)),f332(f332(f267(x101061,x101061),x101063),x101064)),f332(f332(f113(f875(f874(x101061,x101061),a862)),x101062),f308(x101061,f196(f875(f874(x101061,x101061),a862))))))+P24(f332(f332(f332(f332(f113(f875(x101061,f875(x101061,a862))),f332(f332(f7(x101061,f875(f874(x101061,x101061),a862),f875(x101061,a862)),f332(f332(f8(f875(x101061,f875(f875(f874(x101061,x101061),a862),a862)),f875(f875(f874(x101061,x101061),a862),f875(x101061,a862)),x101061),f7(x101061,f875(f874(x101061,x101061),a862),a862)),f332(f332(f8(f875(x101061,f874(x101061,x101061)),f875(x101061,f875(f875(f874(x101061,x101061),a862),a862)),x101061),f332(f8(f874(x101061,x101061),f875(f875(f874(x101061,x101061),a862),a862),x101061),f334(f874(x101061,x101061)))),f267(x101061,x101061)))),x101062)),a329),x101063),x101064)) % 165.28/165.05 [10116]P24(f332(f332(f334(f874(x101161,x101161)),f332(f332(f267(x101161,x101161),x101162),x101163)),f332(f332(f113(f875(f874(x101161,x101161),a862)),x101164),f308(x101161,f196(f875(f874(x101161,x101161),a862))))))+~P24(f332(f332(f332(f332(f113(f875(x101161,f875(x101161,a862))),f332(f332(f7(x101161,f875(f874(x101161,x101161),a862),f875(x101161,a862)),f332(f332(f8(f875(x101161,f875(f875(f874(x101161,x101161),a862),a862)),f875(f875(f874(x101161,x101161),a862),f875(x101161,a862)),x101161),f7(x101161,f875(f874(x101161,x101161),a862),a862)),f332(f332(f8(f875(x101161,f874(x101161,x101161)),f875(x101161,f875(f875(f874(x101161,x101161),a862),a862)),x101161),f332(f8(f874(x101161,x101161),f875(f875(f874(x101161,x101161),a862),a862),x101161),f334(f874(x101161,x101161)))),f267(x101161,x101161)))),x101164)),a329),x101162),x101163)) % 165.28/165.05 [10065]E(f332(f332(f152(f869(x100651)),f332(f332(f152(x100651),x100652),f332(f143(f869(x100651),f869(x100651),f135(x100651),f116(x100651)),f332(f332(f155(f869(x100651),f869(x100651)),f157(f869(x100651),x100651,f116(x100651),f332(f332(f8(f869(x100651),f875(f869(x100651),f869(x100651)),x100651),f16(f869(x100651),f869(x100651))),f332(f332(f7(x100651,f869(x100651),f869(x100651)),f152(x100651)),f116(x100651))))),x100653)))),f182(x100651,f332(f332(f152(f869(x100651)),x100654),f332(f143(f869(f869(x100651)),f869(f869(x100651)),f135(f869(x100651)),f116(f869(x100651))),f332(f332(f155(f869(x100651),f869(f869(x100651))),f157(f869(f869(x100651)),x100651,f116(f869(x100651)),f332(f16(f875(f869(x100651),f869(f869(x100651))),x100651),f332(f332(f7(f869(x100651),f869(f869(x100651)),f869(f869(x100651))),f152(f869(x100651))),f116(f869(x100651)))))),x100653))))),f182(x100651,f332(f332(f152(f869(x100651)),f332(f332(f152(x100651),x100652),x100654)),x100653)))+~P24(f332(f320(f869(f869(x100651)),f183(x100651)),f332(f332(f152(f869(x100651)),f332(f332(f152(x100651),x100652),x100654)),x100653))) % 165.28/165.05 [10105]~P24(f332(f62(x101052),f332(f252(x101052),x101054)))+P24(f332(f62(x101051),f332(f252(x101051),f332(f332(f8(f875(x101052,a862),a862,x101051),f88(x101052)),f332(f332(f7(x101051,f875(x101052,a862),f875(x101052,a862)),f332(f332(f8(f875(x101052,f875(a862,a862)),f875(f875(x101052,a862),f875(x101052,a862)),x101051),f18(x101052,a862,a862)),f332(f332(f8(f875(x101052,a862),f875(x101052,f875(a862,a862)),x101051),f332(f8(a862,f875(a862,a862),x101052),a330)),f332(f332(f7(x101051,f875(x101052,x101051),f875(x101052,a862)),f332(f332(f8(f875(x101051,a862),f875(f875(x101052,x101051),f875(x101052,a862)),x101051),f8(x101051,a862,x101052)),a329)),x101053)))),x101054))))) % 165.28/165.05 [5256]E(x52561,x52562)+~E(f128(x52563,x52564,x52561),f128(x52563,x52565,x52562)) % 165.28/165.05 [5257]E(x52571,x52572)+~E(f128(x52573,x52571,x52574),f128(x52573,x52572,x52575)) % 165.28/165.05 [5258]E(x52581,x52582)+~E(f171(x52583,x52581,x52584),f171(x52583,x52582,x52585)) % 165.28/165.05 [5636]E(f332(f332(f310(x56361),x56362),f186(x56361,x56363,x56364)),f186(x56361,x56363,x56364))+~E(f332(x56364,x56362),f332(f208(x56363),x56365)) % 165.28/165.05 [6045]P24(f332(f262(x60451,x60452,x60453),x60454))+~P24(f332(f332(x60453,x60455),x60454)) % 165.28/165.05 [6047]P24(f332(f261(x60471,x60472,x60473),x60474))+~P24(f332(f332(x60473,x60474),x60475)) % 165.28/165.05 [6050]~E(f332(x60504,x60502),f332(f208(x60503),x60505))+P24(f332(f332(f334(x60501),x60502),f186(x60501,x60503,x60504))) % 165.28/165.05 [6051]~E(f332(x60514,x60515),f332(f208(x60511),x60512))+P24(f332(f332(f334(x60511),x60512),f188(x60513,x60511,x60514))) % 165.28/165.05 [6521]~E(x65215,f2(a102))+E(f332(f207(x65211,x65212,x65213,x65214),x65215),f118(x65212)) % 165.28/165.05 [6522]~E(x65225,f2(a102))+E(f332(f204(x65221,x65222,x65223,x65224),x65225),f129(x65222)) % 165.28/165.05 [6656]~E(x66563,f2(a102))+E(f332(f281(x66561,x66562,x66563,x66564),x66565),f332(f267(x66561,x66562),x66565)) % 165.28/165.05 [6728]~E(f332(x67284,x67285),f209(x67282))+E(f332(f241(f872(x67281),x67282,f209(x67281),x67283),f332(x67284,x67285)),f209(x67281)) % 165.28/165.05 [7346]E(f332(x73461,x73462),f209(x73463))+~E(f332(f187(x73464,x73463,x73465,x73461),x73462),f209(x73463)) % 165.28/165.05 [7347]E(f332(x73471,x73472),f209(x73473))+~E(f332(f187(x73474,x73473,x73471,x73475),x73472),f209(x73473)) % 165.28/165.05 [7384]E(f332(f187(x73841,x73842,x73843,x73844),x73845),f332(x73843,x73845))+P24(f332(f332(f334(x73841),x73845),f186(x73841,x73842,x73844))) % 165.28/165.05 [7385]E(f332(f187(x73851,x73852,x73853,x73854),x73855),f332(x73854,x73855))+P24(f332(f332(f334(x73851),x73855),f186(x73851,x73852,x73853))) % 165.28/165.05 [7706]~P16(x77064,x77061,x77062,x77065)+E(f332(f74(x77061,x77061,x77061,f332(x77062,x77063)),f332(x77062,x77063)),f332(x77062,x77063)) % 165.28/165.05 [7750]E(f332(f187(x77501,x77502,x77503,x77504),x77505),f332(x77504,x77505))+~P24(f332(f332(f334(x77501),x77505),f186(x77501,x77502,x77504))) % 165.28/165.05 [8089]~P12(x80895,x80891,x80892)+E(f332(f74(x80891,x80891,x80891,f332(x80892,x80893)),f332(x80892,x80894)),f332(f74(x80891,x80891,x80891,f332(x80892,x80894)),f332(x80892,x80893))) % 165.28/165.05 [8412]P24(f332(f332(f334(f874(x84121,x84121)),f332(f332(f267(x84121,x84121),x84122),x84123)),f326(x84121,x84124,x84125)))+~P24(f332(f332(f247(a868),f332(x84124,x84122)),f332(x84124,x84123))) % 165.28/165.05 [8500]~P24(f332(f332(f334(x85004),x85003),f296(x85004,x85001,x85002,x85005)))+P24(f332(f332(x85001,x85002),x85003)) % 165.28/165.05 [8501]~P24(f332(f332(f334(x85014),x85013),f299(x85014,x85011,x85012,x85015)))+P24(f332(f332(x85011,x85012),x85013)) % 165.28/165.05 [8502]~P24(f332(f332(f334(x85024),x85022),f296(x85024,x85021,x85025,x85023)))+P24(f332(f332(x85021,x85022),x85023)) % 165.28/165.05 [8503]~P24(f332(f332(f334(x85034),x85032),f299(x85034,x85031,x85035,x85033)))+P24(f332(f332(x85031,x85032),x85033)) % 165.28/165.05 [8641]~P55(x86412,x86411,x86415,x86413,x86414)+E(f332(f311(x86411,x86412,x86413),x86414),f255(f875(x86412,a862))) % 165.28/165.05 [9069]~P38(x90691,x90692,x90693,x90694,x90695)+P38(x90691,x90692,x90693,f332(f170(x90691),x90694),f332(f170(x90692),x90695)) % 165.28/165.05 [9071]~P38(x90711,x90712,x90713,f332(f170(x90711),x90714),x90715)+P38(x90711,x90712,x90713,x90714,f332(f170(x90712),x90715)) % 165.28/165.05 [9072]~P38(x90721,x90722,x90723,x90724,f332(f170(x90722),x90725))+P38(x90721,x90722,x90723,f332(f170(x90721),x90724),x90725) % 165.28/165.05 [9078]P38(x90781,x90782,x90783,x90784,x90785)+~P38(x90781,x90782,x90783,f332(f170(x90781),x90784),f332(f170(x90782),x90785)) % 165.28/165.05 [9452]P24(f332(f332(f334(f874(f869(x94521),f869(x94521))),f332(f332(f267(f869(x94521),f869(x94521)),f332(f332(f152(x94521),x94522),x94523)),f332(f332(f152(x94521),x94522),x94524))),f158(x94521,x94525)))+~P24(f332(f332(f334(f874(f869(x94521),f869(x94521))),f332(f332(f267(f869(x94521),f869(x94521)),x94523),x94524)),f158(x94521,x94525))) % 165.28/165.05 [9453]P24(f332(f332(f334(f874(f869(x94531),f869(x94531))),f332(f332(f267(f869(x94531),f869(x94531)),f332(f332(f135(x94531),x94532),x94533)),f332(f332(f135(x94531),x94532),x94534))),f148(x94531,x94535)))+~P24(f332(f332(f334(f874(f869(x94531),f869(x94531))),f332(f332(f267(f869(x94531),f869(x94531)),x94533),x94534)),f148(x94531,x94535))) % 165.28/165.05 [9643]E(f332(f332(f152(x96431),f562(x96432,x96433,x96434,x96435,x96431)),f563(x96432,x96433,x96434,x96435,x96431)),x96435)+~P24(f332(f332(f334(f874(f869(x96431),f869(x96431))),f332(f332(f267(f869(x96431),f869(x96431)),x96435),f332(f332(f152(x96431),x96434),x96433))),f159(x96431,x96432))) % 165.28/165.05 [9665]E(f332(f332(f152(x96651),f564(x96652,x96653,x96654,x96655,x96651)),f565(x96652,x96653,x96654,x96655,x96651)),x96653)+~P24(f332(f332(f334(f874(f869(x96651),f869(x96651))),f332(f332(f267(f869(x96651),f869(x96651)),f332(f332(f152(x96651),x96655),x96654)),x96653)),f159(x96651,x96652))) % 165.28/165.05 [9827]~P24(f332(f332(f334(f874(f869(x98271),f869(x98271))),f332(f332(f267(f869(x98271),f869(x98271)),f332(f332(f152(x98271),x98275),x98272)),x98274)),f159(x98271,x98273)))+P24(f332(f332(f334(f874(f869(x98271),f869(x98271))),f332(f332(f267(f869(x98271),f869(x98271)),x98272),f565(x98273,x98274,x98272,x98275,x98271))),f159(x98271,x98273))) % 165.28/165.05 [9897]~P24(f332(f332(f334(f874(f869(x98971),f869(x98971))),f332(f332(f267(f869(x98971),f869(x98971)),x98975),f332(f332(f152(x98971),x98974),x98973))),f159(x98971,x98972)))+P24(f332(f332(f334(f874(f869(x98971),f869(x98971))),f332(f332(f267(f869(x98971),f869(x98971)),f563(x98972,x98973,x98974,x98975,x98971)),x98973)),f159(x98971,x98972))) % 165.28/165.05 [10060]P24(f332(f332(f334(f874(x100601,x100601)),f332(f332(f267(x100601,x100601),f332(x100602,f332(f332(f81(a868),x100603),x100604))),f332(x100602,x100603))),f308(x100601,x100605)))+~P24(f332(f332(f334(f874(x100601,x100601)),f332(f332(f267(x100601,x100601),f332(x100602,f332(a115,f731(x100604,x100603,x100605,x100602,x100601)))),f332(x100602,f731(x100604,x100603,x100605,x100602,x100601)))),f308(x100601,x100605))) % 165.28/165.05 [5219]E(x52191,x52192)+~E(f332(f332(f152(x52193),x52194),x52191),f332(f332(f152(x52193),x52195),x52192)) % 165.28/165.05 [5220]E(x52201,x52202)+~E(f332(f332(f152(x52203),x52201),x52204),f332(f332(f152(x52203),x52202),x52205)) % 165.28/165.05 [5274]P24(f332(x52741,x52742))+~E(f332(f137(x52743,x52741),x52744),f332(f332(f152(x52743),x52742),x52745)) % 165.28/165.05 [5275]P24(f332(x52751,x52752))+~E(f332(f332(f152(x52753),x52752),x52754),f332(f137(x52753,x52751),x52755)) % 165.28/165.05 [5432]~E(f332(f332(f139(x54321),x54323),x54322),f332(f332(f152(x54321),x54324),x54325))+E(f332(f332(f166(x54321),x54322),x54323),x54324) % 165.28/165.05 [5566]~P11(x55664,x55665,x55661)+E(f332(f332(x55661,x55662),f332(f332(x55661,x55662),x55663)),f332(f332(x55661,x55662),x55663)) % 165.28/165.05 [6103]~E(x61034,f2(a102))+E(f332(f332(f120(x61031,x61032,x61033),x61034),x61035),f332(f332(f267(f869(x61032),x61031),f116(x61032)),x61035)) % 165.28/165.05 [6178]~P106(x61782)+~E(f332(f332(f149(x61781,x61782,x61783),x61784),x61785),f116(x61781)) % 165.28/165.05 [6558]E(x65581,x65582)+~E(f332(f332(f135(x65583),x65584),f332(f332(f152(x65583),x65581),f116(x65583))),f332(f332(f135(x65583),x65585),f332(f332(f152(x65583),x65582),f116(x65583)))) % 165.28/165.05 [6559]E(x65591,x65592)+~E(f332(f332(f135(x65593),x65591),f332(f332(f152(x65593),x65594),f116(x65593))),f332(f332(f135(x65593),x65592),f332(f332(f152(x65593),x65595),f116(x65593)))) % 165.28/165.05 [6812]E(f332(f190(x68121,x68122,x68123,x68124),x68125),f209(x68122))+P24(f332(f332(f334(x68121),x68125),x68124)) % 165.28/165.05 [6874]E(f332(f332(f310(x68741),f332(x68742,x68743)),f332(f311(x68744,x68741,x68742),x68745)),f332(f311(x68744,x68741,x68742),x68745))+~P24(f332(f332(f334(x68744),x68743),x68745)) % 165.28/165.05 [6881]~P24(f332(x68814,f332(x68813,x68815)))+P24(f332(f332(f312(x68811,x68812,x68813),x68814),x68815)) % 165.28/165.05 [6884]~P24(f332(f332(x68843,x68845),x68844))+P24(f332(f332(f256(x68841,x68842,x68843),x68844),x68845)) % 165.28/165.05 [6977]~E(f332(f311(x69771,x69772,x69773),x69774),x69775)+E(f332(f311(f875(x69771,a862),f875(x69772,a862),f311(x69771,x69772,x69773)),f332(f309(x69771),x69774)),f332(f309(x69772),x69775)) % 165.28/165.05 [7007]E(f332(f190(x70071,x70072,x70073,x70074),x70075),f332(x70073,x70075))+~P24(f332(f332(f334(x70071),x70075),x70074)) % 165.28/165.05 [7306]P21(x73061,x73062,x73063,x73064)+~P21(x73061,x73062,x73063,f332(f332(f310(x73061),x73065),x73064)) % 165.28/165.05 [7373]P24(f332(x73731,x73732))+~P24(f332(f332(f95(x73733,x73734,x73731),x73735),x73732)) % 165.28/165.05 [7418]~P24(f332(f332(f334(x74184),x74183),x74185))+P24(f332(f332(f334(x74181),f332(x74182,x74183)),f332(f311(x74184,x74181,x74182),x74185))) % 165.28/165.05 [7441]~P106(x74412)+E(f151(x74411,x74412,x74413,f332(f137(x74411,x74414),x74415)),f332(f137(x74411,x74414),f151(x74411,x74412,x74413,x74415))) % 165.28/165.05 [7474]P24(f332(x74741,f332(x74742,x74743)))+~P24(f332(f332(f312(x74744,x74745,x74742),x74741),x74743)) % 165.28/165.05 [7477]P24(f332(f332(x74771,x74772),x74773))+~P24(f332(f332(f256(x74774,x74775,x74771),x74773),x74772)) % 165.28/165.05 [7478]P24(f332(f332(x74781,x74782),x74783))+~P24(f332(f332(f95(x74784,x74781,x74785),x74782),x74783)) % 165.28/165.05 [7542]~P24(f332(f332(f334(x75423),f332(x75424,x75422)),x75425))+P24(f332(f332(f334(x75421),x75422),f332(f312(x75421,x75423,x75424),x75425))) % 165.28/165.05 [7935]~P24(f332(f332(f334(x79355),x79353),f332(f312(x79355,x79351,x79352),x79354)))+P24(f332(f332(f334(x79351),f332(x79352,x79353)),x79354)) % 165.28/165.05 [8154]~E(x81543,f332(f332(f332(f73(x81541,f872(x81542)),f332(f16(f872(x81542),x81541),f209(x81542))),x81544),f332(f208(x81542),x81545)))+E(f186(x81541,x81542,x81543),f332(f332(f310(x81541),x81544),f196(f875(x81541,a862)))) % 165.28/165.05 [8234]~P12(x82342,x82341,x82343)+E(f332(f143(x82341,x82342,f332(f7(x82342,x82341,x82341),x82343),x82344),f153(x82342,x82345)),f332(f332(f65(x82342,x82341,x82343),x82344),f332(f174(x82342),x82345))) % 165.28/165.05 [8253]E(f332(x82531,f426(x82532,x82531,x82533,x82534)),x82534)+~P24(f332(f332(f334(x82535),x82534),f332(f311(x82533,x82535,x82531),x82532))) % 165.28/165.05 [8546]~E(x85462,f332(f332(f152(x85461),x85464),x85465))+P24(f332(f332(f334(f874(f869(x85461),f869(x85461))),f332(f332(f267(f869(x85461),f869(x85461)),f116(x85461)),x85462)),f148(x85461,x85463))) % 165.28/165.05 [8597]~P38(x85971,x85973,x85975,x85972,x85974)+E(f332(f197(f869(x85971)),x85972),f332(f197(f869(x85973)),x85974)) % 165.28/165.05 [8608]P24(f332(f332(f246(f875(x86081,a862)),f332(f332(f43(x86082,f875(x86081,a862)),x86083),x86084)),f332(x86084,x86085)))+~P24(f332(f332(f334(x86082),x86085),x86083)) % 165.28/165.05 [8657]~P55(x86571,x86572,x86573,x86575,x86574)+E(f332(f311(x86571,x86572,x86573),f255(f875(x86571,a862))),x86574) % 165.28/165.05 [8861]E(f332(f332(f332(f73(x88611,f872(x88612)),f190(x88611,x88612,x88613,x88614)),x88615),f209(x88612)),f190(x88611,x88612,x88613,x88614))+P24(f332(f332(f334(x88611),x88615),x88614)) % 165.28/165.05 [8866]E(f332(f137(x88661,x88662),f712(x88663,x88664,x88665,x88662,x88661)),x88663)+~E(f332(f137(x88661,x88662),x88665),f332(f332(f152(x88661),x88664),x88663)) % 165.28/165.05 [8867]E(f332(f137(x88671,x88672),f713(x88673,x88672,x88674,x88675,x88671)),x88674)+~E(f332(f332(f152(x88671),x88675),x88674),f332(f137(x88671,x88672),x88673)) % 165.28/165.05 [8868]E(f332(x88681,f827(x88682,x88683,x88681,x88684,x88685)),x88682)+~E(f332(f332(f210(x88685,x88684),x88681),x88683),f332(f208(x88684),x88682)) % 165.28/165.05 [8871]E(f332(f208(x88711),f827(x88712,x88713,x88714,x88715,x88711)),x88713)+~E(f332(f332(f210(x88711,x88715),x88714),x88713),f332(f208(x88715),x88712)) % 165.28/165.05 [8961]E(f332(f197(f869(x89611)),x89612),x89613)+~P24(f332(f332(f334(f874(f869(x89611),f869(x89611))),f332(f332(f267(f869(x89611),f869(x89611)),x89614),x89612)),f332(f144(x89611,x89615),x89613))) % 165.28/165.05 [8962]E(f332(f197(f869(x89621)),x89622),x89623)+~P24(f332(f332(f334(f874(f869(x89621),f869(x89621))),f332(f332(f267(f869(x89621),f869(x89621)),x89622),x89624)),f332(f144(x89621,x89625),x89623))) % 165.28/165.05 [9028]P24(f332(f332(f334(x90281),f426(x90282,x90283,x90281,x90284)),x90282))+~P24(f332(f332(f334(x90285),x90284),f332(f311(x90281,x90285,x90283),x90282))) % 165.28/165.05 [9181]E(f332(f311(x91811,x91812,x91813),f835(x91814,x91813,x91811,x91815,x91812)),x91815)+~P24(f332(f332(f246(f875(x91812,a862)),x91815),f332(f311(x91811,x91812,x91813),x91814))) % 165.28/165.05 [9425]E(f332(x94251,f615(x94252,x94251,x94253,x94254,x94255)),f332(f208(x94255),x94254))+~P24(f332(f332(f334(x94255),x94254),f188(x94253,x94255,f190(x94253,x94255,x94251,x94252)))) % 165.28/165.05 [9468]P24(f332(f332(f334(f874(f869(x94681),f869(x94681))),f332(f332(f267(f869(x94681),f869(x94681)),f332(f332(f152(x94681),x94682),x94683)),f332(f332(f152(x94681),x94682),x94684))),f308(f869(x94681),f158(x94681,x94685))))+~P24(f332(f332(f334(f874(f869(x94681),f869(x94681))),f332(f332(f267(f869(x94681),f869(x94681)),x94683),x94684)),f308(f869(x94681),f158(x94681,x94685)))) % 165.28/165.05 [9499]~E(f332(x94993,f525(x94995,x94994,x94993,x94992,x94991)),f332(x94995,f525(x94995,x94994,x94993,x94992,x94991)))+E(f332(f332(f155(x94991,x94992),x94993),x94994),f332(f332(f155(x94991,x94992),x94995),x94994)) % 165.28/165.05 [9575]~E(f332(f137(x95751,x95755),x95754),f332(f332(f152(x95751),x95753),x95752))+E(f332(f332(f135(x95751),f715(x95752,x95753,x95754,x95755,x95751)),f332(f332(f152(x95751),x95753),f712(x95752,x95753,x95754,x95755,x95751))),x95754) % 165.28/165.05 [9576]~E(f332(f332(f152(x95761),x95765),x95764),f332(f137(x95761,x95763),x95762))+E(f332(f332(f135(x95761),f714(x95762,x95763,x95764,x95765,x95761)),f332(f332(f152(x95761),x95765),f713(x95762,x95763,x95764,x95765,x95761))),x95762) % 165.28/165.05 [9580]E(f332(f332(f155(x95801,x95802),x95803),x95804),f332(f332(f155(x95801,x95802),x95805),x95804))+P24(f332(f332(f334(x95801),f525(x95803,x95804,x95805,x95802,x95801)),f332(f174(x95801),x95804))) % 165.28/165.05 [9610]~P24(f332(f332(f334(x96105),x96104),f332(f286(x96101,x96105,x96103),x96102)))+P24(f332(f332(f334(x96101),f491(x96102,x96103,x96101,x96104,x96105)),x96102)) % 165.28/165.05 [9611]~P24(f332(f332(f334(x96115),x96114),f332(f286(x96111,x96115,x96113),x96112)))+P24(f332(f332(f334(x96111),f518(x96112,x96113,x96111,x96114,x96115)),x96112)) % 165.28/165.05 [9637]~P24(f332(f332(f246(f875(x96375,a862)),x96374),f332(f311(x96371,x96375,x96373),x96372)))+P24(f332(f332(f246(f875(x96371,a862)),f835(x96372,x96373,x96371,x96374,x96375)),x96372)) % 165.28/165.05 [9688]~P24(f332(f332(f334(x96885),x96884),f188(x96881,x96885,f190(x96881,x96885,x96883,x96882))))+P24(f332(f332(f334(x96881),f615(x96882,x96883,x96881,x96884,x96885)),x96882)) % 165.28/165.05 [10082]E(x100821,f2(a102))+E(f332(f241(f874(f869(x100822),x100823),f874(x100822,x100823),f332(f332(f267(f869(x100822),x100823),f116(x100822)),x100824),f332(f271(x100822,x100823,f874(f869(x100822),x100823)),f332(f332(f7(x100822,f875(x100823,f874(f869(x100822),x100823)),f875(x100823,f874(f869(x100822),x100823))),f332(f332(f8(f875(f874(f869(x100822),x100823),f874(f869(x100822),x100823)),f875(f875(x100823,f874(f869(x100822),x100823)),f875(x100823,f874(f869(x100822),x100823))),x100822),f8(f874(f869(x100822),x100823),f874(f869(x100822),x100823),x100823)),f332(f332(f8(f875(f869(x100822),f875(x100823,f874(f869(x100822),x100823))),f875(f874(f869(x100822),x100823),f874(f869(x100822),x100823)),x100822),f271(f869(x100822),x100823,f874(f869(x100822),x100823))),f332(f332(f8(f875(f869(x100822),f869(x100822)),f875(f869(x100822),f875(x100823,f874(f869(x100822),x100823))),x100822),f332(f8(f869(x100822),f875(x100823,f874(f869(x100822),x100823)),f869(x100822)),f267(f869(x100822),x100823))),f152(x100822))))),f332(f120(x100823,x100822,x100825),f332(f332(f22(a102),x100821),f79(a102)))))),f332(x100825,x100824)),f332(f332(f120(x100823,x100822,x100825),x100821),x100824)) % 165.28/165.05 [5445]~E(f332(x54453,x54454),x54455)+E(f332(f332(f332(f73(x54451,x54452),x54453),x54454),x54455),x54453) % 165.28/165.05 [5889]E(f332(x58891,x58892),x58893)+~E(f332(f332(f332(f73(x58894,x58895),x58891),x58892),x58893),x58891) % 165.28/165.05 [5982]E(x59821,x59822)+~E(f332(f270(x59823,x59824),f332(f332(f267(x59823,x59824),x59825),x59821)),x59822) % 165.28/165.05 [5983]E(x59831,x59832)+~E(f332(f266(x59833,x59834),f332(f332(f267(x59833,x59834),x59831),x59835)),x59832) % 165.28/165.05 [6253]~E(x62533,f332(f332(f135(x62531),x62534),f332(f332(f152(x62531),x62532),x62535)))+P24(f332(f332(f334(x62531),x62532),f332(f174(x62531),x62533))) % 165.28/165.05 [6643]E(f332(f311(x66431,x66432,f332(f16(x66432,x66431),x66433)),x66434),f332(f332(f310(x66432),x66433),f196(f875(x66432,a862))))+~P24(f332(f332(f334(x66431),x66435),x66434)) % 165.28/165.05 [6713]E(f332(f332(f113(f875(x67131,a862)),f332(f174(x67131),x67132)),f332(f174(x67131),x67133)),f332(f174(x67131),x67134))+~E(f168(x67131,x67135,x67134),f332(f332(f267(f869(x67131),f869(x67131)),x67132),x67133)) % 165.28/165.05 [6816]~P106(x68162)+E(f332(f197(f869(x68161)),f332(f332(f149(x68161,x68162,x68163),x68164),x68165)),f332(a115,f332(f197(f869(x68161)),x68165))) % 165.28/165.05 [6828]~P106(x68282)+E(f332(f174(x68281),f332(f332(f149(x68281,x68282,x68283),x68284),x68285)),f332(f332(f310(x68281),x68284),f332(f174(x68281),x68285))) % 165.28/165.05 [7098]~P113(x70981)+E(f332(f332(f81(x70981),f332(f332(f81(x70981),x70982),x70983)),f332(f332(f81(x70981),x70984),x70985)),f332(f332(f81(x70981),f332(f332(f81(x70981),x70982),x70984)),f332(f332(f81(x70981),x70983),x70985))) % 165.28/165.05 [7099]~P113(x70991)+E(f332(f332(f82(x70991),f332(f332(f82(x70991),x70992),x70993)),f332(f332(f82(x70991),x70994),x70995)),f332(f332(f82(x70991),f332(f332(f82(x70991),x70992),x70994)),f332(f332(f82(x70991),x70993),x70995))) % 165.28/165.05 [7100]~P60(x71001)+E(f332(f332(f290(x71001),f332(f332(f82(x71001),x71002),x71003)),f332(f332(f82(x71001),x71004),x71005)),f332(f332(f82(x71001),f332(f332(f290(x71001),x71002),x71004)),f332(f332(f290(x71001),x71003),x71005))) % 165.28/165.05 [7114]~P106(x71141)+E(f306(x71141,f332(f332(f245(x71141),x71142),x71143),f332(f332(f244(x71141),x71144),x71145)),f332(f332(f104(f875(x71141,a862)),f306(x71141,x71142,x71144)),f306(x71141,x71143,x71145))) % 165.28/165.05 [7115]~P106(x71151)+E(f305(x71151,f332(f332(f245(x71151),x71152),x71153),f332(f332(f244(x71151),x71154),x71155)),f332(f332(f104(f875(x71151,a862)),f305(x71151,x71152,x71154)),f305(x71151,x71153,x71155))) % 165.28/165.05 [7116]~P106(x71161)+E(f303(x71161,f332(f332(f245(x71161),x71162),x71163),f332(f332(f244(x71161),x71164),x71165)),f332(f332(f104(f875(x71161,a862)),f303(x71161,x71162,x71164)),f303(x71161,x71163,x71165))) % 165.28/165.05 [7117]~P106(x71171)+E(f332(f332(f104(f875(x71171,a862)),f332(f302(x71171,x71172),x71173)),f332(f302(x71171,x71174),x71175)),f332(f302(x71171,f332(f332(f245(x71171),x71172),x71174)),f332(f332(f244(x71171),x71173),x71175))) % 165.28/165.05 [7232]~P24(f332(x72321,f489(x72323,x72322,x72321)))+P24(f332(x72321,f332(f332(f267(x72322,x72323),x72324),x72325))) % 165.28/165.05 [7319]~E(f332(x73193,x73194),f209(x73192))+E(f188(x73191,x73192,f332(f332(f332(f73(x73191,f872(x73192)),x73193),x73194),f332(f208(x73192),x73195))),f332(f332(f310(x73192),x73195),f188(x73191,x73192,x73193))) % 165.28/165.05 [7338]~E(x73382,f332(x73384,x73385))+P24(f332(f332(f334(x73381),x73382),f332(f311(x73383,x73381,x73384),f255(f875(x73383,a862))))) % 165.28/165.05 [7396]~E(f332(x73963,x73964),f209(x73962))+E(f332(f332(f22(f875(x73961,a862)),f186(x73961,x73962,x73963)),f332(f332(f310(x73961),x73964),x73965)),f332(f332(f22(f875(x73961,a862)),f186(x73961,x73962,x73963)),x73965)) % 165.28/165.05 [7415]~P11(x74153,x74152,x74154)+P11(x74151,x74152,f332(f332(f8(x74153,f875(x74152,x74152),x74151),x74154),x74155)) % 165.28/165.05 [7416]~P12(x74163,x74162,x74164)+P12(x74161,x74162,f332(f332(f8(x74163,f875(x74162,x74162),x74161),x74164),x74165)) % 165.28/165.05 [7558]~P21(x75581,x75582,x75583,x75584)+P21(x75581,x75582,x75583,f332(f332(f22(f875(x75581,a862)),x75584),x75585)) % 165.28/165.05 [7715]~P24(f332(f332(x77153,x77154),x77155))+P24(f332(f332(f271(x77151,x77152,a862),x77153),f332(f332(f267(x77151,x77152),x77154),x77155))) % 165.28/165.05 [7825]~P24(f332(x78252,x78254))+~E(f332(f332(f139(x78251),f332(f197(f869(x78251)),f179(x78251,x78252,x78253))),x78253),f332(f332(f152(x78251),x78254),x78255)) % 165.28/165.05 [7845]P21(x78451,x78452,x78453,x78454)+~P21(x78451,x78452,x78453,f332(f332(f113(f875(x78451,a862)),x78455),x78454)) % 165.28/165.05 [7846]P21(x78461,x78462,x78463,x78464)+~P21(x78461,x78462,x78463,f332(f332(f113(f875(x78461,a862)),x78464),x78465)) % 165.28/165.05 [7892]~P106(x78922)+E(f332(f332(f149(x78921,x78922,x78923),x78924),f151(x78921,x78922,x78923,x78925)),f151(x78921,x78922,x78923,f332(f332(f152(x78921),x78924),x78925))) % 165.28/165.05 [8049]~P33(x80491,f332(a115,x80492),f332(f332(f332(f93(x80491),x80493),f332(a28,x80494)),x80495))+P33(x80491,x80492,f332(f332(f332(f93(x80491),x80493),f332(f243(a863),f332(a26,x80494))),x80495)) % 165.28/165.05 [8181]P33(x81811,f332(a115,x81812),f332(f332(f332(f93(x81811),x81813),f332(a28,x81814)),x81815))+~P33(x81811,x81812,f332(f332(f332(f93(x81811),x81813),f332(f243(a863),f332(a26,x81814))),x81815)) % 165.28/165.05 [8210]~P11(x82102,x82101,x82103)+E(f332(f143(x82101,x82102,f332(f7(x82102,x82101,x82101),x82103),x82104),x82105),f332(f332(f65(x82102,x82101,x82103),x82104),f332(f174(x82102),x82105))) % 165.28/165.05 [8239]~E(f332(f332(f139(x82391),f332(f197(f869(x82391)),f179(x82391,x82392,x82393))),x82393),f332(f332(f152(x82391),x82394),x82395))+E(f332(f332(f135(x82391),f179(x82391,x82392,x82393)),f332(f332(f152(x82391),x82394),x82395)),x82393) % 165.28/165.05 [8263]P24(f332(f332(x82631,x82632),x82633))+~P24(f332(f332(f271(x82634,x82635,a862),x82631),f332(f332(f267(x82634,x82635),x82632),x82633))) % 165.28/165.05 [8324]~E(f332(f332(f180(x83241,x83242),x83245),x83243),f332(f208(x83242),x83244))+P24(f332(f332(f334(f874(x83241,x83242)),f332(f332(f267(x83241,x83242),x83243),x83244)),f332(f174(f874(x83241,x83242)),x83245))) % 165.28/165.05 [8712]P24(f332(f332(f246(f875(x87121,a862)),f332(f311(x87122,x87121,x87123),x87124)),f332(f311(x87122,x87121,x87123),x87125)))+~P24(f332(f332(f246(f875(x87122,a862)),x87124),x87125)) % 165.28/165.05 [8713]P24(f332(f332(f246(f875(x87131,a862)),f332(f312(x87131,x87132,x87133),x87134)),f332(f312(x87131,x87132,x87133),x87135)))+~P24(f332(f332(f246(f875(x87132,a862)),x87134),x87135)) % 165.28/165.05 [8788]E(x87881,f2(a102))+E(f332(f332(f273(x87882,x87883,x87882,f874(x87883,x87882)),f332(x87884,x87885)),f281(x87883,x87882,f332(f332(f22(a102),x87881),f79(a102)),x87884)),f332(f281(x87883,x87882,x87881,x87884),x87885)) % 165.28/165.05 [9286]E(f332(f208(x92861),f524(x92862,x92863,x92864,x92861,x92865)),f332(f332(f180(x92865,x92861),x92862),x92864))+~P24(f332(f332(f334(f874(x92865,x92861)),f332(f332(f267(x92865,x92861),x92864),x92863)),f332(f174(f874(x92865,x92861)),x92862))) % 165.28/165.05 [9389]~P20(x93891,x93892,f332(f332(f310(f867(x93891)),f332(f332(f332(f93(x93891),x93893),f332(f243(a863),f332(a26,x93894))),x93895)),f196(f875(f867(x93891),a862))))+P20(x93891,x93892,f332(f332(f310(f867(x93891)),f332(f332(f332(f93(x93891),x93893),f332(a28,x93894)),x93895)),f196(f875(f867(x93891),a862)))) % 165.28/165.05 [9417]~P24(f332(f62(x94173),f332(f311(x94172,x94173,x94175),f255(f875(x94172,a862)))))+P24(f332(f62(x94171),f332(f311(x94172,x94171,f332(f332(f8(x94173,x94171,x94172),x94174),x94175)),f255(f875(x94172,a862))))) % 165.28/165.05 [9438]P24(f332(f332(f246(f875(f875(x94381,a862),a862)),f332(f311(f875(x94382,a862),f875(x94381,a862),f311(x94382,x94381,x94383)),f332(f309(x94382),x94384))),f332(f309(x94381),x94385)))+~P24(f332(f332(f246(f875(x94381,a862)),f332(f311(x94382,x94381,x94383),x94384)),x94385)) % 165.28/165.05 [9448]~P24(f332(f62(f872(x94481)),f332(f311(x94482,f872(x94481),x94483),f255(f875(x94482,a862)))))+P24(f332(f62(f872(x94481)),f332(f311(x94482,f872(x94481),f332(f332(f332(f73(x94482,f872(x94481)),x94483),x94484),f332(f208(x94481),x94485))),f255(f875(x94482,a862))))) % 165.28/165.05 [9508]E(x95081,x95082)+~P24(f332(f67(x95083,x95084,x95085,x95081,f196(f875(x95083,a862))),x95082)) % 165.28/165.05 [9523]E(f332(f332(f267(x95231,x95232),f656(x95233,x95234,x95235,x95232,x95231)),f659(x95233,x95234,x95235,x95232,x95231)),x95235)+~P24(f332(f332(f334(f874(x95231,x95232)),x95235),f332(f332(f269(x95231,x95232),x95234),x95233))) % 165.28/165.05 [9615]P24(f332(f332(f334(x96151),f656(x96152,x96153,x96154,x96155,x96151)),x96153))+~P24(f332(f332(f334(f874(x96151,x96155)),x96154),f332(f332(f269(x96151,x96155),x96153),x96152))) % 165.28/165.05 [9724]P20(x97245,x97244,f332(f332(f310(f867(x97245)),f332(f332(f332(f93(x97245),x97241),x97243),x97242)),f196(f875(f867(x97245),a862))))+P24(f332(f332(x97241,f474(x97242,x97243,x97244,x97245,x97241)),f484(x97242,x97243,x97244,x97245,x97241))) % 165.28/165.05 [9777]P24(f332(f332(f334(x97771),f659(x97772,x97773,x97774,x97771,x97775)),f332(x97772,f656(x97772,x97773,x97774,x97771,x97775))))+~P24(f332(f332(f334(f874(x97775,x97771)),x97774),f332(f332(f269(x97775,x97771),x97773),x97772))) % 165.28/165.05 [9802]P24(f332(f332(f334(f874(x98021,x98021)),f332(f332(f267(x98021,x98021),x98022),f755(x98023,x98024,x98025,x98022,x98021))),x98023))+~P24(f332(f332(f334(f874(x98021,x98021)),f332(f332(f267(x98021,x98021),x98022),x98025)),f332(f332(f191(f874(x98021,x98021),a862),f332(a115,x98024)),x98023))) % 165.28/165.05 [9803]P24(f332(f332(f334(f874(x98031,x98031)),f332(f332(f267(x98031,x98031),x98032),f757(x98033,x98034,x98035,x98032,x98031))),x98033))+~P24(f332(f332(f334(f874(x98031,x98031)),f332(f332(f267(x98031,x98031),x98032),x98035)),f332(f332(f191(f874(x98031,x98031),a862),f332(a115,x98034)),x98033))) % 165.28/165.05 [9822]~P24(f332(f332(f334(f874(f869(x98221),f869(x98221))),f332(f332(f267(f869(x98221),f869(x98221)),f332(f332(f152(x98221),x98222),x98225)),x98224)),f159(x98221,x98223)))+P24(f332(f332(f334(f874(x98221,x98221)),f332(f332(f267(x98221,x98221),x98222),f564(x98223,x98224,x98225,x98222,x98221))),x98223)) % 165.28/165.05 [9824]~P20(x98241,x98242,f332(f332(f310(f867(x98241)),f332(f332(f332(f93(x98241),f95(x98241,x98243,x98244)),x98245),x98243)),f196(f875(f867(x98241),a862))))+P20(x98241,x98242,f332(f332(f310(f867(x98241)),f332(f332(f332(f93(x98241),x98243),f33(x98244,x98245)),f95(x98241,x98243,f332(f74(a862,a862,a864,a327),x98244)))),f196(f875(f867(x98241),a862)))) % 165.28/165.05 [9825]~P23(x98251,x98252,f332(f332(f310(f867(x98251)),f332(f332(f332(f93(x98251),f95(x98251,x98253,x98254)),x98255),x98253)),f196(f875(f867(x98251),a862))))+P23(x98251,x98252,f332(f332(f310(f867(x98251)),f332(f332(f332(f93(x98251),x98253),f33(x98254,x98255)),f95(x98251,x98253,f332(f74(a862,a862,a864,a327),x98254)))),f196(f875(f867(x98251),a862)))) % 165.28/165.05 [10083]P20(x100831,x100832,f332(f332(f310(f867(x100831)),f332(f332(f332(f93(x100831),x100833),x100834),x100835)),f196(f875(f867(x100831),a862))))+~P20(x100831,x100832,f332(f332(f310(f867(x100831)),f332(f332(f332(f93(x100831),f332(f16(f875(a864,a862),x100831),f332(f332(f7(a864,a864,a862),a329),f484(x100835,x100834,x100832,x100831,x100833)))),x100834),f332(f16(f875(a864,a862),x100831),f332(x100835,f474(x100835,x100834,x100832,x100831,x100833))))),f196(f875(f867(x100831),a862)))) % 165.28/165.05 [6326]P24(f332(x63262,x63264))+E(f179(x63261,x63262,f332(f332(f135(x63261),x63263),f332(f332(f152(x63261),x63264),x63265))),f179(x63261,x63262,x63263)) % 165.28/165.05 [6376]~P26(x63762)+E(f332(f332(f332(f113(f875(x63761,x63762)),x63763),x63764),x63765),f332(f332(f113(x63762),f332(x63763,x63765)),f332(x63764,x63765))) % 165.28/165.05 [6378]~P65(x63782)+E(f332(f332(f332(f22(f875(x63781,x63782)),x63783),x63784),x63785),f332(f332(f22(x63782),f332(x63783,x63785)),f332(x63784,x63785))) % 165.28/165.05 [6380]~P26(x63802)+E(f332(f332(f332(f104(f875(x63801,x63802)),x63803),x63804),x63805),f332(f332(f104(x63802),f332(x63803,x63805)),f332(x63804,x63805))) % 165.28/165.05 [6398]E(x63981,x63982)+E(f332(f332(f166(x63983),f332(f332(f160(x63983,x63984),x63981),x63985)),x63982),f332(f332(f166(x63983),x63984),x63982)) % 165.28/165.05 [6661]~E(x66614,f196(f875(x66613,a862)))+E(f332(f332(f113(f875(x66611,a862)),x66612),f332(f332(f42(x66613,f875(x66611,a862)),x66614),x66615)),x66612) % 165.28/165.05 [6662]~E(x66624,f196(f875(x66623,a862)))+E(f332(f332(f22(f875(x66621,a862)),x66622),f332(f332(f42(x66623,f875(x66621,a862)),x66624),x66625)),x66622) % 165.28/165.05 [6663]~E(x66634,f196(f875(x66633,a862)))+E(f332(f332(f104(f875(x66631,a862)),x66632),f332(f332(f43(x66633,f875(x66631,a862)),x66634),x66635)),x66632) % 165.28/165.05 [6677]~E(x66774,f196(f875(x66773,a862)))+E(f332(f332(f310(x66771),x66772),f332(f332(f42(x66773,f875(x66771,a862)),x66774),x66775)),f332(f332(f310(x66771),x66772),f196(f875(x66771,a862)))) % 165.28/165.05 [7463]E(f332(f332(f166(x74631),f332(f332(f155(x74632,x74631),x74633),x74634)),x74635),f332(x74633,f332(f332(f166(x74632),x74634),x74635)))+~P24(f332(f332(f247(a868),x74635),f332(f197(f869(x74632)),x74634))) % 165.28/165.05 [7530]E(f332(f332(f113(f875(x75301,a862)),f332(x75302,x75303)),f332(f332(f42(x75304,f875(x75301,a862)),x75305),x75302)),f332(f332(f42(x75304,f875(x75301,a862)),x75305),x75302))+~P24(f332(f332(f334(x75304),x75303),x75305)) % 165.28/165.05 [7531]E(f332(f332(f104(f875(x75311,a862)),f332(x75312,x75313)),f332(f332(f43(x75314,f875(x75311,a862)),x75315),x75312)),f332(f332(f43(x75314,f875(x75311,a862)),x75315),x75312))+~P24(f332(f332(f334(x75314),x75313),x75315)) % 165.28/165.05 [8127]~E(x81273,f196(f875(x81271,a862)))+E(f332(f332(f42(x81271,f875(x81272,a862)),x81273),f332(f332(f8(f875(x81272,a862),f875(x81272,a862),x81271),f332(f310(x81272),x81274)),x81275)),f196(f875(x81272,a862))) % 165.28/165.05 [8132]~P24(f332(f332(f334(x81324),x81323),x81325))+P24(f332(f332(f246(f875(x81321,a862)),f332(x81322,x81323)),f332(f332(f42(x81324,f875(x81321,a862)),x81325),x81322))) % 165.28/165.05 [8262]~E(f332(x82624,x82622),x82625)+P24(f332(f332(f334(x82621),x82622),f332(f312(x82621,x82623,x82624),f332(f332(f310(x82623),x82625),f196(f875(x82623,a862)))))) % 165.28/165.05 [8306]~P53(x83061,x83062,f332(f287(x83062,x83061),x83063))+E(f332(f332(f104(f875(x83061,a862)),f332(f286(x83062,x83061,x83063),x83064)),f332(f286(x83062,x83061,x83063),x83065)),f332(f286(x83062,x83061,x83063),f332(f332(f104(f875(x83062,a862)),x83064),x83065))) % 165.28/165.05 [8380]E(x83801,f2(a102))+E(f332(f121(x83802,x83803,f332(x83804,f332(f332(f22(a102),x83801),f79(a102)))),f332(f332(f7(x83802,a102,f870(x83803)),x83805),x83801)),f332(f207(x83802,x83803,x83804,x83805),x83801)) % 165.28/165.05 [8419]E(x84191,f196(f875(x84192,a862)))+E(f332(f332(f42(x84192,f875(x84193,a862)),x84191),f332(f332(f8(f875(x84193,a862),f875(x84193,a862),x84192),f332(f310(x84193),x84194)),x84195)),f332(f332(f310(x84193),x84194),f332(f332(f42(x84192,f875(x84193,a862)),x84191),x84195))) % 165.28/165.05 [8467]~P21(x84672,x84671,x84673,f255(f875(x84672,a862)))+E(f332(f332(f22(f875(x84671,a862)),f332(f311(x84672,x84671,x84673),x84674)),f332(f311(x84672,x84671,x84673),x84675)),f332(f311(x84672,x84671,x84673),f332(f332(f22(f875(x84672,a862)),x84674),x84675))) % 165.28/165.05 [8468]~P21(x84682,x84681,x84683,f255(f875(x84682,a862)))+E(f332(f332(f104(f875(x84681,a862)),f332(f311(x84682,x84681,x84683),x84684)),f332(f311(x84682,x84681,x84683),x84685)),f332(f311(x84682,x84681,x84683),f332(f332(f104(f875(x84682,a862)),x84684),x84685))) % 165.28/165.05 [8532]~P24(f332(f332(f68(x85321,x85322,x85325),x85323),x85324))+P24(f332(f332(f334(f874(x85321,x85322)),f332(f332(f267(x85321,x85322),x85323),x85324)),x85325)) % 165.28/165.05 [8564]P24(f332(f332(f334(x85641),x85642),f332(f263(x85643,x85641),x85644)))+~P24(f332(f332(f334(f874(x85643,x85641)),f332(f332(f267(x85643,x85641),x85645),x85642)),x85644)) % 165.28/165.05 [8566]P24(f332(f332(f334(x85661),x85662),f332(f265(x85661,x85663),x85664)))+~P24(f332(f332(f334(f874(x85661,x85663)),f332(f332(f267(x85661,x85663),x85662),x85665)),x85664)) % 165.28/165.05 [8699]P24(f332(f332(f68(x86991,x86992,x86993),x86994),x86995))+~P24(f332(f332(f334(f874(x86991,x86992)),f332(f332(f267(x86991,x86992),x86994),x86995)),x86993)) % 165.28/165.05 [8734]E(f332(x87341,x87342),x87343)+~P24(f332(f332(f334(x87344),x87342),f332(f312(x87344,x87345,x87341),f332(f332(f310(x87345),x87343),f196(f875(x87345,a862)))))) % 165.28/165.05 [8933]E(x89331,f2(a102))+E(f124(x89332,f123(x89333,f870(f872(x89332)),f332(f332(f7(x89333,a102,f870(f872(x89332))),x89334),x89331),f332(x89335,f332(f332(f22(a102),x89331),f79(a102))))),f332(f204(x89333,x89332,x89335,x89334),x89331)) % 165.28/165.05 [8958]P24(f332(f332(f334(f874(x89581,x89582)),f332(f332(f267(x89581,x89582),x89583),x89584)),f332(f287(x89582,x89581),x89585)))+~P24(f332(f332(f334(f874(x89582,x89581)),f332(f332(f267(x89582,x89581),x89584),x89583)),x89585)) % 165.28/165.05 [8976]~P24(f332(f332(x89761,x89765),x89764))+P24(f332(f332(x89761,f332(f270(x89762,x89763),f332(f332(f267(x89762,x89763),x89764),x89765))),f332(f266(x89762,x89763),f332(f332(f267(x89762,x89763),x89764),x89765)))) % 165.28/165.05 [9005]~P24(f332(f332(f334(f874(x90052,x90051)),f332(f332(f267(x90052,x90051),x90054),x90053)),f332(f287(x90051,x90052),x90055)))+P24(f332(f332(f334(f874(x90051,x90052)),f332(f332(f267(x90051,x90052),x90053),x90054)),x90055)) % 165.28/165.05 [9035]~P24(f332(f332(f334(f874(x90353,x90351)),f332(f332(f267(x90353,x90351),x90355),x90352)),x90354))+P24(f332(f332(f334(x90351),x90352),f332(f286(x90353,x90351,x90354),f332(f332(f310(x90353),x90355),f196(f875(x90353,a862)))))) % 165.28/165.05 [9081]P24(f332(f332(f334(f874(x90811,x90812)),f332(f332(f267(x90811,x90812),x90813),x90814)),x90815))+~P24(f332(f332(f334(x90812),x90814),f332(f286(x90811,x90812,x90815),f332(f332(f310(x90811),x90813),f196(f875(x90811,a862)))))) % 165.28/165.05 [9101]E(f332(f332(f332(f73(x91011,f872(x91012)),f190(x91011,x91012,x91013,x91014)),x91015),f209(x91012)),f190(x91011,x91012,x91013,f332(f332(f22(f875(x91011,a862)),x91014),f332(f332(f310(x91011),x91015),f196(f875(x91011,a862))))))+~P24(f332(f332(f334(x91011),x91015),x91014)) % 165.28/165.05 [9167]~P74(x91671)+E(f332(f332(f6(a868,x91671),x91672),f303(a868,f332(f332(f81(a868),x91673),x91674),f332(f332(f81(a868),x91675),x91674))),f332(f332(f6(a868,x91671),f332(f332(f8(a868,x91671,a868),x91672),f332(f332(f7(a868,a868,a868),f81(a868)),x91674))),f303(a868,x91673,x91675))) % 165.28/165.05 [9185]~P74(x91851)+E(f332(f332(f6(a868,x91851),x91852),f332(f302(a868,f332(f332(f81(a868),x91853),x91854)),f332(f332(f81(a868),x91855),x91854))),f332(f332(f6(a868,x91851),f332(f332(f8(a868,x91851,a868),x91852),f332(f332(f7(a868,a868,a868),f81(a868)),x91854))),f332(f302(a868,x91853),x91855))) % 165.28/165.05 [9236]~P21(x92361,x92362,x92363,f255(f875(x92361,a862)))+E(f332(f332(f155(x92361,x92362),x92363),f332(f137(x92361,f332(f332(f8(a862,a862,x92361),a327),f332(a329,x92364))),x92365)),f332(f137(x92362,f332(f332(f8(a862,a862,x92362),a327),f332(a329,f332(x92363,x92364)))),f332(f332(f155(x92361,x92362),x92363),x92365))) % 165.28/165.05 [9252]~P21(x92521,x92522,x92523,f332(f332(f310(x92521),x92524),f332(f174(x92521),x92525)))+E(f332(f332(f155(x92521,x92522),x92523),f332(f137(x92521,f332(f332(f8(a862,a862,x92521),a327),f332(a329,x92524))),x92525)),f332(f137(x92522,f332(f332(f8(a862,a862,x92522),a327),f332(a329,f332(x92523,x92524)))),f332(f332(f155(x92521,x92522),x92523),x92525))) % 165.28/165.05 [9404]P24(f332(f332(f334(f874(f869(x94041),f869(x94041))),f332(f332(f267(f869(x94041),f869(x94041)),f332(f332(f152(x94041),x94042),x94043)),f332(f332(f152(x94041),x94044),x94043))),f158(x94041,x94045)))+~P24(f332(f332(f334(f874(x94041,x94041)),f332(f332(f267(x94041,x94041),x94042),x94044)),x94045)) % 165.28/165.05 [9506]P20(x95061,x95062,f332(f332(f310(f867(x95061)),f332(f332(f332(f93(x95061),x95063),f332(a28,x95064)),x95065)),f196(f875(f867(x95061),a862))))+~P20(x95061,f332(f332(f310(f867(x95061)),f332(f332(f332(f93(x95061),x95063),f332(a28,x95064)),x95065)),x95062),f332(f332(f310(f867(x95061)),f332(f332(f332(f93(x95061),x95063),f332(f243(a863),f332(a26,x95064))),x95065)),f196(f875(f867(x95061),a862)))) % 165.28/165.05 [9518]E(f332(f332(f310(x95181),f829(x95182,x95183,x95184,x95185,x95181)),f830(x95182,x95183,x95184,x95185,x95181)),f332(f332(f310(x95181),x95184),x95183))+~P24(f332(f63(x95181,x95185,f332(f332(f310(x95181),x95184),x95183)),x95182)) % 165.28/165.05 [9519]E(f332(f332(f310(x95191),f831(x95192,x95193,x95194,x95195,x95191)),f832(x95192,x95193,x95194,x95195,x95191)),f332(f332(f310(x95191),x95194),x95193))+~P24(f332(f63(x95191,x95195,f332(f332(f310(x95191),x95194),x95193)),x95192)) % 165.28/165.05 [9601]P24(f332(f332(f334(x96011),f603(x96012,x96013,x96014,x96015,x96011)),x96014))+P24(f332(f332(f332(f43(x96011,f875(x96015,a862)),x96014),x96013),x96012)) % 165.28/165.05 [9606]P24(f332(f332(f334(x96061),f601(x96062,x96063,x96061,x96064,x96065)),x96063))+P24(f332(f332(f334(x96065),x96064),f332(f332(f43(x96061,f875(x96065,a862)),x96063),x96062))) % 165.28/165.05 [9614]P24(f332(f332(f334(x96141),f600(x96142,x96143,x96141,x96144,x96145)),x96143))+P24(f332(f332(f246(f875(x96145,a862)),x96144),f332(f332(f43(x96141,f875(x96145,a862)),x96143),x96142))) % 165.28/165.05 [9616]P24(f332(f332(x96161,f468(x96162,x96161,x96163,x96164,x96165)),x96162))+~P24(f332(f332(f332(f42(x96165,f875(x96164,a862)),x96163),x96161),x96162)) % 165.28/165.05 [9619]P24(f332(f332(f334(x96191),f468(x96192,x96193,x96194,x96195,x96191)),x96194))+~P24(f332(f332(f332(f42(x96191,f875(x96195,a862)),x96194),x96193),x96192)) % 165.28/165.05 [9620]P43(x96204,f332(f332(f43(x96201,f875(x96204,a862)),x96205),x96203),f332(f332(f43(x96201,f875(f874(x96204,x96204),a862)),x96205),x96202))+P24(f332(f332(f334(x96201),f808(x96202,x96203,x96204,x96205,x96201)),x96205)) % 165.28/165.05 [9630]P24(f332(f332(f334(x96301),f473(x96302,x96303,x96301,x96304,x96305)),x96303))+~P24(f332(f332(f334(x96305),x96304),f332(f332(f42(x96301,f875(x96305,a862)),x96303),x96302))) % 165.28/165.05 [9635]P24(f332(f332(f334(x96351),x96352),f332(x96353,f473(x96353,x96354,x96355,x96352,x96351))))+~P24(f332(f332(f334(x96351),x96352),f332(f332(f42(x96355,f875(x96351,a862)),x96354),x96353))) % 165.28/165.05 [9729]~P24(f332(f332(x97294,f603(x97295,x97294,x97293,x97292,x97291)),x97295))+P24(f332(f332(f332(f43(x97291,f875(x97292,a862)),x97293),x97294),x97295)) % 165.28/165.05 [9732]~P24(f332(f332(f334(x97321),x97322),f332(x97325,f601(x97325,x97324,x97323,x97322,x97321))))+P24(f332(f332(f334(x97321),x97322),f332(f332(f43(x97323,f875(x97321,a862)),x97324),x97325))) % 165.28/165.05 [9736]~P43(x97361,f332(x97364,f808(x97365,x97364,x97361,x97363,x97362)),f332(x97365,f808(x97365,x97364,x97361,x97363,x97362)))+P43(x97361,f332(f332(f43(x97362,f875(x97361,a862)),x97363),x97364),f332(f332(f43(x97362,f875(f874(x97361,x97361),a862)),x97363),x97365)) % 165.28/165.05 [9737]~P24(f332(f332(f246(f875(x97371,a862)),x97372),f332(x97375,f600(x97375,x97374,x97373,x97372,x97371))))+P24(f332(f332(f246(f875(x97371,a862)),x97372),f332(f332(f43(x97373,f875(x97371,a862)),x97374),x97375))) % 165.28/165.05 [9807]~P24(f332(f332(f334(x98071),f829(x98075,x98074,x98073,x98072,x98071)),f830(x98075,x98074,x98073,x98072,x98071)))+~P24(f332(f63(x98071,x98072,f332(f332(f310(x98071),x98073),x98074)),x98075)) % 165.28/165.05 [9808]~P24(f332(f332(f334(x98081),f831(x98085,x98084,x98083,x98082,x98081)),f832(x98085,x98084,x98083,x98082,x98081)))+~P24(f332(f63(x98081,x98082,f332(f332(f310(x98081),x98083),x98084)),x98085)) % 165.28/165.05 [9809]~P24(f332(f332(f334(f874(x98091,x98091)),f332(f332(f267(x98091,x98091),x98092),x98095)),f332(f332(f191(f874(x98091,x98091),a862),f332(a115,x98094)),x98093)))+P24(f332(f332(f334(f874(x98091,x98091)),f332(f332(f267(x98091,x98091),x98092),f756(x98093,x98094,x98095,x98092,x98091))),f332(f332(f191(f874(x98091,x98091),a862),x98094),x98093))) % 165.28/165.05 [9816]P24(f332(f67(x98161,x98161,x98162,f829(x98163,x98164,x98165,x98162,x98161),f830(x98163,x98164,x98165,x98162,x98161)),x98163))+~P24(f332(f63(x98161,x98162,f332(f332(f310(x98161),x98165),x98164)),x98163)) % 165.28/165.05 [9817]P24(f332(f67(x98171,x98171,x98172,f831(x98173,x98174,x98175,x98172,x98171),f832(x98173,x98174,x98175,x98172,x98171)),x98173))+~P24(f332(f63(x98171,x98172,f332(f332(f310(x98171),x98175),x98174)),x98173)) % 165.28/165.05 [9829]~P106(x98291)+P32(x98291,f332(f332(f155(x98292,x98291),x98293),f332(f137(x98292,f332(f332(f7(x98292,x98291,a862),f332(f332(f8(x98291,f875(x98291,a862),x98292),a329),x98293)),f332(x98294,x98295))),x98295))) % 165.28/165.05 [9869]~P24(f332(f332(f334(x98692),x98695),f332(f286(x98691,x98692,x98694),x98693)))+P24(f332(f332(f334(f874(x98691,x98692)),f332(f332(f267(x98691,x98692),f491(x98693,x98694,x98691,x98695,x98692)),x98695)),x98694)) % 165.28/165.05 [9870]~P24(f332(f332(f334(x98702),x98705),f332(f286(x98701,x98702,x98704),x98703)))+P24(f332(f332(f334(f874(x98701,x98702)),f332(f332(f267(x98701,x98702),f518(x98703,x98704,x98701,x98705,x98702)),x98705)),x98704)) % 165.28/165.05 [9890]~P24(f332(f332(f334(f874(x98901,x98901)),f332(f332(f267(x98901,x98901),x98905),x98904)),f332(f332(f191(f874(x98901,x98901),a862),f332(a115,x98903)),x98902)))+P24(f332(f332(f334(f874(x98901,x98901)),f332(f332(f267(x98901,x98901),f756(x98902,x98903,x98904,x98905,x98901)),x98904)),x98902)) % 165.28/165.05 [9893]~P24(f332(f332(f334(f874(x98931,x98931)),f332(f332(f267(x98931,x98931),x98935),x98934)),f332(f332(f191(f874(x98931,x98931),a862),f332(a115,x98933)),x98932)))+P24(f332(f332(f334(f874(x98931,x98931)),f332(f332(f267(x98931,x98931),f755(x98932,x98933,x98934,x98935,x98931)),x98934)),f332(f332(f191(f874(x98931,x98931),a862),x98933),x98932))) % 165.28/165.05 [9894]~P24(f332(f332(f334(f874(x98941,x98941)),f332(f332(f267(x98941,x98941),x98945),x98944)),f332(f332(f191(f874(x98941,x98941),a862),f332(a115,x98943)),x98942)))+P24(f332(f332(f334(f874(x98941,x98941)),f332(f332(f267(x98941,x98941),f757(x98942,x98943,x98944,x98945,x98941)),x98944)),f332(f332(f191(f874(x98941,x98941),a862),x98943),x98942))) % 165.28/165.05 [9895]~P24(f332(f332(f334(f874(f869(x98951),f869(x98951))),f332(f332(f267(f869(x98951),f869(x98951)),x98955),f332(f332(f152(x98951),x98954),x98953))),f159(x98951,x98952)))+P24(f332(f332(f334(f874(x98951,x98951)),f332(f332(f267(x98951,x98951),f562(x98952,x98953,x98954,x98955,x98951)),x98954)),x98952)) % 165.28/165.05 [7060]E(x70601,f209(x70602))+E(f186(x70603,x70602,f332(f332(f332(f73(x70603,f872(x70602)),x70604),x70605),x70601)),f332(f332(f310(x70603),x70605),f186(x70603,x70602,x70604))) % 165.28/165.05 [7551]~E(x75513,f196(f875(x75512,a862)))+E(f332(f332(f113(f875(x75511,a862)),f332(f332(f42(x75512,f875(x75511,a862)),x75513),x75514)),x75515),x75515) % 165.28/165.05 [7552]~E(x75523,f196(f875(x75522,a862)))+E(f332(f332(f104(f875(x75521,a862)),f332(f332(f43(x75522,f875(x75521,a862)),x75523),x75524)),x75525),x75525) % 165.28/165.05 [7907]~E(x79075,f209(x79072))+E(f186(x79071,x79072,f332(f332(f332(f73(x79071,f872(x79072)),x79073),x79074),x79075)),f332(f332(f22(f875(x79071,a862)),f186(x79071,x79072,x79073)),f332(f332(f310(x79071),x79074),f196(f875(x79071,a862))))) % 165.28/165.05 [7974]~E(x79743,f196(f875(x79742,a862)))+E(f332(f332(f22(f875(x79741,a862)),f332(f332(f43(x79742,f875(x79741,a862)),x79743),x79744)),x79745),f332(f332(f22(f875(x79741,a862)),f255(f875(x79741,a862))),x79745)) % 165.28/165.05 [8099]E(f332(f332(f160(x80991,f332(f332(f135(x80991),x80992),x80993)),x80994),x80995),f332(f332(f135(x80991),f332(f332(f160(x80991,x80992),x80994),x80995)),x80993))+~P24(f332(f332(f247(a868),x80994),f332(f197(f869(x80991)),x80992))) % 165.28/165.05 [8214]P24(f332(f332(f334(x82141),x82145),f332(f174(x82141),x82143)))+E(f332(f332(f180(x82141,x82142),f332(f332(f184(x82141,x82142),x82143),f332(f332(f155(x82141,x82142),x82144),x82143))),x82145),f209(x82142)) % 165.28/165.05 [8333]~P24(f332(f332(f334(x83331),x83335),f332(f174(x83331),x83333)))+E(f332(f332(f180(x83331,x83332),f332(f332(f184(x83331,x83332),x83333),f332(f332(f155(x83331,x83332),x83334),x83333))),x83335),f332(f208(x83332),f332(x83334,x83335))) % 165.28/165.05 [8370]E(f332(f332(f166(x83701),f332(f332(f155(a868,x83701),x83702),f140(a868,f332(f302(a868,x83703),x83704)))),x83705),f332(x83702,f332(f332(f81(a868),x83703),x83705)))+~P24(f332(f332(f247(a868),x83705),f332(f332(f22(a868),x83704),x83703))) % 165.28/165.05 [8409]~E(x84093,f196(f875(x84091,a862)))+E(f332(f332(f42(x84091,f875(x84092,a862)),x84093),f332(f332(f8(f875(x84092,a862),f875(x84092,a862),x84091),f332(f113(f875(x84092,a862)),x84094)),x84095)),f196(f875(x84092,a862))) % 165.28/165.05 [8410]~E(x84103,f196(f875(x84101,a862)))+E(f332(f332(f43(x84101,f875(x84102,a862)),x84103),f332(f332(f8(f875(x84102,a862),f875(x84102,a862),x84101),f332(f22(f875(x84102,a862)),x84104)),x84105)),f255(f875(x84102,a862))) % 165.28/165.05 [8411]~E(x84113,f196(f875(x84111,a862)))+E(f332(f332(f43(x84111,f875(x84112,a862)),x84113),f332(f332(f8(f875(x84112,a862),f875(x84112,a862),x84111),f332(f104(f875(x84112,a862)),x84114)),x84115)),f255(f875(x84112,a862))) % 165.28/165.05 [8413]~P140(x84132)+E(f332(f332(f6(x84131,x84132),f332(f332(f8(x84132,x84132,x84131),f332(f82(x84132),x84133)),x84134)),x84135),f332(f332(f82(x84132),x84133),f332(f332(f6(x84131,x84132),x84134),x84135))) % 165.28/165.05 [8684]E(x86841,f196(f875(x86842,a862)))+E(f332(f332(f42(x86842,f875(x86843,a862)),x86841),f332(f332(f8(f875(x86843,a862),f875(x86843,a862),x86842),f332(f113(f875(x86843,a862)),x86844)),x86845)),f332(f332(f113(f875(x86843,a862)),x86844),f332(f332(f42(x86842,f875(x86843,a862)),x86841),x86845))) % 165.28/165.05 [8685]E(x86851,f196(f875(x86852,a862)))+E(f332(f332(f43(x86852,f875(x86853,a862)),x86851),f332(f332(f8(f875(x86853,a862),f875(x86853,a862),x86852),f332(f22(f875(x86853,a862)),x86854)),x86855)),f332(f332(f22(f875(x86853,a862)),x86854),f332(f332(f42(x86852,f875(x86853,a862)),x86851),x86855))) % 165.28/165.05 [8686]E(x86861,f196(f875(x86862,a862)))+E(f332(f332(f43(x86862,f875(x86863,a862)),x86861),f332(f332(f8(f875(x86863,a862),f875(x86863,a862),x86862),f332(f104(f875(x86863,a862)),x86864)),x86865)),f332(f332(f104(f875(x86863,a862)),x86864),f332(f332(f43(x86862,f875(x86863,a862)),x86861),x86865))) % 165.28/165.05 [8880]~P24(f332(f332(f247(a868),f332(x88804,x88802)),f332(x88804,x88803)))+P24(f332(f332(f334(f874(x88801,x88801)),f332(f332(f267(x88801,x88801),x88802),x88803)),f154(x88801,f332(f332(f152(f875(x88801,a868)),x88804),x88805)))) % 165.28/165.05 [9134]~P21(x91342,x91341,x91343,f332(f332(f113(f875(x91342,a862)),x91344),x91345))+E(f332(f332(f104(f875(x91341,a862)),f332(f311(x91342,x91341,x91343),f332(f332(f22(f875(x91342,a862)),x91344),x91345))),f332(f311(x91342,x91341,x91343),f332(f332(f22(f875(x91342,a862)),x91345),x91344))),f196(f875(x91341,a862))) % 165.28/165.05 [9400]~P24(f332(f332(f246(f875(x94003,a862)),f332(f286(x94001,x94003,x94004),x94002)),x94005))+P24(f332(f332(f246(f875(x94001,a862)),x94002),f332(f80(f875(x94001,a862)),f332(f286(x94003,x94001,f332(f287(x94001,x94003),x94004)),f332(f80(f875(x94003,a862)),x94005))))) % 165.28/165.05 [9424]~P21(x94241,x94242,x94243,f332(f332(f310(x94241),x94244),x94245))+~P24(f332(f332(f334(x94242),f332(x94243,x94244)),f332(f311(x94241,x94242,x94243),f332(f332(f22(f875(x94241,a862)),x94245),f332(f332(f310(x94241),x94244),f196(f875(x94241,a862))))))) % 165.28/165.05 [9472]P24(f332(f332(f246(f875(x94721,a862)),f332(f286(x94722,x94721,x94723),x94724)),x94725))+~P24(f332(f332(f246(f875(x94722,a862)),x94724),f332(f80(f875(x94722,a862)),f332(f286(x94721,x94722,f332(f287(x94722,x94721),x94723)),f332(f80(f875(x94721,a862)),x94725))))) % 165.28/165.05 [9546]~P85(x95461)+P24(f332(f332(f246(x95461),f332(f76(x95461),f332(f332(f22(x95461),f332(f332(f81(x95461),x95462),x95463)),f332(f332(f81(x95461),x95464),x95465)))),f332(f332(f81(x95461),f332(f76(x95461),f332(f332(f22(x95461),x95462),x95464))),f332(f76(x95461),f332(f332(f22(x95461),x95463),x95465))))) % 165.28/165.05 [9650]P24(f332(f332(f334(x96501),f477(x96502,x96503,x96504,x96501,x96505)),x96504))+P24(f332(f332(f246(f875(x96505,a862)),f332(f332(f42(x96501,f875(x96505,a862)),x96504),x96503)),x96502)) % 165.28/165.05 [9847]~P24(f332(f332(f246(f875(x98471,a862)),f332(x98474,f477(x98475,x98474,x98473,x98472,x98471))),x98475))+P24(f332(f332(f246(f875(x98471,a862)),f332(f332(f42(x98472,f875(x98471,a862)),x98473),x98474)),x98475)) % 165.28/165.05 [8513]E(f332(f332(f135(x85131),x85132),f332(f332(f160(x85131,x85133),f332(f332(f22(a868),x85134),f332(f197(f869(x85131)),x85132))),x85135)),f332(f332(f160(x85131,f332(f332(f135(x85131),x85132),x85133)),x85134),x85135))+P24(f332(f332(f247(a868),x85134),f332(f197(f869(x85131)),x85132))) % 165.28/165.05 [8540]~P124(x85401)+E(f332(f332(f81(x85401),f332(f332(f82(x85401),x85402),x85403)),f332(f332(f81(x85401),f332(f332(f82(x85401),x85404),x85403)),x85405)),f332(f332(f81(x85401),f332(f332(f82(x85401),f332(f332(f81(x85401),x85402),x85404)),x85403)),x85405)) % 165.28/165.05 [9091]~P140(x90911)+E(f332(f167(x90911),f332(f332(f155(x90912,x90911),f332(f332(f8(x90911,x90911,x90912),f332(f82(x90911),x90913)),x90914)),x90915)),f332(f332(f82(x90911),x90913),f332(f167(x90911),f332(f332(f155(x90912,x90911),x90914),x90915)))) % 165.28/165.05 [9251]E(f332(f197(f869(x92511)),f332(f332(f177(x92511),f332(f332(f244(a868),f332(f197(f869(x92511)),x92512)),f332(f197(f869(x92513)),x92514))),x92512)),f332(f197(f869(x92513)),f332(f332(f177(x92513),f332(f332(f244(a868),f332(f197(f869(x92511)),x92512)),f332(f197(f869(x92513)),x92514))),x92514)))+P24(f332(x92515,f332(f332(f184(x92511,x92513),x92512),x92514))) % 165.28/165.05 [9483]~P140(x94832)+E(f332(f332(f6(x94831,x94832),f332(f332(f7(x94831,x94832,x94832),f332(f332(f8(x94832,f875(x94832,x94832),x94831),f82(x94832)),x94833)),x94834)),x94835),f332(f332(f82(x94832),f332(f332(f6(x94831,x94832),x94833),x94835)),x94834)) % 165.28/165.05 [9484]~P61(x94842)+E(f332(f332(f6(x94841,x94842),f332(f332(f7(x94841,x94842,x94842),f332(f332(f8(x94842,f875(x94842,x94842),x94841),f290(x94842)),x94843)),x94844)),x94845),f332(f332(f290(x94842),f332(f332(f6(x94841,x94842),x94843),x94845)),x94844)) % 165.28/165.05 [9491]~P66(x94912)+E(f332(f332(f6(x94911,x94912),f332(f332(f18(x94911,x94912,x94912),f332(f332(f8(x94912,f875(x94912,x94912),x94911),f22(x94912)),x94913)),x94914)),x94915),f332(f332(f22(x94912),f332(f332(f6(x94911,x94912),x94913),x94915)),f332(f332(f6(x94911,x94912),x94914),x94915))) % 165.28/165.05 [9492]~P74(x94922)+E(f332(f332(f6(x94921,x94922),f332(f332(f18(x94921,x94922,x94922),f332(f332(f8(x94922,f875(x94922,x94922),x94921),f81(x94922)),x94923)),x94924)),x94925),f332(f332(f81(x94922),f332(f332(f6(x94921,x94922),x94923),x94925)),f332(f332(f6(x94921,x94922),x94924),x94925))) % 165.28/165.05 [9493]~P73(x94932)+E(f332(f332(f9(x94931,x94932),f332(f332(f18(x94931,x94932,x94932),f332(f332(f8(x94932,f875(x94932,x94932),x94931),f82(x94932)),x94933)),x94934)),x94935),f332(f332(f82(x94932),f332(f332(f9(x94931,x94932),x94933),x94935)),f332(f332(f9(x94931,x94932),x94934),x94935))) % 165.28/165.05 [9531]~E(x95313,f196(f875(x95311,a862)))+E(f332(f332(f42(x95311,f875(x95312,a862)),x95313),f332(f332(f7(x95311,f875(x95312,a862),f875(x95312,a862)),f332(f332(f8(f875(x95312,a862),f875(f875(x95312,a862),f875(x95312,a862)),x95311),f113(f875(x95312,a862))),x95314)),x95315)),f196(f875(x95312,a862))) % 165.28/165.05 [9532]~E(x95323,f196(f875(x95321,a862)))+E(f332(f332(f43(x95321,f875(x95322,a862)),x95323),f332(f332(f7(x95321,f875(x95322,a862),f875(x95322,a862)),f332(f332(f8(f875(x95322,a862),f875(f875(x95322,a862),f875(x95322,a862)),x95321),f22(f875(x95322,a862))),x95324)),x95325)),f255(f875(x95322,a862))) % 165.28/165.05 [9533]~E(x95333,f196(f875(x95331,a862)))+E(f332(f332(f43(x95331,f875(x95332,a862)),x95333),f332(f332(f7(x95331,f875(x95332,a862),f875(x95332,a862)),f332(f332(f8(f875(x95332,a862),f875(f875(x95332,a862),f875(x95332,a862)),x95331),f104(f875(x95332,a862))),x95334)),x95335)),f255(f875(x95332,a862))) % 165.28/165.05 [9554]E(x95541,f196(f875(x95542,a862)))+E(f332(f332(f42(x95542,f875(x95543,a862)),x95541),f332(f332(f7(x95542,f875(x95543,a862),f875(x95543,a862)),f332(f332(f8(f875(x95543,a862),f875(f875(x95543,a862),f875(x95543,a862)),x95542),f113(f875(x95543,a862))),x95544)),x95545)),f332(f332(f113(f875(x95543,a862)),f332(f332(f42(x95542,f875(x95543,a862)),x95541),x95544)),x95545)) % 165.28/165.05 [9555]E(x95551,f196(f875(x95552,a862)))+E(f332(f332(f43(x95552,f875(x95553,a862)),x95551),f332(f332(f7(x95552,f875(x95553,a862),f875(x95553,a862)),f332(f332(f8(f875(x95553,a862),f875(f875(x95553,a862),f875(x95553,a862)),x95552),f22(f875(x95553,a862))),x95554)),x95555)),f332(f332(f22(f875(x95553,a862)),f332(f332(f43(x95552,f875(x95553,a862)),x95551),x95554)),x95555)) % 165.28/165.05 [9556]E(x95561,f196(f875(x95562,a862)))+E(f332(f332(f43(x95562,f875(x95563,a862)),x95561),f332(f332(f7(x95562,f875(x95563,a862),f875(x95563,a862)),f332(f332(f8(f875(x95563,a862),f875(f875(x95563,a862),f875(x95563,a862)),x95562),f104(f875(x95563,a862))),x95564)),x95565)),f332(f332(f104(f875(x95563,a862)),f332(f332(f43(x95562,f875(x95563,a862)),x95561),x95564)),x95565)) % 165.28/165.05 [9141]~P24(f332(f332(f246(a868),x91411),x91414))+E(f332(f332(f22(a868),f332(f332(f81(a868),f332(f332(f82(a868),x91411),x91412)),x91413)),f332(f332(f81(a868),f332(f332(f82(a868),x91414),x91412)),x91415)),f332(f332(f22(a868),x91413),f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x91414),x91411)),x91412)),x91415))) % 165.28/165.05 [9710]~P140(x97101)+E(f332(f167(x97101),f332(f332(f155(x97102,x97101),f332(f332(f7(x97102,x97101,x97101),f332(f332(f8(x97101,f875(x97101,x97101),x97102),f82(x97101)),x97103)),x97104)),x97105)),f332(f332(f82(x97101),f332(f167(x97101),f332(f332(f155(x97102,x97101),x97103),x97105))),x97104)) % 165.28/165.05 [9716]~P66(x97161)+E(f332(f167(x97161),f332(f332(f155(x97162,x97161),f332(f332(f18(x97162,x97161,x97161),f332(f332(f8(x97161,f875(x97161,x97161),x97162),f22(x97161)),x97163)),x97164)),x97165)),f332(f332(f22(x97161),f332(f167(x97161),f332(f332(f155(x97162,x97161),x97163),x97165))),f332(f167(x97161),f332(f332(f155(x97162,x97161),x97164),x97165)))) % 165.28/165.05 [9717]~P74(x97171)+E(f332(f167(x97171),f332(f332(f155(x97172,x97171),f332(f332(f18(x97172,x97171,x97171),f332(f332(f8(x97171,f875(x97171,x97171),x97172),f81(x97171)),x97173)),x97174)),x97175)),f332(f332(f81(x97171),f332(f167(x97171),f332(f332(f155(x97172,x97171),x97173),x97175))),f332(f167(x97171),f332(f332(f155(x97172,x97171),x97174),x97175)))) % 165.28/165.05 [9860]P24(f332(x98601,f332(f332(f184(x98602,x98603),x98604),x98605)))+~P24(f332(x98601,f332(f332(f184(x98602,x98603),f332(f332(f177(x98602),f332(f332(f244(a868),f332(f197(f869(x98602)),x98604)),f332(f197(f869(x98603)),x98605))),x98604)),f332(f332(f177(x98603),f332(f332(f244(a868),f332(f197(f869(x98602)),x98604)),f332(f197(f869(x98603)),x98605))),x98605)))) % 165.28/165.05 [10092]~P24(f332(f332(f334(f874(x100922,x100921)),f332(f332(f267(x100922,x100921),x100924),x100925)),f332(f287(x100921,x100922),x100923)))+P24(f332(f332(f256(x100921,x100922,f332(f332(f7(x100921,f875(f874(x100921,x100922),a862),f875(x100922,a862)),f332(f332(f8(f875(x100922,f875(f875(f874(x100921,x100922),a862),a862)),f875(f875(f874(x100921,x100922),a862),f875(x100922,a862)),x100921),f7(x100922,f875(f874(x100921,x100922),a862),a862)),f332(f332(f8(f875(x100922,f874(x100921,x100922)),f875(x100922,f875(f875(f874(x100921,x100922),a862),a862)),x100921),f332(f8(f874(x100921,x100922),f875(f875(f874(x100921,x100922),a862),a862),x100922),f334(f874(x100921,x100922)))),f267(x100921,x100922)))),x100923)),x100924),x100925)) % 165.28/165.05 [10101]P24(f332(f332(f334(f874(x101011,x101012)),f332(f332(f267(x101011,x101012),x101013),x101014)),f332(f287(x101012,x101011),x101015)))+~P24(f332(f332(f256(x101012,x101011,f332(f332(f7(x101012,f875(f874(x101012,x101011),a862),f875(x101011,a862)),f332(f332(f8(f875(x101011,f875(f875(f874(x101012,x101011),a862),a862)),f875(f875(f874(x101012,x101011),a862),f875(x101011,a862)),x101012),f7(x101011,f875(f874(x101012,x101011),a862),a862)),f332(f332(f8(f875(x101011,f874(x101012,x101011)),f875(x101011,f875(f875(f874(x101012,x101011),a862),a862)),x101012),f332(f8(f874(x101012,x101011),f875(f875(f874(x101012,x101011),a862),a862),x101011),f334(f874(x101012,x101011)))),f267(x101012,x101011)))),x101015)),x101013),x101014)) % 165.28/165.05 [9369]~P24(f332(f332(f246(a868),x93694),x93691))+E(f332(f332(f22(a868),f332(f332(f81(a868),f332(f332(f82(a868),x93691),x93692)),x93693)),f332(f332(f81(a868),f332(f332(f82(a868),x93694),x93692)),x93695)),f332(f332(f22(a868),f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x93691),x93694)),x93692)),x93693)),x93695)) % 165.28/165.05 [10110]P20(x101101,x101102,f332(f311(a865,f867(x101101),f332(f332(f18(a865,f875(x101101,f875(a864,a862)),f867(x101101)),f332(f332(f18(a865,a863,f875(f875(x101101,f875(a864,a862)),f867(x101101))),f332(f332(f8(f875(x101101,f875(a864,a862)),f875(a863,f875(f875(x101101,f875(a864,a862)),f867(x101101))),a865),f93(x101101)),x101103)),a28)),x101104)),x101105))+~P20(x101101,f332(f332(f113(f875(f867(x101101),a862)),x101102),f332(f311(a865,f867(x101101),f332(f332(f18(a865,f875(x101101,f875(a864,a862)),f867(x101101)),f332(f332(f18(a865,a863,f875(f875(x101101,f875(a864,a862)),f867(x101101))),f332(f332(f8(f875(x101101,f875(a864,a862)),f875(a863,f875(f875(x101101,f875(a864,a862)),f867(x101101))),a865),f93(x101101)),x101103)),a28)),x101104)),x101105)),f332(f311(a865,f867(x101101),f332(f332(f18(a865,f875(x101101,f875(a864,a862)),f867(x101101)),f332(f332(f18(a865,a863,f875(f875(x101101,f875(a864,a862)),f867(x101101))),f332(f332(f8(f875(x101101,f875(a864,a862)),f875(a863,f875(f875(x101101,f875(a864,a862)),f867(x101101))),a865),f93(x101101)),x101103)),f332(f332(f8(f872(a863),a863,a865),f243(a863)),a26))),x101104)),x101105)) % 165.28/165.05 [10111]P23(x101111,x101112,f332(f311(a865,f867(x101111),f332(f332(f18(a865,f875(x101111,f875(a864,a862)),f867(x101111)),f332(f332(f18(a865,a863,f875(f875(x101111,f875(a864,a862)),f867(x101111))),f332(f332(f8(f875(x101111,f875(a864,a862)),f875(a863,f875(f875(x101111,f875(a864,a862)),f867(x101111))),a865),f93(x101111)),x101113)),a28)),x101114)),x101115))+~P23(x101111,f332(f332(f113(f875(f867(x101111),a862)),x101112),f332(f311(a865,f867(x101111),f332(f332(f18(a865,f875(x101111,f875(a864,a862)),f867(x101111)),f332(f332(f18(a865,a863,f875(f875(x101111,f875(a864,a862)),f867(x101111))),f332(f332(f8(f875(x101111,f875(a864,a862)),f875(a863,f875(f875(x101111,f875(a864,a862)),f867(x101111))),a865),f93(x101111)),x101113)),a28)),x101114)),x101115)),f332(f311(a865,f867(x101111),f332(f332(f18(a865,f875(x101111,f875(a864,a862)),f867(x101111)),f332(f332(f18(a865,a863,f875(f875(x101111,f875(a864,a862)),f867(x101111))),f332(f332(f8(f875(x101111,f875(a864,a862)),f875(a863,f875(f875(x101111,f875(a864,a862)),f867(x101111))),a865),f93(x101111)),x101113)),f332(f332(f8(f872(a863),a863,a865),f243(a863)),a26))),x101114)),x101115)) % 165.28/165.05 [5247]E(x52471,x52472)+~E(f29(x52473,x52474,x52471),f29(x52475,x52476,x52472)) % 165.28/165.05 [5248]E(x52481,x52482)+~E(f29(x52483,x52481,x52484),f29(x52485,x52482,x52486)) % 165.28/165.05 [5249]E(x52491,x52492)+~E(f29(x52491,x52493,x52494),f29(x52492,x52495,x52496)) % 165.28/165.05 [5250]E(x52501,x52502)+~E(f31(x52503,x52504,x52501),f31(x52505,x52506,x52502)) % 165.28/165.05 [5251]E(x52511,x52512)+~E(f31(x52513,x52511,x52514),f31(x52515,x52512,x52516)) % 165.28/165.05 [5252]E(x52521,x52522)+~E(f31(x52521,x52523,x52524),f31(x52522,x52525,x52526)) % 165.28/165.05 [5253]E(x52531,x52532)+~E(f30(x52533,x52534,x52531),f30(x52535,x52536,x52532)) % 165.28/165.05 [5254]E(x52541,x52542)+~E(f30(x52543,x52541,x52544),f30(x52545,x52542,x52546)) % 165.28/165.05 [5255]E(x52551,x52552)+~E(f30(x52551,x52553,x52554),f30(x52552,x52555,x52556)) % 165.28/165.05 [6704]E(f332(f187(x67041,x67042,x67043,x67044),x67045),f332(f208(x67042),x67046))+~E(f332(x67044,x67045),f332(f208(x67042),x67046)) % 165.28/165.05 [6848]E(f332(f241(f872(x68481),x68482,f209(x68481),x68483),f332(x68484,x68485)),f332(x68483,x68486))+~E(f332(x68484,x68485),f332(f208(x68482),x68486)) % 165.28/165.05 [8356]~P15(x83565,x83561,x83562,x83566)+E(f332(f74(x83561,x83561,x83561,f332(x83562,x83563)),f332(x83562,x83564)),f332(f74(x83561,x83561,x83561,f332(x83562,x83564)),f332(x83562,x83563))) % 165.28/165.05 [8581]~P55(x85814,x85815,x85812,x85811,x85816)+E(f332(x85811,f332(x85812,x85813)),x85813) % 165.28/165.05 [8732]P21(x87321,x87322,x87323,x87324)+~P21(x87321,x87325,f332(f74(x87322,x87325,x87321,x87326),x87323),x87324) % 165.28/165.05 [8815]~P21(x88154,x88152,f332(f74(x88151,x88152,x88154,x88153),x88155),x88156)+P21(x88151,x88152,x88153,f332(f311(x88154,x88151,x88155),x88156)) % 165.28/165.05 [9494]P24(f332(f62(x94941),x94942))+~P24(f332(f67(x94941,x94943,x94944,x94945,x94942),x94946)) % 165.28/165.05 [9502]~P24(f332(f332(f334(x95024),x95023),f300(x95024,x95025,x95021,x95022,x95026)))+P24(f332(f332(x95021,x95022),x95023)) % 165.28/165.05 [9503]~P24(f332(f332(f334(x95034),x95033),f297(x95034,x95031,x95035,x95032,x95036)))+P24(f332(f332(x95031,x95032),x95033)) % 165.28/165.05 [9504]~P24(f332(f332(f334(x95044),x95042),f300(x95044,x95041,x95045,x95046,x95043)))+P24(f332(f332(x95041,x95042),x95043)) % 165.28/165.05 [9505]~P24(f332(f332(f334(x95054),x95052),f297(x95054,x95055,x95051,x95056,x95053)))+P24(f332(f332(x95051,x95052),x95053)) % 165.28/165.05 [5757]E(x57571,x57572)+~E(f332(f332(f267(x57573,x57574),x57575),x57571),f332(f332(f267(x57573,x57574),x57576),x57572)) % 165.28/165.05 [5759]E(x57591,x57592)+~E(f332(f332(f267(x57593,x57594),x57591),x57595),f332(f332(f267(x57593,x57594),x57592),x57596)) % 165.28/165.05 [5883]~P12(x58835,x58836,x58831)+E(f332(f332(x58831,x58832),f332(f332(x58831,x58833),x58834)),f332(f332(x58831,x58833),f332(f332(x58831,x58832),x58834))) % 165.28/165.05 [7300]~P36(x73004,x73001,f332(f332(f152(x73004),x73002),x73005),f332(f332(f152(x73004),x73003),x73006))+P24(f332(f332(x73001,x73002),x73003)) % 165.28/165.05 [7665]P36(x76651,x76652,x76653,x76654)+~P36(x76651,x76652,f332(f332(f152(x76651),x76655),x76653),f332(f332(f152(x76651),x76656),x76654)) % 165.28/165.05 [8675]~P55(x86755,x86751,x86752,x86756,x86754)+P24(f332(f332(f334(x86751),f332(x86752,x86753)),x86754)) % 165.28/165.05 [8843]E(f332(f77(x88431,x88432,x88433,x88434,x88435),x88436),f332(x88433,x88436))+P24(f332(f332(f334(x88431),x88436),x88435)) % 165.28/165.05 [8864]~E(x88643,f332(f332(f152(x88641),x88645),x88646))+P24(f332(f332(f334(f874(f869(x88641),f869(x88641))),f332(f332(f267(f869(x88641),f869(x88641)),x88642),f332(f332(f135(x88641),x88642),x88643))),f148(x88641,x88644))) % 165.28/165.05 [8870]E(f332(f77(x88701,x88702,x88703,x88704,x88705),x88706),f332(x88704,x88706))+~P24(f332(f332(f334(x88701),x88706),x88705)) % 165.28/165.05 [8875]E(f332(f189(x88751,x88752,x88753,x88754,x88755),x88756),f332(x88753,x88756))+P24(f332(f332(f334(x88751),x88756),f332(f174(x88751),x88754))) % 165.28/165.05 [9095]~P38(x90951,x90952,x90953,x90955,x90956)+P38(x90951,x90952,x90953,f332(f332(f177(x90951),x90954),x90955),f332(f332(f177(x90952),x90954),x90956)) % 165.28/165.05 [9096]~P38(x90961,x90962,x90963,x90965,x90966)+P38(x90961,x90962,x90963,f332(f332(f139(x90961),x90964),x90965),f332(f332(f139(x90962),x90964),x90966)) % 165.28/165.05 [9566]~P19(x95664,x95662,x95665,x95663,x95666,x95661)+E(f332(x95661,f196(f875(x95662,a862))),x95663) % 165.28/165.05 [9810]~E(f332(x98104,f332(f266(x98101,x98103),x98105)),f332(x98106,f332(f266(x98101,x98103),x98105)))+E(f332(f272(x98101,x98102,x98103,x98103,x98104,f35(x98103)),x98105),f332(f272(x98101,x98102,x98103,x98103,x98106,f35(x98103)),x98105)) % 165.28/165.05 [9811]~E(f332(x98114,f332(f270(x98111,x98112),x98115)),f332(x98116,f332(f270(x98111,x98112),x98115)))+E(f332(f272(x98111,x98111,x98112,x98113,f35(x98111),x98114),x98115),f332(f272(x98111,x98111,x98112,x98113,f35(x98111),x98116),x98115)) % 165.28/165.05 [9856]~E(f332(f272(x98562,x98566,x98563,x98563,x98561,f35(x98563)),x98564),f332(f272(x98562,x98566,x98563,x98563,x98565,f35(x98563)),x98564))+E(f332(x98561,f332(f266(x98562,x98563),x98564)),f332(x98565,f332(f266(x98562,x98563),x98564))) % 165.28/165.05 [9857]~E(f332(f272(x98572,x98572,x98573,x98576,f35(x98572),x98571),x98574),f332(f272(x98572,x98572,x98573,x98576,f35(x98572),x98575),x98574))+E(f332(x98571,f332(f270(x98572,x98573),x98574)),f332(x98575,f332(f270(x98572,x98573),x98574))) % 165.28/165.05 [8771]P24(f332(f332(f334(x87711),x87712),x87713))+~P24(f332(f332(f334(f874(x87711,x87714)),f332(f332(f267(x87711,x87714),x87712),x87715)),f332(f332(f269(x87711,x87714),x87713),x87716))) % 165.28/165.05 [8785]P24(f332(f332(f334(x87851),x87852),f332(x87853,x87854)))+~P24(f332(f332(f334(f874(x87855,x87851)),f332(f332(f267(x87855,x87851),x87854),x87852)),f332(f332(f269(x87855,x87851),x87856),x87853))) % 165.28/165.05 [8872]~E(f332(f197(f869(x88721)),x88724),f332(f197(f869(x88722)),x88725))+E(f189(x88721,x88722,x88723,x88724,f332(f332(f135(x88722),x88725),x88726)),f189(x88721,x88722,x88723,x88724,x88725)) % 165.28/165.05 [8873]~E(f332(f197(f869(x88731)),x88734),f332(f197(f869(x88732)),x88736))+E(f189(x88731,x88732,x88733,f332(f332(f135(x88731),x88734),x88735),x88736),f189(x88731,x88732,x88733,x88734,x88736)) % 165.28/165.05 [9113]P24(f332(f332(f334(x91131),x91134),f186(x91131,x91132,x91136)))+E(f187(x91131,x91132,f332(f332(f332(f73(x91131,f872(x91132)),x91133),x91134),f332(f208(x91132),x91135)),x91136),f332(f332(f332(f73(x91131,f872(x91132)),f187(x91131,x91132,x91133,x91136)),x91134),f332(f208(x91132),x91135))) % 165.28/165.05 [9207]P24(f332(f332(f334(f874(x92071,x92071)),f332(f332(f267(x92071,x92071),f332(x92072,x92073)),f332(x92072,x92074))),x92075))+~P24(f332(f332(f334(f874(x92076,x92076)),f332(f332(f267(x92076,x92076),x92073),x92074)),f332(f332(f288(x92071,x92076),x92075),x92072))) % 165.28/165.05 [9224]~P24(f332(f332(f334(f874(x92244,x92244)),f332(f332(f267(x92244,x92244),f332(x92246,x92242)),f332(x92246,x92243))),x92245))+P24(f332(f332(f334(f874(x92241,x92241)),f332(f332(f267(x92241,x92241),x92242),x92243)),f332(f332(f288(x92244,x92241),x92245),x92246))) % 165.28/165.05 [9859]E(f332(f332(f267(x98591,x98592),f778(x98593,x98594,x98595,x98596,x98592,x98591)),f785(x98593,x98594,x98595,x98596,x98592,x98591)),x98596)+~P24(f332(f332(f334(f874(x98591,x98592)),x98596),f332(f332(f289(x98591,x98595,x98592),x98594),x98593))) % 165.28/165.05 [10058]~P24(f332(f332(f334(f874(x100581,x100586)),x100585),f332(f332(f289(x100581,x100582,x100586),x100584),x100583)))+P24(f332(f332(f334(f874(x100581,x100582)),f332(f332(f267(x100581,x100582),f778(x100583,x100584,x100582,x100585,x100586,x100581)),f786(x100583,x100584,x100582,x100585,x100586,x100581))),x100584)) % 165.28/165.05 [10059]~P24(f332(f332(f334(f874(x100596,x100592)),x100595),f332(f332(f289(x100596,x100591,x100592),x100594),x100593)))+P24(f332(f332(f334(f874(x100591,x100592)),f332(f332(f267(x100591,x100592),f786(x100593,x100594,x100591,x100595,x100592,x100596)),f785(x100593,x100594,x100591,x100595,x100592,x100596))),x100593)) % 165.28/165.05 [6166]~E(x61666,x61664)+E(f332(f332(f332(f332(f73(x61661,x61662),x61663),x61664),x61665),x61666),x61665) % 165.28/165.05 [6216]E(x62161,x62162)+E(f332(f332(f332(f332(f73(x62163,x62164),x62165),x62162),x62166),x62161),f332(x62165,x62161)) % 165.28/165.05 [7736]~P30(x77362)+E(f332(f332(f42(x77361,x77362),x77363),f332(f332(f7(x77361,x77364,x77362),x77365),x77366)),f332(f332(f332(f42(x77361,f875(x77364,x77362)),x77363),x77365),x77366)) % 165.28/165.05 [7737]~P30(x77372)+E(f332(f332(f43(x77371,x77372),x77373),f332(f332(f7(x77371,x77374,x77372),x77375),x77376)),f332(f332(f332(f43(x77371,f875(x77374,x77372)),x77373),x77375),x77376)) % 165.28/165.05 [8495]E(f332(f332(f42(x84951,f875(x84952,a862)),x84953),f332(f332(f8(f875(x84952,a862),f875(x84952,a862),x84951),f332(f310(x84952),x84954)),x84955)),f332(f332(f310(x84952),x84954),f332(f332(f42(x84951,f875(x84952,a862)),x84953),x84955)))+~P24(f332(f332(f334(x84951),x84956),x84953)) % 165.28/165.05 [8918]~P30(x89182)+E(f332(f332(f42(x89181,x89182),x89183),f332(f332(f8(f875(x89184,x89182),x89182,x89181),f332(f42(x89184,x89182),x89185)),f332(f7(x89184,x89181,x89182),x89186))),f332(f332(f42(x89184,x89182),x89185),f332(f332(f8(f875(x89181,x89182),x89182,x89184),f332(f42(x89181,x89182),x89183)),x89186))) % 165.28/165.05 [8919]~P30(x89192)+E(f332(f332(f43(x89191,x89192),x89193),f332(f332(f8(f875(x89194,x89192),x89192,x89191),f332(f43(x89194,x89192),x89195)),f332(f7(x89194,x89191,x89192),x89196))),f332(f332(f43(x89194,x89192),x89195),f332(f332(f8(f875(x89191,x89192),x89192,x89194),f332(f43(x89191,x89192),x89193)),x89196))) % 165.28/165.05 [9122]P24(f332(f332(f334(x91221),x91222),f332(f174(x91221),x91223)))+~P24(f332(f332(f334(f874(x91224,x91221)),f332(f332(f267(x91224,x91221),x91225),x91222)),f332(f174(f874(x91224,x91221)),f332(f332(f184(x91224,x91221),x91226),x91223)))) % 165.28/165.05 [9123]P24(f332(f332(f334(x91231),x91232),f332(f174(x91231),x91233)))+~P24(f332(f332(f334(f874(x91231,x91234)),f332(f332(f267(x91231,x91234),x91232),x91235)),f332(f174(f874(x91231,x91234)),f332(f332(f184(x91231,x91234),x91233),x91236)))) % 165.28/165.05 [9221]P24(f332(f332(f246(f875(x92211,a862)),f332(f286(x92212,x92211,x92213),x92214)),x92215))+~P24(f332(f332(f246(f875(f874(x92212,x92211),a862)),x92213),f332(f332(f269(x92212,x92211),x92216),f332(f16(f875(x92211,a862),x92212),x92215)))) % 165.28/165.05 [9403]P24(f332(f332(f334(f874(f869(x94031),f869(x94031))),f332(f332(f267(f869(x94031),f869(x94031)),f332(f332(f152(x94031),x94032),x94033)),f332(f332(f152(x94031),x94034),x94035))),f148(x94031,x94036)))+~P24(f332(f332(f334(f874(x94031,x94031)),f332(f332(f267(x94031,x94031),x94032),x94034)),x94036)) % 165.28/165.05 [9855]E(f332(f332(f267(x98551,x98552),f697(x98553,x98554,x98555,x98552,x98551,x98556)),f698(x98553,x98554,x98555,x98552,x98551,x98556)),x98556)+P24(f332(f332(f334(x98555),x98554),f332(f332(f271(x98551,x98552,f875(x98555,a862)),x98553),x98556))) % 165.28/165.05 [9861]E(f332(f332(f267(x98611,x98612),f699(x98613,x98614,x98612,x98611,x98615,x98616)),f700(x98613,x98614,x98612,x98611,x98615,x98616)),x98613)+~P24(f332(f332(f334(x98616),x98615),f332(f332(f271(x98611,x98612,f875(x98616,a862)),x98614),x98613))) % 165.28/165.05 [10018]P24(f332(f332(f334(x100181),x100182),f332(f332(x100183,f699(x100184,x100183,x100185,x100186,x100182,x100181)),f700(x100184,x100183,x100185,x100186,x100182,x100181))))+~P24(f332(f332(f334(x100181),x100182),f332(f332(f271(x100186,x100185,f875(x100181,a862)),x100183),x100184))) % 165.28/165.05 [10036]~P24(f332(f332(f334(x100361),x100362),f332(f332(x100365,f697(x100365,x100362,x100361,x100364,x100363,x100366)),f698(x100365,x100362,x100361,x100364,x100363,x100366))))+P24(f332(f332(f334(x100361),x100362),f332(f332(f271(x100363,x100364,f875(x100361,a862)),x100365),x100366))) % 165.28/165.05 [7854]P24(f332(f332(f334(x78541),x78544),x78546))+E(f190(x78541,x78542,f332(f332(f332(f73(x78541,f872(x78542)),x78543),x78544),x78545),x78546),f190(x78541,x78542,x78543,x78546)) % 165.28/165.05 [7930]P24(f332(f332(f334(x79301),x79304),x79306))+E(f332(f311(x79301,x79302,f332(f332(f332(f73(x79301,x79302),x79303),x79304),x79305)),x79306),f332(f311(x79301,x79302,x79303),x79306)) % 165.28/165.05 [7957]P24(f332(f332(f334(x79571),x79574),f332(f174(x79571),x79576)))+E(f332(f332(f155(x79571,x79572),f332(f332(f332(f73(x79571,x79572),x79573),x79574),x79575)),x79576),f332(f332(f155(x79571,x79572),x79573),x79576)) % 165.28/165.05 [8401]E(x84011,x84012)+E(f332(f332(f160(x84013,f332(f332(f160(x84013,x84014),x84011),x84015)),x84012),x84016),f332(f332(f160(x84013,f332(f332(f160(x84013,x84014),x84012),x84016)),x84011),x84015)) % 165.28/165.05 [8924]~P24(f332(f332(f334(x89243),x89246),x89245))+E(f332(f332(f310(x89241),x89242),f332(f311(x89243,x89241,x89244),f332(f332(f22(f875(x89243,a862)),x89245),f332(f332(f310(x89243),x89246),f196(f875(x89243,a862)))))),f332(f311(x89243,x89241,f332(f332(f332(f73(x89243,x89241),x89244),x89246),x89242)),x89245)) % 165.28/165.05 [9672]E(f189(x96721,x96722,x96723,f332(f332(f135(x96721),x96724),f332(f332(f152(x96721),x96725),f116(x96721))),x96726),f332(f332(f332(f73(x96721,f872(x96722)),f189(x96721,x96722,x96723,x96724,x96726)),x96725),f332(f208(x96722),f332(f332(f166(x96722),x96726),f332(f197(f869(x96721)),x96724)))))+~P24(f332(f332(f247(a868),f332(f197(f869(x96721)),x96724)),f332(f197(f869(x96722)),x96726))) % 165.28/165.05 [8714]~E(x87143,x87146)+E(f332(f332(f180(x87141,x87142),f332(f332(f152(f874(x87141,x87142)),f332(f332(f267(x87141,x87142),x87143),x87144)),x87145)),x87146),f332(f208(x87142),x87144)) % 165.28/165.05 [8741]E(x87411,x87412)+E(f332(f332(f180(x87413,x87414),f332(f332(f152(f874(x87413,x87414)),f332(f332(f267(x87413,x87414),x87411),x87415)),x87416)),x87412),f332(f332(f180(x87413,x87414),x87416),x87412)) % 165.28/165.05 [8999]~P24(f332(f332(x89994,x89995),x89996))+P24(f332(f332(f332(f332(f113(f875(x89991,f875(x89992,a862))),x89993),x89994),x89995),x89996)) % 165.28/165.05 [9001]~P24(f332(f332(x90013,x90015),x90016))+P24(f332(f332(f332(f332(f113(f875(x90011,f875(x90012,a862))),x90013),x90014),x90015),x90016)) % 165.28/165.05 [9273]P24(f332(f332(x92731,x92732),x92733))+~P24(f332(f332(f332(f332(f104(f875(x92734,f875(x92735,a862))),x92736),x92731),x92732),x92733)) % 165.28/165.05 [9274]P24(f332(f332(x92741,x92742),x92743))+~P24(f332(f332(f332(f332(f104(f875(x92744,f875(x92745,a862))),x92741),x92746),x92742),x92743)) % 165.28/165.05 [9694]~P74(x96942)+E(f332(f332(f6(x96941,x96942),f332(f332(f7(x96941,f875(x96943,a862),x96942),f332(f332(f8(f875(x96943,x96942),f875(f875(x96943,a862),x96942),x96941),f6(x96943,x96942)),x96944)),x96945)),x96946),f332(f332(f6(f874(x96941,x96943),x96942),f332(f271(x96941,x96943,x96942),x96944)),f332(f332(f269(x96941,x96943),x96946),f332(f16(f875(x96943,a862),x96941),x96945)))) % 165.28/165.05 [9695]~P73(x96952)+E(f332(f332(f9(x96951,x96952),f332(f332(f7(x96951,f875(x96953,a862),x96952),f332(f332(f8(f875(x96953,x96952),f875(f875(x96953,a862),x96952),x96951),f9(x96953,x96952)),x96954)),x96955)),x96956),f332(f332(f9(f874(x96951,x96953),x96952),f332(f271(x96951,x96953,x96952),x96954)),f332(f332(f269(x96951,x96953),x96956),f332(f16(f875(x96953,a862),x96951),x96955)))) % 165.28/165.05 [9838]~P74(x98382)+E(f332(f332(f6(x98381,x98382),f332(f332(f7(x98381,f875(x98383,a862),x98382),f332(f332(f8(f875(x98383,x98382),f875(f875(x98383,a862),x98382),x98381),f6(x98383,x98382)),f332(f7(x98383,x98381,x98382),x98384))),x98385)),x98386),f332(f332(f6(x98383,x98382),f332(f332(f7(x98383,f875(x98381,a862),x98382),f332(f332(f8(f875(x98381,x98382),f875(f875(x98381,a862),x98382),x98383),f6(x98381,x98382)),x98384)),x98386)),x98385)) % 165.28/165.05 [9535]~P24(f332(f332(f334(x95351),x95355),x95354))+E(f332(f332(f332(f73(x95351,f872(x95352)),f190(x95351,x95352,x95353,f332(f332(f22(f875(x95351,a862)),x95354),f332(f332(f310(x95351),x95355),f196(f875(x95351,a862)))))),x95355),x95356),f190(x95351,x95352,f332(f332(f332(f73(x95351,f872(x95352)),x95353),x95355),x95356),x95354)) % 165.28/165.05 [10114]~P24(f332(f332(f334(f874(x101141,x101142)),f332(f332(f267(x101141,x101142),x101145),x101146)),f332(f332(f113(f875(f874(x101141,x101142),a862)),x101143),x101144)))+P24(f332(f332(f332(f332(f113(f875(x101141,f875(x101142,a862))),f332(f332(f7(x101141,f875(f874(x101141,x101142),a862),f875(x101142,a862)),f332(f332(f8(f875(x101142,f875(f875(f874(x101141,x101142),a862),a862)),f875(f875(f874(x101141,x101142),a862),f875(x101142,a862)),x101141),f7(x101142,f875(f874(x101141,x101142),a862),a862)),f332(f332(f8(f875(x101142,f874(x101141,x101142)),f875(x101142,f875(f875(f874(x101141,x101142),a862),a862)),x101141),f332(f8(f874(x101141,x101142),f875(f875(f874(x101141,x101142),a862),a862),x101142),f334(f874(x101141,x101142)))),f267(x101141,x101142)))),x101143)),f332(f332(f7(x101141,f875(f874(x101141,x101142),a862),f875(x101142,a862)),f332(f332(f8(f875(x101142,f875(f875(f874(x101141,x101142),a862),a862)),f875(f875(f874(x101141,x101142),a862),f875(x101142,a862)),x101141),f7(x101142,f875(f874(x101141,x101142),a862),a862)),f332(f332(f8(f875(x101142,f874(x101141,x101142)),f875(x101142,f875(f875(f874(x101141,x101142),a862),a862)),x101141),f332(f8(f874(x101141,x101142),f875(f875(f874(x101141,x101142),a862),a862),x101142),f334(f874(x101141,x101142)))),f267(x101141,x101142)))),x101144)),x101145),x101146)) % 165.28/165.05 [10115]~P24(f332(f332(f334(f874(x101151,x101152)),f332(f332(f267(x101151,x101152),x101155),x101156)),f332(f332(f104(f875(f874(x101151,x101152),a862)),x101153),x101154)))+P24(f332(f332(f332(f332(f104(f875(x101151,f875(x101152,a862))),f332(f332(f7(x101151,f875(f874(x101151,x101152),a862),f875(x101152,a862)),f332(f332(f8(f875(x101152,f875(f875(f874(x101151,x101152),a862),a862)),f875(f875(f874(x101151,x101152),a862),f875(x101152,a862)),x101151),f7(x101152,f875(f874(x101151,x101152),a862),a862)),f332(f332(f8(f875(x101152,f874(x101151,x101152)),f875(x101152,f875(f875(f874(x101151,x101152),a862),a862)),x101151),f332(f8(f874(x101151,x101152),f875(f875(f874(x101151,x101152),a862),a862),x101152),f334(f874(x101151,x101152)))),f267(x101151,x101152)))),x101153)),f332(f332(f7(x101151,f875(f874(x101151,x101152),a862),f875(x101152,a862)),f332(f332(f8(f875(x101152,f875(f875(f874(x101151,x101152),a862),a862)),f875(f875(f874(x101151,x101152),a862),f875(x101152,a862)),x101151),f7(x101152,f875(f874(x101151,x101152),a862),a862)),f332(f332(f8(f875(x101152,f874(x101151,x101152)),f875(x101152,f875(f875(f874(x101151,x101152),a862),a862)),x101151),f332(f8(f874(x101151,x101152),f875(f875(f874(x101151,x101152),a862),a862),x101152),f334(f874(x101151,x101152)))),f267(x101151,x101152)))),x101154)),x101155),x101156)) % 165.28/165.05 [10121]P24(f332(f332(f334(f874(x101211,x101212)),f332(f332(f267(x101211,x101212),x101213),x101214)),f332(f332(f113(f875(f874(x101211,x101212),a862)),x101215),x101216)))+~P24(f332(f332(f332(f332(f113(f875(x101211,f875(x101212,a862))),f332(f332(f7(x101211,f875(f874(x101211,x101212),a862),f875(x101212,a862)),f332(f332(f8(f875(x101212,f875(f875(f874(x101211,x101212),a862),a862)),f875(f875(f874(x101211,x101212),a862),f875(x101212,a862)),x101211),f7(x101212,f875(f874(x101211,x101212),a862),a862)),f332(f332(f8(f875(x101212,f874(x101211,x101212)),f875(x101212,f875(f875(f874(x101211,x101212),a862),a862)),x101211),f332(f8(f874(x101211,x101212),f875(f875(f874(x101211,x101212),a862),a862),x101212),f334(f874(x101211,x101212)))),f267(x101211,x101212)))),x101215)),f332(f332(f7(x101211,f875(f874(x101211,x101212),a862),f875(x101212,a862)),f332(f332(f8(f875(x101212,f875(f875(f874(x101211,x101212),a862),a862)),f875(f875(f874(x101211,x101212),a862),f875(x101212,a862)),x101211),f7(x101212,f875(f874(x101211,x101212),a862),a862)),f332(f332(f8(f875(x101212,f874(x101211,x101212)),f875(x101212,f875(f875(f874(x101211,x101212),a862),a862)),x101211),f332(f8(f874(x101211,x101212),f875(f875(f874(x101211,x101212),a862),a862),x101212),f334(f874(x101211,x101212)))),f267(x101211,x101212)))),x101216)),x101213),x101214)) % 165.28/165.05 [10122]P24(f332(f332(f334(f874(x101221,x101222)),f332(f332(f267(x101221,x101222),x101223),x101224)),f332(f332(f104(f875(f874(x101221,x101222),a862)),x101225),x101226)))+~P24(f332(f332(f332(f332(f104(f875(x101221,f875(x101222,a862))),f332(f332(f7(x101221,f875(f874(x101221,x101222),a862),f875(x101222,a862)),f332(f332(f8(f875(x101222,f875(f875(f874(x101221,x101222),a862),a862)),f875(f875(f874(x101221,x101222),a862),f875(x101222,a862)),x101221),f7(x101222,f875(f874(x101221,x101222),a862),a862)),f332(f332(f8(f875(x101222,f874(x101221,x101222)),f875(x101222,f875(f875(f874(x101221,x101222),a862),a862)),x101221),f332(f8(f874(x101221,x101222),f875(f875(f874(x101221,x101222),a862),a862),x101222),f334(f874(x101221,x101222)))),f267(x101221,x101222)))),x101225)),f332(f332(f7(x101221,f875(f874(x101221,x101222),a862),f875(x101222,a862)),f332(f332(f8(f875(x101222,f875(f875(f874(x101221,x101222),a862),a862)),f875(f875(f874(x101221,x101222),a862),f875(x101222,a862)),x101221),f7(x101222,f875(f874(x101221,x101222),a862),a862)),f332(f332(f8(f875(x101222,f874(x101221,x101222)),f875(x101222,f875(f875(f874(x101221,x101222),a862),a862)),x101221),f332(f8(f874(x101221,x101222),f875(f875(f874(x101221,x101222),a862),a862),x101222),f334(f874(x101221,x101222)))),f267(x101221,x101222)))),x101226)),x101223),x101224)) % 165.28/165.05 [10108]~P24(f332(f332(f334(f874(x101082,x101083)),f332(f332(f267(x101082,x101083),x101085),x101086)),f332(f332(f42(x101081,f875(f874(x101082,x101083),a862)),f255(f875(x101081,a862))),x101084)))+P24(f332(f332(f332(f332(f42(x101081,f875(x101082,f875(x101083,a862))),f255(f875(x101081,a862))),f332(f332(f8(f875(f874(x101082,x101083),a862),f875(x101082,f875(x101083,a862)),x101081),f332(f7(x101082,f875(f874(x101082,x101083),a862),f875(x101083,a862)),f332(f332(f8(f875(x101083,f875(f875(f874(x101082,x101083),a862),a862)),f875(f875(f874(x101082,x101083),a862),f875(x101083,a862)),x101082),f7(x101083,f875(f874(x101082,x101083),a862),a862)),f332(f332(f8(f875(x101083,f874(x101082,x101083)),f875(x101083,f875(f875(f874(x101082,x101083),a862),a862)),x101082),f332(f8(f874(x101082,x101083),f875(f875(f874(x101082,x101083),a862),a862),x101083),f334(f874(x101082,x101083)))),f267(x101082,x101083))))),x101084)),x101085),x101086)) % 165.28/165.05 [10109]~P24(f332(f332(f334(f874(x101092,x101093)),f332(f332(f267(x101092,x101093),x101095),x101096)),f332(f332(f43(x101091,f875(f874(x101092,x101093),a862)),f255(f875(x101091,a862))),x101094)))+P24(f332(f332(f332(f332(f43(x101091,f875(x101092,f875(x101093,a862))),f255(f875(x101091,a862))),f332(f332(f8(f875(f874(x101092,x101093),a862),f875(x101092,f875(x101093,a862)),x101091),f332(f7(x101092,f875(f874(x101092,x101093),a862),f875(x101093,a862)),f332(f332(f8(f875(x101093,f875(f875(f874(x101092,x101093),a862),a862)),f875(f875(f874(x101092,x101093),a862),f875(x101093,a862)),x101092),f7(x101093,f875(f874(x101092,x101093),a862),a862)),f332(f332(f8(f875(x101093,f874(x101092,x101093)),f875(x101093,f875(f875(f874(x101092,x101093),a862),a862)),x101092),f332(f8(f874(x101092,x101093),f875(f875(f874(x101092,x101093),a862),a862),x101093),f334(f874(x101092,x101093)))),f267(x101092,x101093))))),x101094)),x101095),x101096)) % 165.28/165.05 [10118]P24(f332(f332(f334(f874(x101181,x101182)),f332(f332(f267(x101181,x101182),x101183),x101184)),f332(f332(f42(x101185,f875(f874(x101181,x101182),a862)),f255(f875(x101185,a862))),x101186)))+~P24(f332(f332(f332(f332(f42(x101185,f875(x101181,f875(x101182,a862))),f255(f875(x101185,a862))),f332(f332(f8(f875(f874(x101181,x101182),a862),f875(x101181,f875(x101182,a862)),x101185),f332(f7(x101181,f875(f874(x101181,x101182),a862),f875(x101182,a862)),f332(f332(f8(f875(x101182,f875(f875(f874(x101181,x101182),a862),a862)),f875(f875(f874(x101181,x101182),a862),f875(x101182,a862)),x101181),f7(x101182,f875(f874(x101181,x101182),a862),a862)),f332(f332(f8(f875(x101182,f874(x101181,x101182)),f875(x101182,f875(f875(f874(x101181,x101182),a862),a862)),x101181),f332(f8(f874(x101181,x101182),f875(f875(f874(x101181,x101182),a862),a862),x101182),f334(f874(x101181,x101182)))),f267(x101181,x101182))))),x101186)),x101183),x101184)) % 165.28/165.05 [10119]P24(f332(f332(f334(f874(x101191,x101192)),f332(f332(f267(x101191,x101192),x101193),x101194)),f332(f332(f43(x101195,f875(f874(x101191,x101192),a862)),f255(f875(x101195,a862))),x101196)))+~P24(f332(f332(f332(f332(f43(x101195,f875(x101191,f875(x101192,a862))),f255(f875(x101195,a862))),f332(f332(f8(f875(f874(x101191,x101192),a862),f875(x101191,f875(x101192,a862)),x101195),f332(f7(x101191,f875(f874(x101191,x101192),a862),f875(x101192,a862)),f332(f332(f8(f875(x101192,f875(f875(f874(x101191,x101192),a862),a862)),f875(f875(f874(x101191,x101192),a862),f875(x101192,a862)),x101191),f7(x101192,f875(f874(x101191,x101192),a862),a862)),f332(f332(f8(f875(x101192,f874(x101191,x101192)),f875(x101192,f875(f875(f874(x101191,x101192),a862),a862)),x101191),f332(f8(f874(x101191,x101192),f875(f875(f874(x101191,x101192),a862),a862),x101192),f334(f874(x101191,x101192)))),f267(x101191,x101192))))),x101196)),x101193),x101194)) % 165.28/165.05 [7411]E(f332(x74111,f332(x74112,x74113)),f332(x74114,x74113))+~E(f332(f74(x74115,x74116,x74117,x74111),x74112),x74114) % 165.28/165.05 [9565]~P18(x95653,x95654,x95651,x95655,x95656,x95657)+E(f332(f332(x95651,x95652),x95652),x95652) % 165.28/165.05 [9935]~E(f332(f241(f872(x99357),x99351,f209(x99357),x99355),f332(x99354,x99353)),f332(f208(x99357),x99352))+E(f332(f208(x99351),f702(x99352,x99353,x99354,x99355,x99356,x99357,x99351)),f332(x99354,x99353)) % 165.28/165.05 [9936]~E(f332(f241(f872(x99366),x99367,f209(x99366),x99361),f332(x99364,x99363)),f332(f208(x99366),x99362))+E(f332(x99361,f702(x99362,x99363,x99364,x99361,x99365,x99366,x99367)),f332(f208(x99366),x99362)) % 165.28/165.05 [5984]~E(f332(f332(f155(x59841,x59845),x59846),x59842),f332(f332(f155(x59843,x59845),x59847),x59844))+E(f332(f197(f869(x59841)),x59842),f332(f197(f869(x59843)),x59844)) % 165.28/165.05 [7488]E(x74881,x74882)+~E(f332(f332(f332(f73(x74883,f872(x74884)),x74885),x74886),f332(f208(x74884),x74881)),f332(f332(f332(f73(x74883,f872(x74884)),x74887),x74886),f332(f208(x74884),x74882))) % 165.28/165.05 [8433]E(f332(x84331,f332(x84332,x84333)),f332(x84334,x84333))+~E(f332(f74(x84335,x84336,x84337,x84331),x84332),f332(f74(x84336,x84336,x84337,f35(x84336)),x84334)) % 165.28/165.05 [8760]~P38(x87604,x87605,x87601,f332(f332(f152(x87604),x87602),x87606),f332(f332(f152(x87605),x87603),x87607))+P24(f332(f332(x87601,x87602),x87603)) % 165.28/165.05 [9129]P38(x91291,x91292,x91293,x91294,x91295)+~P38(x91291,x91292,x91293,f332(f332(f152(x91291),x91296),x91294),f332(f332(f152(x91292),x91297),x91295)) % 165.28/165.05 [9733]P24(f332(f332(x97331,x97332),f670(x97333,x97332,x97334,x97331)))+~P24(f332(f332(f268(x97335,x97336,x97337,x97331,x97334),x97332),x97333)) % 165.28/165.05 [9755]P24(f332(f332(x97551,f670(x97552,x97553,x97551,x97554)),x97552))+~P24(f332(f332(f268(x97555,x97556,x97557,x97554,x97551),x97553),x97552)) % 165.28/165.05 [6030]E(x60301,x60302)+~E(f332(f332(f332(f93(x60303),x60304),x60305),x60301),f332(f332(f332(f93(x60303),x60306),x60307),x60302)) % 165.28/165.05 [6031]E(x60311,x60312)+~E(f332(f332(f332(f93(x60313),x60314),x60311),x60315),f332(f332(f332(f93(x60313),x60316),x60312),x60317)) % 165.28/165.05 [6032]E(x60321,x60322)+~E(f332(f332(f332(f93(x60323),x60321),x60324),x60325),f332(f332(f332(f93(x60323),x60322),x60326),x60327)) % 165.28/165.05 [8878]~P16(x88786,x88781,x88783,x88787)+E(f332(f74(x88781,x88781,x88782,f332(x88783,x88784)),f332(f74(x88781,x88781,x88782,f332(x88783,x88784)),x88785)),f332(f74(x88781,x88781,x88782,f332(x88783,x88784)),x88785)) % 165.28/165.05 [9227]~P38(x92273,x92272,x92274,f332(f332(f155(x92271,x92273),x92275),x92276),x92277)+P38(x92271,x92272,f332(f332(f8(x92273,f875(x92272,a862),x92271),x92274),x92275),x92276,x92277) % 165.28/165.05 [9248]P38(x92481,x92482,x92483,f332(f332(f155(x92484,x92481),x92485),x92486),x92487)+~P38(x92484,x92482,f332(f332(f8(x92481,f875(x92482,a862),x92484),x92483),x92485),x92486,x92487) % 165.28/165.05 [9652]E(f189(x96521,x96522,f332(f332(f332(f73(x96521,f872(x96522)),x96523),x96524),f332(f208(x96522),x96525)),x96526,x96527),f332(f332(f332(f73(x96521,f872(x96522)),f189(x96521,x96522,x96523,x96526,x96527)),x96524),f332(f208(x96522),x96525)))+P24(f332(f332(f334(x96521),x96524),f332(f174(x96521),x96526))) % 165.28/165.05 [8877]~P24(f332(f332(f334(x88771),x88772),f332(f332(x88775,x88776),x88777)))+P24(f332(f332(f334(x88771),x88772),f332(f332(f271(x88773,x88774,f875(x88771,a862)),x88775),f332(f332(f267(x88773,x88774),x88776),x88777)))) % 165.28/165.05 [9155]P24(f332(f332(f332(x91551,x91552),x91553),x91554))+~P24(f332(f332(f332(f271(x91555,x91556,f875(x91557,a862)),x91551),f332(f332(f267(x91555,x91556),x91552),x91553)),x91554)) % 165.28/165.05 [9287]P24(f332(f332(f334(x92871),f332(f332(x92872,x92873),x92874)),f332(f311(f874(x92875,x92876),x92871,f332(f271(x92875,x92876,x92871),x92872)),x92877)))+~P24(f332(f332(f334(f874(x92875,x92876)),f332(f332(f267(x92875,x92876),x92873),x92874)),x92877)) % 165.28/165.05 [9612]P24(f332(f332(f334(f874(f869(x96121),f869(x96121))),f332(f332(f267(f869(x96121),f869(x96121)),f332(f332(f135(x96121),x96122),f332(f332(f152(x96121),x96123),x96124))),f332(f332(f135(x96121),x96122),f332(f332(f152(x96121),x96125),x96126)))),f148(x96121,x96127)))+~P24(f332(f332(f334(f874(x96121,x96121)),f332(f332(f267(x96121,x96121),x96123),x96125)),x96127)) % 165.28/165.05 [9674]~P38(x96741,x96743,x96744,x96746,f332(f332(f155(x96742,x96743),x96745),x96747))+P38(x96741,x96742,f332(f332(f7(x96741,f875(x96742,x96743),f875(x96742,a862)),f332(f332(f8(f875(x96743,a862),f875(f875(x96742,x96743),f875(x96742,a862)),x96741),f8(x96743,a862,x96742)),x96744)),x96745),x96746,x96747) % 165.28/165.05 [9759]P38(x97591,x97592,x97593,x97594,f332(f332(f155(x97595,x97592),x97596),x97597))+~P38(x97591,x97595,f332(f332(f7(x97591,f875(x97595,x97592),f875(x97595,a862)),f332(f332(f8(f875(x97592,a862),f875(f875(x97595,x97592),f875(x97595,a862)),x97591),f8(x97592,a862,x97595)),x97593)),x97596),x97594,x97597) % 165.28/165.05 [9147]E(x91471,x91472)+E(f332(f332(f332(f73(x91473,x91474),f332(f332(f332(f73(x91473,x91474),x91475),x91471),x91476)),x91472),x91477),f332(f332(f332(f73(x91473,x91474),f332(f332(f332(f73(x91473,x91474),x91475),x91472),x91477)),x91471),x91476)) % 165.28/165.05 [9378]E(f189(x93781,x93782,f332(f332(f332(f73(x93781,f872(x93782)),x93783),x93784),f332(f208(x93782),x93785)),x93786,x93787),f189(x93781,x93782,x93783,x93786,x93787))+~P24(f332(f332(f334(x93781),x93784),f332(f174(x93781),f332(f332(f177(x93781),f332(f197(f869(x93782)),x93787)),x93786)))) % 165.28/165.05 [9685]E(f189(x96851,x96852,f332(f332(f332(f73(x96851,f872(x96852)),x96853),x96854),f332(f208(x96852),x96855)),x96856,x96857),f332(f332(f332(f73(x96851,f872(x96852)),f189(x96851,x96852,x96853,x96856,x96857)),x96854),f332(f208(x96852),x96855)))+P24(f332(f332(f334(x96851),x96854),f332(f174(x96851),f332(f332(f177(x96851),f332(f197(f869(x96852)),x96857)),x96856)))) % 165.28/165.05 [10047]P24(f332(f332(f334(x100471),f604(x100472,x100473,x100474,x100475,x100476,x100477,x100471)),x100475))+P24(f332(f332(f332(f332(f43(x100471,f875(x100477,f875(x100476,a862))),x100475),x100474),x100473),x100472)) % 165.28/165.05 [10048]P24(f332(f332(f334(x100481),f482(x100482,x100483,x100484,x100485,x100486,x100487,x100481)),x100485))+~P24(f332(f332(f332(f332(f42(x100481,f875(x100487,f875(x100486,a862))),x100485),x100484),x100483),x100482)) % 165.28/165.05 [10073]P24(f332(f332(f332(x100731,f482(x100732,x100733,x100731,x100734,x100735,x100736,x100737)),x100733),x100732))+~P24(f332(f332(f332(f332(f42(x100737,f875(x100736,f875(x100735,a862))),x100734),x100731),x100733),x100732)) % 165.28/165.05 [10090]~P24(f332(f332(f332(x100905,f604(x100907,x100906,x100905,x100904,x100903,x100902,x100901)),x100906),x100907))+P24(f332(f332(f332(f332(f43(x100901,f875(x100902,f875(x100903,a862))),x100904),x100905),x100906),x100907)) % 165.28/165.05 [10107]~P24(f332(f332(f334(f874(x101071,x101073)),f332(f332(f267(x101071,x101073),x101076),x101077)),f332(f332(f289(x101071,x101072,x101073),x101074),x101075)))+P24(f332(f332(f268(x101071,x101072,x101073,f332(f332(f7(x101071,f875(f874(x101071,x101072),a862),f875(x101072,a862)),f332(f332(f8(f875(x101072,f875(f875(f874(x101071,x101072),a862),a862)),f875(f875(f874(x101071,x101072),a862),f875(x101072,a862)),x101071),f7(x101072,f875(f874(x101071,x101072),a862),a862)),f332(f332(f8(f875(x101072,f874(x101071,x101072)),f875(x101072,f875(f875(f874(x101071,x101072),a862),a862)),x101071),f332(f8(f874(x101071,x101072),f875(f875(f874(x101071,x101072),a862),a862),x101072),f334(f874(x101071,x101072)))),f267(x101071,x101072)))),x101074),f332(f332(f7(x101072,f875(f874(x101072,x101073),a862),f875(x101073,a862)),f332(f332(f8(f875(x101073,f875(f875(f874(x101072,x101073),a862),a862)),f875(f875(f874(x101072,x101073),a862),f875(x101073,a862)),x101072),f7(x101073,f875(f874(x101072,x101073),a862),a862)),f332(f332(f8(f875(x101073,f874(x101072,x101073)),f875(x101073,f875(f875(f874(x101072,x101073),a862),a862)),x101072),f332(f8(f874(x101072,x101073),f875(f875(f874(x101072,x101073),a862),a862),x101073),f334(f874(x101072,x101073)))),f267(x101072,x101073)))),x101075)),x101076),x101077)) % 165.28/165.05 [10117]P24(f332(f332(f334(f874(x101171,x101172)),f332(f332(f267(x101171,x101172),x101173),x101174)),f332(f332(f289(x101171,x101175,x101172),x101176),x101177)))+~P24(f332(f332(f268(x101171,x101175,x101172,f332(f332(f7(x101171,f875(f874(x101171,x101175),a862),f875(x101175,a862)),f332(f332(f8(f875(x101175,f875(f875(f874(x101171,x101175),a862),a862)),f875(f875(f874(x101171,x101175),a862),f875(x101175,a862)),x101171),f7(x101175,f875(f874(x101171,x101175),a862),a862)),f332(f332(f8(f875(x101175,f874(x101171,x101175)),f875(x101175,f875(f875(f874(x101171,x101175),a862),a862)),x101171),f332(f8(f874(x101171,x101175),f875(f875(f874(x101171,x101175),a862),a862),x101175),f334(f874(x101171,x101175)))),f267(x101171,x101175)))),x101176),f332(f332(f7(x101175,f875(f874(x101175,x101172),a862),f875(x101172,a862)),f332(f332(f8(f875(x101172,f875(f875(f874(x101175,x101172),a862),a862)),f875(f875(f874(x101175,x101172),a862),f875(x101172,a862)),x101175),f7(x101172,f875(f874(x101175,x101172),a862),a862)),f332(f332(f8(f875(x101172,f874(x101175,x101172)),f875(x101172,f875(f875(f874(x101175,x101172),a862),a862)),x101175),f332(f8(f874(x101175,x101172),f875(f875(f874(x101175,x101172),a862),a862),x101172),f334(f874(x101175,x101172)))),f267(x101175,x101172)))),x101177)),x101173),x101174)) % 165.28/165.05 [10057]~P140(x100572)+E(f332(f332(f6(x100571,x100572),f332(f332(f7(x100571,f875(x100573,a862),x100572),f332(f332(f8(f875(x100573,x100572),f875(f875(x100573,a862),x100572),x100571),f6(x100573,x100572)),f332(f332(f7(x100571,f875(x100573,x100572),f875(x100573,x100572)),f332(f332(f8(f875(x100572,x100572),f875(f875(x100573,x100572),f875(x100573,x100572)),x100571),f8(x100572,x100572,x100573)),f332(f332(f8(x100572,f875(x100572,x100572),x100571),f82(x100572)),x100574))),x100575))),x100576)),x100577),f332(f332(f82(x100572),f332(f332(f6(x100571,x100572),x100574),x100577)),f332(f332(f6(x100573,x100572),x100575),x100576))) % 165.28/165.05 [9182]~P15(x91827,x91821,x91823,x91828)+E(f332(f74(x91821,x91821,x91822,f332(x91823,x91824)),f332(f74(x91821,x91821,x91822,f332(x91823,x91825)),x91826)),f332(f74(x91821,x91821,x91822,f332(x91823,x91825)),f332(f74(x91821,x91821,x91822,f332(x91823,x91824)),x91826))) % 165.28/165.05 [10112]E(f332(f332(f267(x101121,x101122),f332(x101123,f566(x101124,x101125,x101123,x101126,x101127,x101128,x101122,x101121))),f332(x101125,f567(x101124,x101125,x101123,x101126,x101127,x101128,x101122,x101121))),x101128)+~P24(f332(f332(f334(f874(x101121,x101122)),x101128),f332(f311(f874(x101127,x101126),f874(x101121,x101122),f272(x101127,x101121,x101126,x101122,x101123,x101125)),x101124))) % 165.28/165.05 [10126]~P24(f332(f332(f334(f874(x101268,x101267)),x101266),f332(f311(f874(x101261,x101262),f874(x101268,x101267),f272(x101261,x101268,x101262,x101267,x101265,x101264)),x101263)))+P24(f332(f332(f334(f874(x101261,x101262)),f332(f332(f267(x101261,x101262),f566(x101263,x101264,x101265,x101262,x101261,x101266,x101267,x101268)),f567(x101263,x101264,x101265,x101262,x101261,x101266,x101267,x101268))),x101263)) % 165.28/165.05 [9602]P24(f332(f332(f334(f874(f874(x96021,x96022),f874(x96021,x96022))),f332(f332(f267(f874(x96021,x96022),f874(x96021,x96022)),f332(f332(f267(x96021,x96022),x96023),x96024)),f332(f332(f267(x96021,x96022),x96025),x96026))),f324(x96021,x96022,x96027,x96028)))+~P24(f332(f332(f334(f874(x96021,x96021)),f332(f332(f267(x96021,x96021),x96023),x96025)),x96027)) % 165.28/165.05 [10100]E(f332(f143(x101001,x101002,f332(f7(x101002,x101001,x101001),x101003),f332(x101004,x101005)),x101006),f332(x101004,f332(f143(x101007,x101002,f332(f7(x101002,x101007,x101007),x101008),x101005),x101006)))+P24(f332(f332(f334(x101002),f683(x101005,x101008,x101004,x101003,x101007,x101001,x101006,x101002)),f332(f174(x101002),x101006))) % 165.28/165.05 [10120]~E(f332(f74(x101201,x101201,x101207,f332(x101203,f683(x101205,x101208,x101204,x101203,x101207,x101201,x101206,x101202))),x101204),f332(f74(x101207,x101201,x101207,x101204),f332(x101208,f683(x101205,x101208,x101204,x101203,x101207,x101201,x101206,x101202))))+E(f332(f143(x101201,x101202,f332(f7(x101202,x101201,x101201),x101203),f332(x101204,x101205)),x101206),f332(x101204,f332(f143(x101207,x101202,f332(f7(x101202,x101207,x101207),x101208),x101205),x101206))) % 165.28/165.05 [8439]E(f332(x84391,f332(x84392,x84393)),f332(x84394,f332(x84395,x84393)))+~E(f332(f74(x84396,x84397,x84398,x84391),x84392),f332(f74(x84399,x84397,x84398,x84394),x84395)) % 165.28/165.05 [9987]P24(f332(f332(f334(f874(x99871,x99872)),f332(f332(f267(x99871,x99872),f332(x99873,x99874)),f332(x99875,x99876))),f332(f311(f874(x99877,x99878),f874(x99871,x99872),f272(x99877,x99871,x99878,x99872,x99873,x99875)),x99879)))+~P24(f332(f332(f334(f874(x99877,x99878)),f332(f332(f267(x99877,x99878),x99874),x99876)),x99879)) % 165.28/165.05 [8708]~E(f332(x87084,f332(x87085,x87086)),f332(x87089,f332(x870810,x870811)))+E(f332(f332(f74(x87081,x87082,x87083,x87084),x87085),x87086),f332(f332(f74(x87087,x87082,x87088,x87089),x870810),x870811)) % 165.28/165.05 [4572]~P106(x45721)+~P100(x45721)+E(f104(x45721),f244(x45721)) % 165.28/165.05 [4573]~P106(x45731)+~P99(x45731)+E(f113(x45731),f245(x45731)) % 165.28/165.05 [4817]~P118(x48171)+~P92(x48171)+E(f332(f76(x48171),f332(f106(x48171),a100)),f79(x48171)) % 165.28/165.05 [5097]E(x50971,f2(a1))+E(f83(a1,x50971),f332(f80(a1),f79(a1)))+P24(f332(f332(f247(a1),f2(a1)),x50971)) % 165.28/165.05 [5316]E(x53161,f2(a1))+E(f83(a1,x53161),f79(a1))+~P24(f332(f332(f247(a1),f2(a1)),x53161)) % 165.28/165.05 [7304]~P42(x73041)+P24(f332(f62(a1),x73041))+~P24(f332(f62(a868),f332(f311(a1,a868,a107),x73041))) % 165.28/165.05 [8537]~P1(a5000)+~P24(f332(f332(f334(f874(a865,a863)),x85371),f332(f174(f874(a865,a863)),a27)))+P24(f332(f332(f271(a865,a863,a862),f332(f16(f875(a863,a862),a865),a25)),x85371)) % 165.28/165.05 [9564]E(x95641,f196(f875(f874(a868,a868),a862)))+~P24(f332(f62(f874(a868,a868)),x95641))+P24(f332(f332(f334(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),f196(f875(f874(a868,a868),a862))),x95641)),a37)) % 165.28/165.05 [9734]E(x97341,f2(a868))+E(x97341,f332(a115,f2(a868)))+~P24(f332(f332(f247(a868),x97341),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))) % 165.28/165.05 [10015]E(x100151,f2(a102))+E(f332(f332(f81(a1),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(a20,f332(f332(f39(a102),x100151),f332(f106(a102),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))))),f79(a1)),f332(a20,x100151))+E(f45(a102,x100151,f332(f106(a102),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f2(a102)) % 165.28/165.05 [9866]E(x98661,f2(a102))+~E(f45(a102,x98661,f332(f106(a102),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f2(a102))+E(f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(a20,f332(f332(f39(a102),x98661),f332(f106(a102),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))),f332(a20,x98661)) % 165.28/165.05 [4645]~P56(x46451,x46452)+P47(x46451,x46452)+~P48(a862) % 165.28/165.05 [4582]~P142(x45821)+P34(x45821,x45822)+~E(x45822,f2(x45821)) % 165.28/165.05 [4583]~P106(x45831)+P32(x45831,x45832)+~E(x45832,f116(x45831)) % 165.28/165.05 [4592]~P118(x45921)+~E(x45922,f2(x45921))+E(f83(x45921,x45922),f2(x45921)) % 165.28/165.05 [4593]~P88(x45931)+~E(x45932,f2(x45931))+E(f83(x45931,x45932),f2(x45931)) % 165.28/165.05 [4601]~P142(x46012)+~P34(x46012,x46011)+E(x46011,f2(x46012)) % 165.28/165.05 [4635]~P118(x46352)+~E(f83(x46352,x46351),f2(x46352))+E(x46351,f2(x46352)) % 165.28/165.05 [4652]~P27(x46522)+~P27(x46521)+P27(f875(x46521,x46522)) % 165.28/165.05 [4653]~P27(x46532)+~P27(x46531)+P27(f874(x46531,x46532)) % 165.28/165.05 [4654]~P27(x46542)+~P27(x46541)+P27(f876(x46541,x46542)) % 165.28/165.05 [4655]~P31(x46552)+~P31(x46551)+P31(f202(x46551,x46552)) % 165.28/165.05 [4656]~P143(x46562)+~P143(x46561)+P143(f874(x46561,x46562)) % 165.28/165.05 [4657]~P59(x46572)+~P59(x46571)+P59(f875(x46571,x46572)) % 165.28/165.05 [4658]~P59(x46582)+~P59(x46581)+P59(f874(x46581,x46582)) % 165.28/165.05 [4659]~P59(x46592)+~P59(x46591)+P59(f876(x46591,x46592)) % 165.28/165.05 [4660]~P59(x46601)+~P94(x46602)+P94(f875(x46601,x46602)) % 165.28/165.05 [4661]~P102(x46612)+~P102(x46611)+P102(f874(x46611,x46612)) % 165.28/165.05 [4789]~P106(x47891)+~P32(x47891,x47892)+P32(x47891,f153(x47891,x47892)) % 165.28/165.05 [5028]~P31(x50282)+~P31(x50281)+P31(f45(a1,x50281,x50282)) % 165.28/165.05 [4603]~P75(x46031)+~E(x46032,f2(x46031))+E(f332(f80(x46031),x46032),x46032) % 165.28/165.05 [4607]~P138(x46071)+~E(x46072,f2(a1))+E(f332(f105(x46071),x46072),f2(x46071)) % 165.28/165.05 [4608]~P91(x46081)+~E(x46082,f2(a1))+E(f332(f105(x46081),x46082),f2(x46081)) % 165.28/165.05 [4632]~P67(x46321)+~E(f2(x46321),x46322)+E(f332(f80(x46321),x46322),f2(x46321)) % 165.28/165.05 [4633]~P67(x46331)+~E(x46332,f2(x46331))+E(f332(f80(x46331),x46332),f2(x46331)) % 165.28/165.05 [4634]~P85(x46341)+~E(x46342,f2(x46341))+E(f332(f76(x46341),x46342),f2(x46341)) % 165.28/165.05 [4663]~P75(x46632)+E(x46631,f2(x46632))+~E(f332(f80(x46632),x46631),x46631) % 165.28/165.05 [4669]E(x46691,f332(a107,x46692))+~E(x46691,f2(a868))+~E(x46692,f332(f103(a1),x46691)) % 165.28/165.05 [4670]E(f332(a107,x46701),x46702)+~E(x46702,f2(a868))+~E(x46701,f332(f103(a1),x46702)) % 165.28/165.05 [4674]~P91(x46742)+E(x46741,f2(a1))+~E(f332(f105(x46742),x46741),f2(x46742)) % 165.28/165.05 [4679]~P67(x46792)+E(x46791,f2(x46792))+~E(f332(f80(x46792),x46791),f2(x46792)) % 165.28/165.05 [4680]~P85(x46802)+E(x46801,f2(x46802))+~E(f332(f76(x46802),x46801),f2(x46802)) % 165.28/165.05 [4681]~P67(x46811)+E(f2(x46811),x46812)+~E(f332(f80(x46811),x46812),f2(x46811)) % 165.28/165.05 [4822]~P1(a5000)+~E(f332(a26,x48222),f332(f208(a863),x48221))+P24(f332(a25,x48221)) % 165.28/165.05 [4864]~P106(x48641)+~P32(x48641,x48642)+P32(x48641,f332(f173(x48641),x48642)) % 165.28/165.05 [4890]~P24(x48902)+~P24(x48901)+P24(f332(f332(a330,x48901),x48902)) % 165.28/165.05 [4924]~E(f79(a868),f2(a868))+E(f332(f38(x49241),x49242),f2(a868))+~P24(f332(f62(x49241),x49242)) % 165.28/165.05 [4957]~P140(x49571)+~P110(x49571)+E(f332(f332(f257(x49571),f2(x49571)),f332(a115,x49572)),f2(x49571)) % 165.28/165.05 [4995]~P106(x49951)+P32(x49951,f140(x49951,x49952))+~P24(f332(f62(x49951),x49952)) % 165.28/165.05 [4996]~P106(x49961)+P32(x49961,f690(x49962,x49961))+~P24(f332(f62(x49961),x49962)) % 165.28/165.05 [5018]~P106(x50181)+E(f332(f174(x50181),f140(x50181,x50182)),x50182)+~P24(f332(f62(x50181),x50182)) % 165.28/165.05 [5019]~P106(x50191)+E(f332(f174(x50191),f690(x50192,x50191)),x50192)+~P24(f332(f62(x50191),x50192)) % 165.28/165.05 [5049]P24(x50491)+P24(x50492)+~P24(f332(f332(a331,x50492),x50491)) % 165.28/165.05 [5061]E(x50611,f196(f875(x50612,a862)))+~E(f332(f38(x50612),x50611),f2(a868))+~P24(f332(f62(x50612),x50611)) % 165.28/165.05 [5066]P24(x50661)+~P24(x50662)+~P24(f332(f332(a335,x50662),x50661)) % 165.28/165.05 [5115]~P72(x51151)+E(f332(f76(x51151),x51152),x51152)+P24(f332(f332(f247(x51151),x51152),f2(x51151))) % 165.28/165.05 [5185]~P59(x51852)+~P24(f332(f58(x51852),x51851))+P24(f332(x51851,f608(x51851,x51852))) % 165.28/165.05 [5186]~P59(x51862)+~P24(f332(f58(x51862),x51861))+P24(f332(x51861,f629(x51861,x51862))) % 165.28/165.05 [5214]~P24(f332(a25,x52142))+~P24(f332(a25,x52141))+P24(f332(a25,f34(x52141,x52142))) % 165.28/165.05 [5223]E(x52231,f116(x52232))+P24(f332(f138(x52232),f117(x52232,x52231)))+~P24(f332(f138(x52232),x52231)) % 165.28/165.05 [5228]~P106(x52281)+~P24(f332(f62(x52281),x52282))+P24(f332(f138(x52281),f140(x52281,x52282))) % 165.28/165.05 [5229]~P106(x52291)+~P24(f332(f62(x52291),x52292))+P24(f332(f138(x52291),f690(x52292,x52291))) % 165.28/165.05 [5235]~P138(x52351)+E(f332(f103(x52351),f332(a107,x52352)),f332(f105(x52351),x52352))+P24(f332(f332(f247(a1),x52352),f2(a1))) % 165.28/165.05 [5266]P5(x52662,x52661)+E(f332(x52661,f449(x52661)),f332(x52661,f516(x52661)))+P24(f332(f332(x52661,f449(x52661)),f516(x52661))) % 165.28/165.05 [5281]E(f332(f103(a1),f363(x52811,x52812)),x52811)+P24(f332(x52812,f332(a107,x52811)))+~P24(f332(x52812,f2(a868))) % 165.28/165.05 [5293]~P59(x52931)+~P24(f332(x52932,f630(x52932,x52931)))+P24(f332(f59(x52931),x52932)) % 165.28/165.05 [5294]~P59(x52941)+~P24(f332(x52942,f631(x52942,x52941)))+P24(f332(f59(x52941),x52942)) % 165.28/165.05 [5309]~P59(x53092)+~P39(x53092,x53091,f56(x53092))+P24(f332(x53091,f780(x53091,x53092))) % 165.28/165.05 [5325]~P118(x53251)+~E(f83(x53251,x53252),f332(f80(x53251),f79(x53251)))+P24(f332(f332(f247(x53251),x53252),f2(x53251))) % 165.28/165.05 [5401]~E(x54012,f2(a1))+E(f227(x54011,x54012),f332(f332(f267(a1,a1),f2(a1)),f79(a1)))+P24(f332(f332(f247(a1),x54012),f2(a1))) % 165.28/165.05 [5402]~E(x54021,f2(a1))+E(f227(x54021,x54022),f332(f332(f267(a1,a1),f2(a1)),f79(a1)))+P24(f332(f332(f247(a1),x54022),f2(a1))) % 165.28/165.05 [5454]E(f332(f103(a1),f363(x54541,x54542)),x54541)+P24(f332(x54542,f332(a107,x54541)))+P24(f332(f332(f247(a1),x54541),f2(a1))) % 165.28/165.05 [5517]~P118(x55171)+E(f83(x55171,x55172),f332(f80(x55171),f79(x55171)))+~P24(f332(f332(f247(x55171),x55172),f2(x55171))) % 165.28/165.05 [5518]~P85(x55181)+E(f332(f76(x55181),x55182),f332(f80(x55181),x55182))+~P24(f332(f332(f246(x55181),x55182),f2(x55181))) % 165.28/165.05 [5519]~P85(x55191)+E(f332(f76(x55191),x55192),f332(f80(x55191),x55192))+~P24(f332(f332(f247(x55191),x55192),f2(x55191))) % 165.28/165.05 [5520]~P72(x55201)+E(f332(f76(x55201),x55202),f332(f80(x55201),x55202))+~P24(f332(f332(f247(x55201),x55202),f2(x55201))) % 165.28/165.05 [5617]~P24(f332(x56171,f363(x56172,x56171)))+P24(f332(x56171,f332(a107,x56172)))+~P24(f332(x56171,f2(a868))) % 165.28/165.05 [5624]E(x56241,f2(a868))+E(f332(a115,f822(x56242,x56241)),x56241)+~P24(f332(f332(f247(a868),x56241),f332(a115,x56242))) % 165.28/165.05 [5628]P5(x56281,x56282)+~E(f332(x56282,f449(x56282)),f332(x56282,f516(x56282)))+~P24(f332(f332(x56282,f449(x56282)),f516(x56282))) % 165.28/165.05 [5648]~P106(x56481)+P32(x56481,x56482)+P24(f332(f332(f246(a868),f609(x56482,x56481)),f610(x56482,x56481))) % 165.28/165.05 [5649]~P106(x56491)+P32(x56491,x56492)+P24(f332(f332(f246(a868),f616(x56492,x56491)),f625(x56492,x56491))) % 165.28/165.05 [5737]~P85(x57371)+~E(x57372,f2(x57371))+P24(f332(f332(f246(x57371),f332(f76(x57371),x57372)),f2(x57371))) % 165.28/165.05 [5816]~P59(x58162)+~P59(x58161)+E(f60(x58161,x58162,f56(x58161),f56(x58162)),f56(f874(x58161,x58162))) % 165.28/165.05 [5820]~P24(f332(x58201,f363(x58202,x58201)))+P24(f332(x58201,f332(a107,x58202)))+P24(f332(f332(f247(a1),x58202),f2(a1))) % 165.28/165.05 [5843]~P24(f332(x58431,f332(a107,x58432)))+P24(f332(x58431,f2(a868)))+~P24(f332(f332(f247(a1),x58432),f2(a1))) % 165.28/165.05 [6188]~P118(x61881)+~P24(f332(f332(f247(x61881),x61882),f2(x61881)))+P24(f332(f332(f247(x61881),f83(x61881,x61882)),f2(x61881))) % 165.28/165.05 [6301]~P118(x63011)+P24(f332(f332(f246(x63011),f332(f105(x63011),x63012)),f2(x63011)))+~P24(f332(f332(f246(a1),x63012),f2(a1))) % 165.28/165.05 [6302]~P118(x63021)+P24(f332(f332(f247(x63021),f332(f105(x63021),x63022)),f2(x63021)))+~P24(f332(f332(f247(a1),x63022),f2(a1))) % 165.28/165.05 [6309]~P85(x63092)+E(x63091,f2(x63092))+~P24(f332(f332(f246(x63092),f332(f76(x63092),x63091)),f2(x63092))) % 165.28/165.05 [6387]~P138(x63871)+~P24(f332(f332(f334(x63871),x63872),f112(x63871)))+P24(f332(f332(f334(x63871),f332(f80(x63871),x63872)),f112(x63871))) % 165.28/165.05 [6419]~P118(x64191)+~P24(f332(f332(f247(x64191),f83(x64191,x64192)),f2(x64191)))+P24(f332(f332(f247(x64191),x64192),f2(x64191))) % 165.28/165.05 [6589]~P118(x65892)+~P24(f332(f332(f246(x65892),f332(f105(x65892),x65891)),f2(x65892)))+P24(f332(f332(f246(a1),x65891),f2(a1))) % 165.28/165.05 [6590]~P118(x65902)+~P24(f332(f332(f247(x65902),f332(f105(x65902),x65901)),f2(x65902)))+P24(f332(f332(f247(a1),x65901),f2(a1))) % 165.28/165.05 [7090]~P75(x70901)+~P24(f332(f332(f246(x70901),x70902),f2(x70901)))+P24(f332(f332(f246(x70901),f332(f332(f81(x70901),x70902),x70902)),f2(x70901))) % 165.28/165.05 [7092]~P118(x70921)+~P24(f332(f332(f247(x70921),x70922),f2(x70921)))+P24(f332(f332(f247(x70921),f332(f332(f81(x70921),x70922),x70922)),f2(x70921))) % 165.28/165.05 [7093]~P75(x70931)+~P24(f332(f332(f247(x70931),x70932),f2(x70931)))+P24(f332(f332(f247(x70931),f332(f332(f81(x70931),x70932),x70932)),f2(x70931))) % 165.28/165.05 [7659]~P75(x76591)+~P24(f332(f332(f246(x76591),f332(f332(f81(x76591),x76592),x76592)),f2(x76591)))+P24(f332(f332(f246(x76591),x76592),f2(x76591))) % 165.28/165.05 [7660]~P118(x76601)+~P24(f332(f332(f247(x76601),f332(f332(f81(x76601),x76602),x76602)),f2(x76601)))+P24(f332(f332(f247(x76601),x76602),f2(x76601))) % 165.28/165.05 [7661]~P75(x76611)+~P24(f332(f332(f247(x76611),f332(f332(f81(x76611),x76612),x76612)),f2(x76611)))+P24(f332(f332(f247(x76611),x76612),f2(x76611))) % 165.28/165.05 [4719]~E(x47192,f2(a868))+~E(x47191,f2(a868))+E(f332(f332(f81(a868),x47191),x47192),f2(a868)) % 165.28/165.05 [4720]~E(x47202,f79(a868))+~E(x47201,f79(a868))+E(f332(f332(f82(a868),x47201),x47202),f79(a868)) % 165.28/165.05 [4721]~E(x47212,f79(a1))+~E(x47211,f79(a1))+E(f332(f332(f82(a1),x47211),x47212),f79(a1)) % 165.28/165.05 [4775]~P28(x47752)+E(x47751,f2(x47752))+E(f332(f332(f39(x47752),x47751),x47751),f79(x47752)) % 165.28/165.05 [4776]~P116(x47762)+E(x47761,f2(x47762))+E(f332(f332(f290(x47762),x47761),x47761),f79(x47762)) % 165.28/165.05 [4777]~P117(x47772)+E(x47771,f2(x47772))+E(f332(f332(f290(x47772),x47771),x47771),f79(x47772)) % 165.28/165.05 [4793]~P75(x47931)+~E(x47932,f2(x47931))+E(f332(f332(f81(x47931),x47932),x47932),f2(x47931)) % 165.28/165.05 [4796]~P137(x47961)+~E(x47962,f79(x47961))+E(f332(f332(f82(x47961),x47962),x47962),f79(x47961)) % 165.28/165.05 [4797]~P117(x47971)+~E(x47972,f2(x47971))+E(f332(f332(f290(x47971),x47972),x47972),f2(x47971)) % 165.28/165.05 [4843]~E(x48432,f2(a868))+~E(x48431,f2(a868))+E(f332(f80(a1),f332(f103(a1),x48431)),f332(f103(a1),x48432)) % 165.28/165.05 [4861]E(x48611,f79(a868))+E(x48612,f2(a868))+~E(f332(f332(f82(a868),x48612),x48611),x48612) % 165.28/165.05 [4871]E(x48711,f2(a868))+E(x48712,f2(a868))+~E(f332(f332(f82(a868),x48712),x48711),f2(a868)) % 165.28/165.05 [4899]~E(x48992,f2(a868))+~E(x48991,f332(a115,f2(a868)))+E(f332(f332(f81(a868),x48991),x48992),f332(a115,f2(a868))) % 165.28/165.05 [4900]~E(x49001,f2(a868))+~E(x49002,f332(a115,f2(a868)))+E(f332(f332(f81(a868),x49001),x49002),f332(a115,f2(a868))) % 165.28/165.05 [4907]E(x49071,f79(a1))+E(x49072,f332(f106(a1),a100))+~E(f332(f332(f82(a1),x49071),x49072),f79(a1)) % 165.28/165.05 [4908]E(x49081,f79(a1))+E(x49082,f332(f106(a1),a100))+~E(f332(f332(f82(a1),x49082),x49081),f79(a1)) % 165.28/165.05 [4909]E(x49091,f79(a1))+E(x49091,f332(f106(a1),a100))+~E(f332(f332(f82(a1),x49092),x49091),f79(a1)) % 165.28/165.05 [4911]E(x49111,f79(a1))+E(x49111,f332(f106(a1),a100))+~E(f332(f332(f82(a1),x49111),x49112),f79(a1)) % 165.28/165.05 [4928]~P75(x49282)+E(x49281,f2(x49282))+~E(f332(f332(f81(x49282),x49281),x49281),f2(x49282)) % 165.28/165.05 [4934]~E(x49341,f332(f106(a1),a100))+~E(x49342,f332(f106(a1),a100))+E(f332(f332(f82(a1),x49341),x49342),f79(a1)) % 165.28/165.05 [4946]E(x49461,f2(a868))+E(x49462,f2(a868))+~E(f332(f332(f81(a868),x49462),x49461),f332(a115,f2(a868))) % 165.28/165.05 [4956]~P60(x49561)+~P92(x49561)+E(f332(f332(f290(x49561),x49562),f332(f106(x49561),a84)),f2(x49561)) % 165.28/165.05 [4962]~P137(x49621)+~E(x49622,f332(f80(x49621),f79(x49621)))+E(f332(f332(f82(x49621),x49622),x49622),f79(x49621)) % 165.28/165.05 [4967]~P31(x49672)+~P31(x49671)+P31(f332(f332(f81(a1),x49671),x49672)) % 165.28/165.05 [4968]~P31(x49682)+~P31(x49681)+P31(f332(f332(f82(a1),x49681),x49682)) % 165.28/165.05 [4969]~P31(x49692)+~P31(x49691)+P31(f332(f332(f39(a1),x49691),x49692)) % 165.28/165.05 [4971]~E(x49712,f2(a1))+E(x49711,f2(a1))+E(f46(x49711,x49712),f332(f332(f267(a1,a1),f2(a1)),x49711)) % 165.28/165.05 [4993]~E(x49932,f332(a115,f2(a868)))+~E(x49931,f332(a115,f2(a868)))+E(f332(f332(f82(a868),x49931),x49932),f332(a115,f2(a868))) % 165.28/165.05 [5008]E(x50081,f2(a868))+E(x50082,f332(a115,f2(a868)))+~E(f332(f332(f257(a868),x50082),x50081),f332(a115,f2(a868))) % 165.28/165.05 [5009]E(x50091,f2(a868))+E(x50091,f332(a115,f2(a868)))+~E(f332(f332(f81(a868),x50092),x50091),f332(a115,f2(a868))) % 165.28/165.05 [5010]E(x50101,f2(a868))+E(x50101,f332(a115,f2(a868)))+~E(f332(f332(f81(a868),x50101),x50102),f332(a115,f2(a868))) % 165.28/165.05 [5020]~P60(x50201)+~P92(x50201)+E(f332(f332(f290(x50201),x50202),f332(f106(x50201),a100)),f332(f80(x50201),x50202)) % 165.28/165.05 [5041]E(x50411,f332(a107,x50412))+~E(x50411,f2(a868))+P24(f332(f332(f246(a1),f2(a1)),x50412)) % 165.28/165.05 [5042]E(f332(a107,x50421),x50422)+~E(x50422,f2(a868))+P24(f332(f332(f246(a1),f2(a1)),x50421)) % 165.28/165.05 [5057]E(x50571,f332(a115,f2(a868)))+E(x50572,f332(a115,f2(a868)))+~E(f332(f332(f81(a868),x50571),x50572),f332(a115,f2(a868))) % 165.28/165.05 [5068]~E(x50681,f332(a107,x50682))+E(x50681,f2(a868))+P24(f332(f332(f246(a1),f2(a1)),x50682)) % 165.28/165.05 [5069]~E(f332(a107,x50692),x50691)+E(x50691,f2(a868))+P24(f332(f332(f246(a1),f2(a1)),x50692)) % 165.28/165.05 [5091]~P26(x50911)+E(f332(f64(x50911,f113(x50911)),x50912),f10(x50911,x50912))+~P24(f332(f62(x50911),x50912)) % 165.28/165.05 [5092]~P26(x50921)+E(f332(f64(x50921,f104(x50921)),x50922),f11(x50921,x50922))+~P24(f332(f62(x50921),x50922)) % 165.28/165.05 [5093]~P106(x50931)+E(f332(f64(x50931,f245(x50931)),x50932),f14(x50931,x50932))+~P24(f332(f62(x50931),x50932)) % 165.28/165.05 [5094]~P106(x50941)+E(f332(f64(x50941,f244(x50941)),x50942),f15(x50941,x50942))+~P24(f332(f62(x50941),x50942)) % 165.28/165.05 [5096]~P59(x50961)+~P24(f332(x50962,f209(x50961)))+P24(f332(f58(f872(x50961)),x50962)) % 165.28/165.05 [5178]~P59(x51782)+P24(f332(x51781,f209(x51782)))+~P24(f332(f59(f872(x51782)),x51781)) % 165.28/165.05 [5179]E(x51791,x51792)+~E(f332(f332(f22(a868),x51792),x51791),f2(a868))+~E(f332(f332(f22(a868),x51791),x51792),f2(a868)) % 165.28/165.05 [5193]P31(x51931)+~P42(x51932)+~P24(f332(f332(f334(a1),x51931),x51932)) % 165.28/165.05 [5224]~P118(x52241)+~E(f83(x52241,x52242),f79(x52241))+P24(f332(f332(f247(x52241),f2(x52241)),x52242)) % 165.28/165.05 [5236]~P92(x52361)+E(f332(f103(x52361),f332(f106(a868),x52362)),f332(f106(x52361),x52362))+P24(f332(a201,f332(f106(a1),x52362))) % 165.28/165.05 [5242]~P47(x52421,x52422)+P48(a862)+P24(f332(f62(f874(x52421,x52421)),x52422)) % 165.28/165.05 [5318]~P106(x53181)+E(f332(f64(x53181,f244(x53181)),x53182),f12(x53181,f244(x53181),x53182))+~P24(f332(f62(x53181),x53182)) % 165.28/165.05 [5319]~P106(x53191)+E(f332(f64(x53191,f245(x53191)),x53192),f13(x53191,f245(x53191),x53192))+~P24(f332(f62(x53191),x53192)) % 165.28/165.05 [5332]E(x53321,x53322)+P24(f332(f332(f247(a868),x53322),x53321))+P24(f332(f332(f247(a868),x53321),x53322)) % 165.28/165.05 [5333]E(x53331,x53332)+P24(f332(f332(f247(a1),x53332),x53331))+P24(f332(f332(f247(a1),x53331),x53332)) % 165.28/165.05 [5388]~P92(x53881)+E(f332(f103(x53881),f332(f106(a868),x53882)),f2(x53881))+~P24(f332(a201,f332(f106(a1),x53882))) % 165.28/165.05 [5391]~E(x53912,f332(a107,x53911))+E(x53911,f332(f103(a1),x53912))+~P24(f332(f332(f246(a1),f2(a1)),x53911)) % 165.28/165.05 [5392]~E(f332(a107,x53921),x53922)+E(x53921,f332(f103(a1),x53922))+~P24(f332(f332(f246(a1),f2(a1)),x53921)) % 165.28/165.05 [5393]~E(x53931,f332(a107,x53932))+E(f332(f103(a1),x53931),x53932)+~P24(f332(f332(f246(a1),f2(a1)),x53932)) % 165.28/165.05 [5403]E(x54031,f332(a107,x54032))+~E(x54032,f332(f103(a1),x54031))+~P24(f332(f332(f246(a1),f2(a1)),x54032)) % 165.28/165.05 [5404]E(f332(a107,x54041),x54042)+~E(x54041,f332(f103(a1),x54042))+~P24(f332(f332(f246(a1),f2(a1)),x54041)) % 165.28/165.05 [5443]~P85(x54432)+E(x54431,f2(x54432))+P24(f332(f332(f247(x54432),f2(x54432)),f332(f76(x54432),x54431))) % 165.28/165.05 [5510]~P118(x55101)+E(f83(x55101,x55102),f79(x55101))+~P24(f332(f332(f247(x55101),f2(x55101)),x55102)) % 165.28/165.05 [5514]~P92(x55141)+E(f332(f103(x55141),f332(f106(a868),x55142)),f2(x55141))+P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x55142))) % 165.28/165.05 [5521]~P85(x55211)+E(f332(f76(x55211),x55212),x55212)+~P24(f332(f332(f246(x55211),f2(x55211)),x55212)) % 165.28/165.05 [5522]~P85(x55221)+E(f332(f76(x55221),x55222),x55222)+~P24(f332(f332(f247(x55221),f2(x55221)),x55222)) % 165.28/165.05 [5531]E(x55311,f2(a868))+~E(f140(a868,f332(f302(a868,x55312),x55311)),f116(a868))+P24(f332(f332(f246(a868),x55311),x55312)) % 165.28/165.05 [5541]~P74(x55411)+E(f332(f332(f6(x55411,x55411),f5(x55411)),f332(f174(x55411),x55412)),f332(f167(x55411),x55412))+~P24(f332(f138(x55411),x55412)) % 165.28/165.05 [5544]~P138(x55441)+E(f332(f103(x55441),f332(a107,x55442)),f332(f105(x55441),x55442))+~P24(f332(f332(f246(a1),f2(a1)),x55442)) % 165.28/165.05 [5571]E(x55711,x55712)+P24(f332(f332(f247(a868),x55711),x55712))+~P24(f332(f332(f246(a868),x55711),x55712)) % 165.28/165.05 [5572]E(x55721,x55722)+P24(f332(f332(f247(a1),x55721),x55722))+~P24(f332(f332(f246(a1),x55721),x55722)) % 165.28/165.05 [5575]E(x55751,f79(a1))+~E(f332(f332(f82(a1),x55752),x55751),f79(a1))+~P24(f332(f332(f247(a1),f2(a1)),x55752)) % 165.28/165.05 [5576]E(x55761,f79(a1))+~E(f332(f332(f82(a1),x55761),x55762),f79(a1))+~P24(f332(f332(f247(a1),f2(a1)),x55761)) % 165.28/165.05 [5614]~P42(x56142)+P24(f332(f332(f246(a1),f2(a1)),x56141))+~P24(f332(f332(f334(a1),x56141),x56142)) % 165.28/165.05 [5633]~P56(x56331,x56332)+P41(x56331,x56332)+~P24(f332(f62(f874(x56331,x56331)),x56332)) % 165.28/165.05 [5635]~P56(x56351,x56352)+P47(x56351,x56352)+~P24(f332(f62(f874(x56351,x56351)),x56352)) % 165.28/165.05 [5679]E(x56791,f196(f875(x56792,a862)))+~P24(f332(f62(x56792),x56791))+P24(f332(f332(f247(a868),f2(a868)),f332(f38(x56792),x56791))) % 165.28/165.05 [5706]~P24(f332(x57061,x57062))+P24(f332(x57061,f2(a868)))+P24(f332(f332(f247(a868),f408(x57062,x57061)),x57062)) % 165.28/165.05 [5731]E(x57311,f2(a868))+~E(f332(f167(a868),x57312),f2(a868))+~P24(f332(f332(f334(a868),x57311),f332(f174(a868),x57312))) % 165.28/165.05 [5797]E(x57971,x57972)+~P24(f332(f332(f246(a868),x57972),x57971))+~P24(f332(f332(f246(a868),x57971),x57972)) % 165.28/165.05 [5798]E(x57981,x57982)+~P24(f332(f332(f246(a1),x57982),x57981))+~P24(f332(f332(f246(a1),x57981),x57982)) % 165.28/165.05 [5799]E(f332(f38(x57991),x57992),f2(a868))+~P24(f332(f62(x57991),x57992))+P24(f332(f332(f334(x57991),f450(x57992,x57991)),x57992)) % 165.28/165.05 [5808]E(f50(x58081,x58082),f46(x58081,x58082))+P24(f332(f332(f246(a1),f2(a1)),x58081))+~P24(f332(f332(f247(a1),f2(a1)),x58082)) % 165.28/165.05 [5832]~P24(f332(x58321,f360(x58321)))+P24(f332(x58321,f332(a107,x58322)))+~P24(f332(f332(f246(a1),f2(a1)),x58322)) % 165.28/165.05 [5834]P24(f332(f332(f246(a868),x58341),f793(x58342)))+~P24(f332(f62(a868),x58342))+~P24(f332(f332(f334(a868),x58341),x58342)) % 165.28/165.05 [5835]P24(f332(f332(f247(a868),x58351),f815(x58352)))+~P24(f332(f62(a868),x58352))+~P24(f332(f332(f334(a868),x58351),x58352)) % 165.28/165.05 [5864]E(x58641,x58642)+~P24(f332(f332(f247(a868),x58641),f332(a115,x58642)))+P24(f332(f332(f247(a868),x58641),x58642)) % 165.28/165.05 [5898]E(x58981,f332(a115,x58982))+~P24(f332(f332(f246(a868),x58981),f332(a115,x58982)))+P24(f332(f332(f246(a868),x58981),x58982)) % 165.28/165.05 [5911]P24(f332(x59111,f361(x59111)))+~P24(f332(x59111,f332(a107,x59112)))+~P24(f332(f332(f246(a1),f2(a1)),x59112)) % 165.28/165.05 [5925]~P24(f332(x59251,x59252))+~P24(f332(f332(f246(a1),f2(a1)),x59252))+P24(f332(x59251,f332(f103(a1),f344(x59251)))) % 165.28/165.05 [5939]~P85(x59392)+~E(x59391,f2(x59392))+~P24(f332(f332(f247(x59392),f2(x59392)),f332(f76(x59392),x59391))) % 165.28/165.05 [5963]~P56(x59631,x59632)+P41(x59631,f332(f287(x59631,x59631),x59632))+~P24(f332(f62(f874(x59631,x59631)),x59632)) % 165.28/165.05 [5971]~P92(x59711)+E(f332(f103(x59711),f332(f106(a868),x59712)),f332(f106(x59711),x59712))+~P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x59712))) % 165.28/165.05 [5974]E(f332(a115,x59741),x59742)+~P24(f332(f332(f247(a868),x59741),x59742))+P24(f332(f332(f247(a868),f332(a115,x59741)),x59742)) % 165.28/165.05 [5990]E(f332(f332(f39(a1),x59901),x59902),f2(a1))+~P24(f332(f332(f246(a1),x59901),f2(a1)))+~P24(f332(f332(f247(a1),x59902),x59901)) % 165.28/165.05 [6003]E(f45(a1,x60031,x60032),x60031)+~P24(f332(f332(f246(a1),x60031),f2(a1)))+~P24(f332(f332(f247(a1),x60032),x60031)) % 165.28/165.05 [6016]E(f47(x60161,x60162),f46(x60161,x60162))+~P24(f332(f332(f246(a1),f2(a1)),x60161))+~P24(f332(f332(f246(a1),f2(a1)),x60162)) % 165.28/165.05 [6024]E(f332(f332(f39(a1),x60241),x60242),f2(a1))+~P24(f332(f332(f246(a1),f2(a1)),x60241))+~P24(f332(f332(f247(a1),x60241),x60242)) % 165.28/165.05 [6036]E(f45(a868,f332(f106(a868),x60361),f332(f106(a868),x60362)),f332(f106(a868),x60361))+P24(f332(a201,f332(f106(a1),x60361)))+~P24(f332(a201,f332(f106(a1),x60362))) % 165.28/165.05 [6038]E(f45(a1,x60381,x60382),x60381)+~P24(f332(f332(f246(a1),f2(a1)),x60381))+~P24(f332(f332(f247(a1),x60381),x60382)) % 165.28/165.05 [6039]E(x60391,x60392)+~P24(f332(f332(f247(a868),x60391),f332(a115,x60392)))+~P24(f332(f332(f246(a868),x60392),x60391)) % 165.28/165.05 [6056]~P75(x60561)+~P24(f332(f332(f246(x60561),x60562),f2(x60561)))+P24(f332(f332(f246(x60561),x60562),f332(f80(x60561),x60562))) % 165.28/165.05 [6057]~P118(x60571)+~P24(f332(f332(f247(x60571),x60572),f2(x60571)))+P24(f332(f332(f247(x60571),x60572),f332(f80(x60571),x60572))) % 165.28/165.05 [6067]~P30(x60671)+E(f332(f332(f65(x60671,x60671,f113(x60671)),f196(x60671)),x60672),f40(x60671,x60672))+~P24(f332(f62(x60671),x60672)) % 165.28/165.05 [6068]~P30(x60681)+E(f332(f332(f65(x60681,x60681,f104(x60681)),f255(x60681)),x60682),f41(x60681,x60682))+~P24(f332(f62(x60681),x60682)) % 165.28/165.05 [6082]~P118(x60821)+~P24(f332(f332(f246(a1),f2(a1)),x60822))+P24(f332(f332(f246(x60821),f2(x60821)),f332(f105(x60821),x60822))) % 165.28/165.05 [6083]~P112(x60831)+~P24(f332(f332(f247(a868),f2(a868)),x60832))+P24(f332(f332(f247(x60831),f2(x60831)),f332(f103(x60831),x60832))) % 165.28/165.05 [6084]~P118(x60841)+~P24(f332(f332(f247(a1),f2(a1)),x60842))+P24(f332(f332(f247(x60841),f2(x60841)),f332(f105(x60841),x60842))) % 165.28/165.05 [6087]~P31(x60872)+~P31(x60871)+E(f332(f311(a868,a1,f103(a1)),f303(a868,f332(a107,x60871),f332(a107,x60872))),f303(a1,x60871,x60872)) % 165.28/165.05 [6093]P24(f332(x60931,x60932))+~P24(f332(f332(f246(a1),f2(a1)),x60932))+~P24(f332(x60931,f332(f103(a1),f348(x60931)))) % 165.28/165.05 [6120]E(f332(f332(f81(a868),f332(f106(a868),x61201)),f332(f106(a868),x61202)),f332(f106(a868),x61201))+P24(f332(f332(f247(a1),x61201),a84))+~P24(f332(f332(f247(a1),x61202),a84)) % 165.28/165.05 [6124]~P118(x61241)+P24(f332(f332(f247(x61241),f2(x61241)),f83(x61241,x61242)))+~P24(f332(f332(f247(x61241),f2(x61241)),x61242)) % 165.28/165.05 [6135]~P77(x61351)+~P24(f332(f332(f246(x61351),x61352),f2(x61351)))+P24(f332(f332(f246(x61351),f2(x61351)),f332(f80(x61351),x61352))) % 165.28/165.05 [6136]~P77(x61361)+~P24(f332(f332(f247(x61361),x61362),f2(x61361)))+P24(f332(f332(f247(x61361),f2(x61361)),f332(f80(x61361),x61362))) % 165.28/165.05 [6139]E(x61391,f255(f875(x61392,a862)))+~E(f332(f38(x61392),x61391),f332(f38(x61392),f255(f875(x61392,a862))))+~P24(f332(f62(x61392),f255(f875(x61392,a862)))) % 165.28/165.05 [6180]~P75(x61801)+P24(f332(f332(f246(x61801),x61802),f2(x61801)))+~P24(f332(f332(f246(x61801),x61802),f332(f80(x61801),x61802))) % 165.28/165.05 [6181]~P118(x61811)+P24(f332(f332(f247(x61811),x61812),f2(x61811)))+~P24(f332(f332(f247(x61811),x61812),f332(f80(x61811),x61812))) % 165.28/165.05 [6190]~P92(x61901)+P24(f332(f332(f334(x61901),f332(f106(x61901),x61902)),f194(x61901)))+~P24(f332(f332(f246(a1),a84),x61902)) % 165.28/165.05 [6221]E(x62211,f2(a868))+~P24(f332(f332(f247(a868),x62211),f332(a115,x62212)))+P24(f332(f332(f247(a868),f822(x62212,x62211)),x62212)) % 165.28/165.05 [6243]~P118(x62431)+~P24(f332(f332(f247(x62431),f2(x62431)),f83(x62431,x62432)))+P24(f332(f332(f247(x62431),f2(x62431)),x62432)) % 165.28/165.05 [6245]~E(f332(f106(a868),x62452),f332(f106(a868),x62451))+P24(f332(f332(f246(a1),f332(f106(a1),x62451)),f2(a1)))+~P24(f332(a201,f332(f106(a1),x62452))) % 165.28/165.05 [6274]E(f332(f266(a1,a1),f50(x62741,x62742)),f332(f332(f39(a1),x62741),x62742))+~P24(f332(f332(f247(a1),x62741),f2(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x62742)) % 165.28/165.05 [6307]E(f332(f270(a1,a1),f50(x63071,x63072)),f45(a1,x63071,x63072))+~P24(f332(f332(f247(a1),x63071),f2(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x63072)) % 165.28/165.05 [6310]~P118(x63102)+~P24(f332(f332(f246(x63102),f2(x63102)),f332(f105(x63102),x63101)))+P24(f332(f332(f246(a1),f2(a1)),x63101)) % 165.28/165.05 [6311]~P112(x63112)+~P24(f332(f332(f247(x63112),f2(x63112)),f332(f103(x63112),x63111)))+P24(f332(f332(f247(a868),f2(a868)),x63111)) % 165.28/165.05 [6312]~P118(x63122)+~P24(f332(f332(f247(x63122),f2(x63122)),f332(f105(x63122),x63121)))+P24(f332(f332(f247(a1),f2(a1)),x63121)) % 165.28/165.05 [6315]E(f332(f266(a1,a1),f47(x63151,x63152)),f332(f332(f39(a1),x63151),x63152))+~P24(f332(f332(f246(a1),f2(a1)),x63152))+~P24(f332(f332(f247(a1),f2(a1)),x63151)) % 165.28/165.05 [6330]E(f332(f270(a1,a1),f47(x63301,x63302)),f45(a1,x63301,x63302))+~P24(f332(f332(f246(a1),f2(a1)),x63302))+~P24(f332(f332(f247(a1),f2(a1)),x63301)) % 165.28/165.05 [6347]~P77(x63471)+P24(f332(f332(f246(x63471),x63472),f2(x63471)))+~P24(f332(f332(f246(x63471),f2(x63471)),f332(f80(x63471),x63472))) % 165.28/165.05 [6348]~P77(x63481)+P24(f332(f332(f247(x63481),x63482),f2(x63481)))+~P24(f332(f332(f247(x63481),f2(x63481)),f332(f80(x63481),x63482))) % 165.28/165.05 [6374]P24(f332(f49(x63741,x63742),f50(x63741,x63742)))+~P24(f332(f332(f247(a1),x63741),f2(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x63742)) % 165.28/165.05 [6399]P24(f332(f49(x63991,x63992),f47(x63991,x63992)))+~P24(f332(f332(f246(a1),f2(a1)),x63991))+~P24(f332(f332(f247(a1),f2(a1)),x63992)) % 165.28/165.05 [6442]~P77(x64421)+P24(f332(f332(f246(x64421),f332(f80(x64421),x64422)),f2(x64421)))+~P24(f332(f332(f246(x64421),f2(x64421)),x64422)) % 165.28/165.05 [6443]~P77(x64431)+P24(f332(f332(f247(x64431),f332(f80(x64431),x64432)),f2(x64431)))+~P24(f332(f332(f247(x64431),f2(x64431)),x64432)) % 165.28/165.05 [6460]E(f332(f332(f22(a868),f332(a107,x64601)),f332(a107,x64602)),f332(a107,f202(x64601,x64602)))+~P24(f332(f332(f246(a1),f2(a1)),x64602))+~P24(f332(f332(f246(a1),f2(a1)),x64601)) % 165.28/165.05 [6477]P24(f332(f332(f246(a1),f2(a1)),f202(x64771,x64772)))+~P24(f332(f332(f246(a1),f2(a1)),x64772))+~P24(f332(f332(f246(a1),f2(a1)),x64771)) % 165.28/165.05 [6515]~P24(f332(x65151,x65152))+P24(f332(x65151,f2(a868)))+P24(f332(x65151,f332(f332(f81(a868),f408(x65152,x65151)),f79(a868)))) % 165.28/165.05 [6596]E(f332(f106(a868),x65961),f332(f106(a868),x65962))+~P24(f332(f332(f246(a1),f332(f106(a1),x65962)),f2(a1)))+~P24(f332(a201,f332(f106(a1),x65961))) % 165.28/165.05 [6606]~E(x66061,f2(a868))+~E(f571(x66062,x66061),f2(a868))+E(f332(f143(a868,a868,f81(a868),x66061),x66062),f2(a868)) % 165.28/165.05 [6631]~P24(f332(f62(x66311),f635(x66312,x66311)))+~P24(f332(f62(f875(x66311,a862)),x66312))+P24(f332(f62(x66311),f40(f875(x66311,a862),x66312))) % 165.28/165.05 [6637]E(x66371,x66372)+P24(f332(f332(f247(a1),x66371),x66372))+~P24(f332(f332(f247(a1),x66371),f332(f332(f81(a1),x66372),f79(a1)))) % 165.28/165.05 [6638]P24(f332(f332(f246(a868),f332(a107,x66381)),f332(a107,x66382)))+~P24(f332(f332(f246(a1),f2(a1)),x66382))+~P24(f332(f332(f246(a1),x66381),x66382)) % 165.28/165.05 [6639]P24(f332(f332(f246(a868),f332(a107,x66391)),f332(a107,x66392)))+~P24(f332(f332(f247(a1),f2(a1)),x66391))+~P24(f332(f332(f246(a1),x66391),x66392)) % 165.28/165.05 [6641]P24(f332(f332(f247(a868),f332(a107,x66411)),f332(a107,x66412)))+~P24(f332(f332(f246(a1),f2(a1)),x66411))+~P24(f332(f332(f247(a1),x66411),x66412)) % 165.28/165.05 [6642]P24(f332(f332(f247(a868),f332(a107,x66421)),f332(a107,x66422)))+~P24(f332(f332(f247(a1),f2(a1)),x66422))+~P24(f332(f332(f247(a1),x66421),x66422)) % 165.28/165.05 [6653]E(f45(a868,f332(a107,x66531),f332(a107,x66532)),f332(a107,f45(a1,x66531,x66532)))+~P24(f332(f332(f246(a1),f2(a1)),x66532))+~P24(f332(f332(f246(a1),f2(a1)),x66531)) % 165.28/165.05 [6675]~P77(x66751)+~P24(f332(f332(f246(x66751),f332(f80(x66751),x66752)),f2(x66751)))+P24(f332(f332(f246(x66751),f2(x66751)),x66752)) % 165.28/165.05 [6676]~P77(x66761)+~P24(f332(f332(f247(x66761),f332(f80(x66761),x66762)),f2(x66761)))+P24(f332(f332(f247(x66761),f2(x66761)),x66762)) % 165.28/165.05 [6691]~P24(f332(f332(f247(a1),a84),x66912))+~P24(f332(f332(f247(a1),x66911),x66912))+P24(f332(f332(f247(a868),f332(f106(a868),x66911)),f332(f106(a868),x66912))) % 165.28/165.05 [6782]~P24(f332(f332(f246(a1),f2(a1)),x67821))+P24(f332(f332(f247(a868),f332(a107,x67821)),x67822))+~P24(f332(f332(f247(a1),x67821),f332(f103(a1),x67822))) % 165.28/165.05 [6799]E(x67991,f2(a1))+E(f45(a1,x67992,x67991),f2(a1))+E(f332(f332(f22(a1),f332(f80(a1),f332(f332(f39(a1),x67992),x67991))),f79(a1)),f332(f332(f39(a1),x67992),f332(f80(a1),x67991))) % 165.28/165.05 [6815]~P24(f332(f332(f246(a1),f2(a1)),x68151))+~P24(f332(f332(f247(a868),f332(a107,x68151)),x68152))+P24(f332(f332(f247(a1),x68151),f332(f103(a1),x68152))) % 165.28/165.05 [6850]~P24(f332(f332(f246(a868),f332(a107,x68501)),f332(a107,x68502)))+~P24(f332(f332(f246(a1),f2(a1)),x68502))+P24(f332(f332(f246(a1),x68501),x68502)) % 165.28/165.05 [6851]~P24(f332(f332(f246(a868),f332(a107,x68511)),f332(a107,x68512)))+~P24(f332(f332(f247(a1),f2(a1)),x68511))+P24(f332(f332(f246(a1),x68511),x68512)) % 165.28/165.05 [6879]P24(f332(f332(f246(a1),x68791),x68792))+~P24(f332(f332(f246(a868),f332(f106(a868),x68791)),f332(f106(a868),x68792)))+P24(f332(f332(f246(a1),x68791),a84)) % 165.28/165.05 [6904]P24(f332(f332(f246(a1),f2(a1)),f45(a1,x69041,x69042)))+~P24(f332(f332(f246(a1),f2(a1)),x69042))+~P24(f332(f332(f246(a1),f2(a1)),x69041)) % 165.28/165.05 [7002]P24(f332(f332(f247(a1),a84),x70021))+~P24(f332(f332(f247(a1),x70022),x70021))+~P24(f332(f332(f247(a868),f332(f106(a868),x70022)),f332(f106(a868),x70021))) % 165.28/165.05 [7053]E(f332(f332(f267(a1,a1),f332(f332(f39(a1),x70531),x70532)),f45(a1,x70531,x70532)),f50(x70531,x70532))+~P24(f332(f332(f247(a1),x70531),f2(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x70532)) % 165.28/165.05 [7074]E(f332(f332(f267(a1,a1),f332(f332(f39(a1),x70741),x70742)),f45(a1,x70741,x70742)),f47(x70741,x70742))+~P24(f332(f332(f246(a1),f2(a1)),x70742))+~P24(f332(f332(f246(a1),f2(a1)),x70741)) % 165.28/165.05 [7125]~P95(x71252)+E(x71251,f116(x71252))+E(f332(f143(x71252,x71252,f82(x71252),f332(f142(x71252),x71251)),f332(f173(x71252),x71251)),f332(f64(x71252,f82(x71252)),f332(f174(x71252),x71251))) % 165.28/165.05 [7237]~E(x72371,f2(a868))+E(f332(f143(a868,a868,f81(a868),x72371),x72372),f2(a868))+P24(f332(f332(f334(a868),f571(x72372,x72371)),f332(f174(a868),x72372))) % 165.28/165.05 [7284]~P24(f332(f332(f246(a1),x72841),f2(a1)))+P24(f332(f332(f246(a1),f332(f332(f39(a1),x72841),x72842)),f2(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x72842)) % 165.28/165.05 [7285]~P24(f332(f332(f247(a1),x72852),f2(a1)))+P24(f332(f332(f246(a1),f332(f332(f39(a1),x72851),x72852)),f2(a1)))+~P24(f332(f332(f246(a1),f2(a1)),x72851)) % 165.28/165.05 [7286]~P24(f332(f332(f247(a1),x72862),f2(a1)))+P24(f332(f332(f247(a1),f332(f332(f39(a1),x72861),x72862)),f2(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x72861)) % 165.28/165.05 [7288]~P24(f332(f332(f247(a1),x72881),f2(a1)))+P24(f332(f332(f247(a1),f332(f332(f39(a1),x72881),x72882)),f2(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x72882)) % 165.28/165.05 [7294]P24(f332(f332(f334(f875(x72941,a862)),f635(x72942,x72941)),x72942))+~P24(f332(f62(f875(x72941,a862)),x72942))+P24(f332(f62(x72941),f40(f875(x72941,a862),x72942))) % 165.28/165.05 [7389]P21(x73891,x73891,x73892,f255(f875(x73891,a862)))+~E(f332(f311(x73891,x73891,x73892),f255(f875(x73891,a862))),f255(f875(x73891,a862)))+~P24(f332(f62(x73891),f255(f875(x73891,a862)))) % 165.28/165.05 [7516]~P21(x75161,x75161,x75162,f255(f875(x75161,a862)))+E(f332(f311(x75161,x75161,x75162),f255(f875(x75161,a862))),f255(f875(x75161,a862)))+~P24(f332(f62(x75161),f255(f875(x75161,a862)))) % 165.28/165.05 [7653]E(f332(f332(f39(a1),x76531),x76532),f332(f106(a1),a100))+~P24(f332(f332(f246(a1),f332(f332(f81(a1),x76531),x76532)),f2(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x76531)) % 165.28/165.05 [7712]~P24(f332(f332(f247(a1),x77122),f2(a1)))+~P24(f332(f332(f247(a1),f332(f332(f39(a1),x77121),x77122)),f2(a1)))+P24(f332(f332(f247(a1),f2(a1)),x77121)) % 165.28/165.05 [7717]E(f332(f332(f81(a1),x77171),x77172),f45(a1,x77171,x77172))+~P24(f332(f332(f246(a1),f332(f332(f81(a1),x77171),x77172)),f2(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x77171)) % 165.28/165.05 [7720]P24(f332(f332(f247(a1),x77201),f2(a1)))+~P24(f332(f332(f247(a1),f332(f332(f39(a1),x77201),x77202)),f2(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x77202)) % 165.28/165.05 [8102]~P59(x81021)+~P24(f332(f59(f872(x81021)),x81022))+P24(f332(f59(x81021),f332(f332(f8(f872(x81021),a862,x81021),x81022),f208(x81021)))) % 165.28/165.05 [8406]~P106(x84061)+P32(x84061,x84062)+~P24(f332(f332(f246(x84061),f332(f332(f166(x84061),x84062),f609(x84062,x84061))),f332(f332(f166(x84061),x84062),f610(x84062,x84061)))) % 165.28/165.05 [8407]~P106(x84071)+P32(x84071,x84072)+~P24(f332(f332(f246(x84071),f332(f332(f166(x84071),x84072),f616(x84072,x84071))),f332(f332(f166(x84071),x84072),f625(x84072,x84071)))) % 165.28/165.05 [8551]~P59(x85511)+P24(f332(f58(f872(x85511)),x85512))+~P24(f332(f58(x85511),f332(f332(f8(f872(x85511),a862,x85511),x85512),f208(x85511)))) % 165.28/165.05 [9682]~P59(x96821)+~P59(x96822)+E(f332(f332(f155(f869(x96821),f875(x96822,x96821)),f332(f332(f8(f875(x96822,f872(x96821)),f875(x96822,x96821),f869(x96821)),f74(f872(x96821),x96821,x96822,f243(x96821))),f332(f332(f8(f869(f874(x96822,x96821)),f875(x96822,f872(x96821)),f869(x96821)),f180(x96822,x96821)),f332(f184(x96822,x96821),f56(x96822))))),f55(x96821,f332(f197(f869(x96822)),f56(x96822)),f56(x96821))),f56(f875(x96822,x96821))) % 165.28/165.05 [5672]E(x56721,f2(a1))+~E(f45(a1,x56722,x56721),f2(a1))+E(f332(f332(f39(a1),x56722),f332(f80(a1),x56721)),f332(f80(a1),f332(f332(f39(a1),x56722),x56721))) % 165.28/165.05 [5690]~P42(x56902)+~P42(x56901)+P42(f332(f332(f113(f875(a1,a862)),x56901),x56902)) % 165.28/165.05 [5691]~P42(x56912)+~P42(x56911)+P42(f332(f332(f104(f875(a1,a862)),x56911),x56912)) % 165.28/165.05 [5709]~P60(x57091)+~P92(x57091)+E(f332(f80(x57091),f332(f332(f290(x57091),f79(x57091)),x57092)),f332(f332(f290(x57091),f332(f106(x57091),a100)),x57092)) % 165.28/165.05 [5824]E(x58241,f2(a1))+~E(f45(a1,x58242,x58241),f2(a1))+E(f332(f332(f39(a1),f332(f80(a1),x58242)),x58241),f332(f80(a1),f332(f332(f39(a1),x58242),x58241))) % 165.28/165.05 [5957]~P106(x59571)+P32(x59571,x59572)+P24(f332(f332(f247(a868),f610(x59572,x59571)),f332(f197(f869(x59571)),x59572))) % 165.28/165.05 [5958]~P106(x59581)+P32(x59581,x59582)+P24(f332(f332(f247(a868),f625(x59582,x59581)),f332(f197(f869(x59581)),x59582))) % 165.28/165.05 [6114]~P92(x61141)+~E(f332(f106(x61141),x61142),f2(x61141))+P34(x61141,f332(f106(x61141),f332(f332(f81(a1),x61142),f332(f80(a1),a84)))) % 165.28/165.05 [6115]~P92(x61151)+~E(f332(f106(x61151),x61152),f2(x61151))+P34(x61151,f332(f106(x61151),f332(f332(f81(a1),a84),f332(f80(a1),x61152)))) % 165.28/165.05 [6117]E(f332(a51,f47(f332(f80(a1),x61171),f332(f80(a1),x61172))),f46(x61171,x61172))+P24(f332(f332(f246(a1),f2(a1)),x61171))+P24(f332(f332(f247(a1),f2(a1)),x61172)) % 165.28/165.05 [6251]~E(x62512,f2(a868))+~E(x62511,f2(a868))+P24(f332(f332(f246(a1),f332(f103(a1),x62511)),f332(f80(a1),f332(f103(a1),x62512)))) % 165.28/165.05 [6278]E(f332(f332(f81(a868),f332(f106(a868),x62781)),f332(f106(a868),x62782)),f332(f106(a868),f332(f332(f81(a1),x62781),x62782)))+P24(f332(f332(f247(a1),x62781),a84))+P24(f332(f332(f247(a1),x62782),a84)) % 165.28/165.05 [6408]~P75(x64081)+~P24(f332(f332(f246(x64081),f2(x64081)),x64082))+P24(f332(f332(f246(x64081),f332(f80(x64081),x64082)),x64082)) % 165.28/165.05 [6409]~P75(x64091)+~P24(f332(f332(f247(x64091),f2(x64091)),x64092))+P24(f332(f332(f247(x64091),f332(f80(x64091),x64092)),x64092)) % 165.28/165.05 [6582]E(f332(f332(f22(a868),f332(a107,x65821)),f332(a107,x65822)),f332(a107,f332(f332(f22(a1),x65821),x65822)))+~P24(f332(f332(f246(a1),f2(a1)),x65822))+~P24(f332(f332(f246(a1),x65822),x65821)) % 165.28/165.05 [6614]E(f332(a107,f45(a1,f332(f106(a1),x66141),f332(f106(a1),x66142))),f45(a868,f332(f106(a868),x66141),f332(f106(a868),x66142)))+P24(f332(a201,f332(f106(a1),x66141)))+P24(f332(a201,f332(f106(a1),x66142))) % 165.28/165.05 [6632]~P75(x66321)+P24(f332(f332(f246(x66321),f2(x66321)),x66322))+~P24(f332(f332(f246(x66321),f332(f80(x66321),x66322)),x66322)) % 165.28/165.05 [6633]~P75(x66331)+P24(f332(f332(f247(x66331),f2(x66331)),x66332))+~P24(f332(f332(f247(x66331),f332(f80(x66331),x66332)),x66332)) % 165.28/165.05 [6645]~P75(x66451)+~P24(f332(f332(f246(x66451),f2(x66451)),x66452))+P24(f332(f332(f246(x66451),f2(x66451)),f332(f332(f81(x66451),x66452),x66452))) % 165.28/165.05 [6647]~P75(x66471)+~P24(f332(f332(f247(x66471),f2(x66471)),x66472))+P24(f332(f332(f247(x66471),f2(x66471)),f332(f332(f81(x66471),x66472),x66472))) % 165.28/165.05 [6658]E(f332(f332(f81(a868),f332(a107,x66581)),f332(a107,x66582)),f332(a107,f332(f332(f81(a1),x66581),x66582)))+~P24(f332(f332(f246(a1),f2(a1)),x66582))+~P24(f332(f332(f246(a1),f2(a1)),x66581)) % 165.28/165.05 [6670]E(x66701,f2(a868))+P24(f332(f332(f247(a868),f2(a868)),x66702))+~P24(f332(f332(f247(a868),f2(a868)),f332(f332(f257(a868),x66702),x66701))) % 165.28/165.05 [6700]~P92(x67001)+E(f332(f106(x67001),x67002),f2(x67001))+~P34(x67001,f332(f106(x67001),f332(f332(f81(a1),a84),f332(f80(a1),x67002)))) % 165.28/165.05 [6701]~P92(x67011)+E(f332(f106(x67011),x67012),f2(x67011))+~P34(x67011,f332(f106(x67011),f332(f332(f81(a1),x67012),f332(f80(a1),a84)))) % 165.28/165.05 [6760]~P24(f332(f62(x67601),x67602))+~P24(f332(f62(x67601),f255(f875(x67601,a862))))+P24(f332(f62(x67601),f332(f80(f875(x67601,a862)),x67602))) % 165.28/165.05 [6783]~P24(f332(f332(f247(a1),f2(a1)),x67832))+~P24(f332(f332(f246(a1),x67832),x67831))+P24(f332(f332(f247(a1),f2(a1)),f332(f332(f39(a1),x67831),x67832))) % 165.28/165.05 [6784]~P24(f332(f332(f246(a1),x67841),f2(a1)))+~P24(f332(f332(f247(a1),x67842),f2(a1)))+P24(f332(f332(f246(a1),f2(a1)),f332(f332(f39(a1),x67841),x67842))) % 165.28/165.05 [6823]~P24(f332(f332(f246(a1),f2(a1)),x68232))+~P24(f332(f332(f246(a1),f2(a1)),x68231))+P24(f332(f332(f246(a1),f2(a1)),f332(f332(f81(a1),x68231),x68232))) % 165.28/165.05 [6824]~P24(f332(f332(f246(a1),f2(a1)),x68242))+~P24(f332(f332(f246(a1),f2(a1)),x68241))+P24(f332(f332(f246(a1),f2(a1)),f332(f332(f82(a1),x68241),x68242))) % 165.28/165.05 [6825]~P24(f332(f332(f246(a1),f2(a1)),x68252))+~P24(f332(f332(f246(a1),f2(a1)),x68251))+P24(f332(f332(f246(a1),f2(a1)),f332(f332(f39(a1),x68251),x68252))) % 165.28/165.05 [6826]~P24(f332(f332(f246(a1),f2(a1)),x68261))+~P24(f332(f332(f247(a1),f2(a1)),x68262))+P24(f332(f332(f246(a1),f2(a1)),f332(f332(f39(a1),x68261),x68262))) % 165.28/165.05 [6827]~P24(f332(f332(f247(a868),f2(a868)),x68272))+~P24(f332(f332(f247(a868),f2(a868)),x68271))+P24(f332(f332(f247(a868),f2(a868)),f332(f332(f82(a868),x68271),x68272))) % 165.28/165.05 [6892]E(x68921,f2(a1))+E(f45(a1,x68922,x68921),f2(a1))+E(f332(f332(f22(a1),f332(f80(a1),f332(f332(f39(a1),x68922),x68921))),f79(a1)),f332(f332(f39(a1),f332(f80(a1),x68922)),x68921)) % 165.28/165.05 [6945]P24(f332(f332(f247(a868),f2(a868)),x69451))+P24(f332(f332(f247(a868),f2(a868)),x69452))+~P24(f332(f332(f247(a868),f2(a868)),f332(f332(f81(a868),x69452),x69451))) % 165.28/165.05 [6949]~P75(x69491)+P24(f332(f332(f246(x69491),f2(x69491)),x69492))+~P24(f332(f332(f246(x69491),f2(x69491)),f332(f332(f81(x69491),x69492),x69492))) % 165.28/165.05 [6950]~P75(x69501)+P24(f332(f332(f247(x69501),f2(x69501)),x69502))+~P24(f332(f332(f247(x69501),f2(x69501)),f332(f332(f81(x69501),x69502),x69502))) % 165.28/165.05 [7003]~P24(f332(f62(x70031),x70032))+P24(f332(f62(x70031),f255(f875(x70031,a862))))+~P24(f332(f62(x70031),f332(f80(f875(x70031,a862)),x70032))) % 165.28/165.05 [7066]P24(f332(f332(f246(a1),x70661),f2(a1)))+~P24(f332(f332(f247(a1),x70662),f2(a1)))+~P24(f332(f332(f246(a1),f2(a1)),f332(f332(f39(a1),x70661),x70662))) % 165.28/165.05 [7072]~P24(f332(f332(f247(a1),f2(a1)),x70721))+P24(f332(f332(f246(a1),x70721),x70722))+~P24(f332(f332(f247(a1),f2(a1)),f332(f332(f39(a1),x70722),x70721))) % 165.28/165.05 [7073]~P24(f332(f332(f246(a1),f2(a1)),x70732))+P24(f332(f332(f246(a1),x70731),x70732))+~P24(f332(f332(f247(a1),f2(a1)),f332(f332(f39(a1),x70732),x70731))) % 165.28/165.05 [7102]P24(f332(f332(f246(a1),f2(a1)),x71021))+~P24(f332(f332(f247(a1),f2(a1)),x71022))+~P24(f332(f332(f246(a1),f2(a1)),f332(f332(f39(a1),x71021),x71022))) % 165.28/165.05 [7103]P24(f332(f332(f247(a1),f2(a1)),x71031))+~P24(f332(f332(f246(a1),f2(a1)),x71032))+~P24(f332(f332(f247(a1),f2(a1)),f332(f332(f39(a1),x71032),x71031))) % 165.28/165.05 [7547]~P24(f332(f62(x75472),f255(f875(x75472,a862))))+~P24(f332(f62(x75471),f255(f875(x75471,a862))))+P24(f332(f62(f874(x75471,x75472)),f255(f875(f874(x75471,x75472),a862)))) % 165.28/165.05 [7548]~P24(f332(f62(x75482),f255(f875(x75482,a862))))+~P24(f332(f62(x75481),f255(f875(x75481,a862))))+P24(f332(f62(f876(x75481,x75482)),f255(f875(f876(x75481,x75482),a862)))) % 165.28/165.05 [7617]~P24(f332(f332(f247(a868),f332(a115,f2(a868))),x76171))+~P24(f332(f332(f247(a868),f332(a115,f2(a868))),x76172))+P24(f332(f332(f247(a868),x76171),f332(f332(f82(a868),x76172),x76171))) % 165.28/165.05 [7618]~P24(f332(f332(f247(a868),f332(a115,f2(a868))),x76181))+~P24(f332(f332(f247(a868),f332(a115,f2(a868))),x76182))+P24(f332(f332(f247(a868),x76181),f332(f332(f82(a868),x76181),x76182))) % 165.28/165.05 [7652]E(f332(f38(x76521),f255(f875(x76521,a862))),f332(a115,f2(a868)))+P24(f332(f62(x76522),f255(f875(x76522,a862))))+~P24(f332(f62(f875(x76522,x76521)),f255(f875(f875(x76522,x76521),a862)))) % 165.28/165.05 [7780]~P24(f332(f332(f246(a868),f332(a115,f2(a868))),x77801))+~P24(f332(f332(f246(a868),f332(a115,f2(a868))),x77802))+P24(f332(f332(f246(a868),f332(a115,f2(a868))),f332(f332(f82(a868),x77801),x77802))) % 165.28/165.05 [7781]~P24(f332(f332(f247(a868),f332(a115,f2(a868))),x77812))+~P24(f332(f332(f247(a868),f332(a115,f2(a868))),x77811))+P24(f332(f332(f247(a868),f332(a115,f2(a868))),f332(f332(f82(a868),x77811),x77812))) % 165.28/165.05 [8450]E(x84501,f116(x84502))+~P24(f332(f138(x84502),x84501))+E(f179(x84502,f332(f332(f8(a862,a862,x84502),a327),f332(f332(f7(x84502,x84502,a862),a329),f145(x84502,x84501))),x84501),f117(x84502,x84501)) % 165.28/165.05 [8542]~P42(x85422)+~P42(x85421)+E(f332(f311(a868,a1,f103(a1)),f332(f332(f113(f875(a868,a862)),f332(f311(a1,a868,a107),x85421)),f332(f311(a1,a868,a107),x85422))),f332(f332(f113(f875(a1,a862)),x85421),x85422)) % 165.28/165.05 [8543]~P42(x85432)+~P42(x85431)+E(f332(f311(a868,a1,f103(a1)),f332(f332(f104(f875(a868,a862)),f332(f311(a1,a868,a107),x85431)),f332(f311(a1,a868,a107),x85432))),f332(f332(f104(f875(a1,a862)),x85431),x85432)) % 165.28/165.05 [9176]~P92(x91761)+~E(f332(f106(x91761),x91762),f79(x91761))+P34(x91761,f332(f106(x91761),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f80(a1),x91762)))) % 165.28/165.05 [9401]~P92(x94011)+E(f332(f106(x94011),x94012),f79(x94011))+~P34(x94011,f332(f106(x94011),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f80(a1),x94012)))) % 165.28/165.05 [10124]E(x101241,f2(a1))+E(x101242,f2(a1))+E(f332(f272(a1,a1,a1,a1,f35(a1),f332(f82(a1),f83(a1,x101242))),f332(f332(f332(f99(f874(a1,a1)),f332(f332(a329,f83(a1,x101241)),f83(a1,x101242))),f53(x101241,x101242)),f332(f332(f271(a1,a1,f874(a1,a1)),f332(f332(f18(a1,f875(a1,f874(a1,a1)),f875(a1,f874(a1,a1))),f332(f332(f8(f875(a1,f875(f874(a1,a1),f874(a1,a1))),f875(f875(a1,f874(a1,a1)),f875(a1,f874(a1,a1))),a1),f18(a1,f874(a1,a1),f874(a1,a1))),f332(f332(f8(f874(a1,a1),f875(a1,f875(f874(a1,a1),f874(a1,a1))),a1),f332(f7(a1,f874(a1,a1),f875(f874(a1,a1),f874(a1,a1))),f332(f332(f8(a862,f875(f874(a1,a1),f875(f874(a1,a1),f874(a1,a1))),a1),f99(f874(a1,a1))),f332(f332(f7(a1,a1,a862),a329),f2(a1))))),f332(f332(f7(a1,a1,f874(a1,a1)),f332(f332(f8(a1,f875(a1,f874(a1,a1)),a1),f267(a1,a1)),f80(a1))),f2(a1))))),f332(f332(f7(a1,f875(a1,a1),f875(a1,f874(a1,a1))),f332(f332(f8(f875(a1,f874(a1,a1)),f875(f875(a1,a1),f875(a1,f874(a1,a1))),a1),f8(a1,f874(a1,a1),a1)),f332(f332(f8(a1,f875(a1,f874(a1,a1)),a1),f267(a1,a1)),f332(f332(f7(a1,a1,a1),f332(f332(f8(a1,f875(a1,a1),a1),f22(a1)),f80(a1))),f79(a1))))),f332(f22(a1),f332(f76(a1),x101242))))),f53(x101241,x101242)))),f46(x101241,x101242)) % 165.28/165.05 [10125]E(x101251,f2(a1))+E(x101252,f2(a1))+E(f332(f272(a1,a1,a1,a1,f35(a1),f332(f82(a1),f83(a1,x101252))),f332(f332(f332(f99(f874(a1,a1)),f332(f332(a331,f332(f332(a330,f332(f332(f247(a1),f2(a1)),x101252)),f332(f332(f246(a1),f2(a1)),x101251))),f332(f332(a330,f332(f332(f247(a1),x101252),f2(a1))),f332(f332(f247(a1),x101251),f2(a1))))),f53(x101251,x101252)),f332(f332(f271(a1,a1,f874(a1,a1)),f332(f332(f18(a1,f875(a1,f874(a1,a1)),f875(a1,f874(a1,a1))),f332(f332(f8(f875(a1,f875(f874(a1,a1),f874(a1,a1))),f875(f875(a1,f874(a1,a1)),f875(a1,f874(a1,a1))),a1),f18(a1,f874(a1,a1),f874(a1,a1))),f332(f332(f8(f874(a1,a1),f875(a1,f875(f874(a1,a1),f874(a1,a1))),a1),f332(f7(a1,f874(a1,a1),f875(f874(a1,a1),f874(a1,a1))),f332(f332(f8(a862,f875(f874(a1,a1),f875(f874(a1,a1),f874(a1,a1))),a1),f99(f874(a1,a1))),f332(f332(f7(a1,a1,a862),a329),f2(a1))))),f332(f332(f7(a1,a1,f874(a1,a1)),f332(f332(f8(a1,f875(a1,f874(a1,a1)),a1),f267(a1,a1)),f80(a1))),f2(a1))))),f332(f332(f7(a1,f875(a1,a1),f875(a1,f874(a1,a1))),f332(f332(f8(f875(a1,f874(a1,a1)),f875(f875(a1,a1),f875(a1,f874(a1,a1))),a1),f8(a1,f874(a1,a1),a1)),f332(f332(f8(a1,f875(a1,f874(a1,a1)),a1),f267(a1,a1)),f332(f332(f7(a1,a1,a1),f332(f332(f8(a1,f875(a1,a1),a1),f22(a1)),f80(a1))),f79(a1))))),f332(f22(a1),f332(f76(a1),x101252))))),f53(x101251,x101252)))),f46(x101251,x101252)) % 165.28/165.05 [5698]~P118(x56981)+~P92(x56981)+E(f332(f76(x56981),f332(f332(f257(x56981),f332(f106(x56981),a100)),x56982)),f79(x56981)) % 165.28/165.05 [6191]~P138(x61911)+~P24(f332(f332(f247(a1),x61912),f2(a1)))+E(f332(f80(x61911),f332(f103(x61911),f332(a107,f332(f80(a1),x61912)))),f332(f105(x61911),x61912)) % 165.28/165.05 [6392]P24(f332(f332(f246(a102),x63921),f79(a102)))+E(f332(f332(f81(a102),f79(a102)),f280(x63921,f332(f332(f39(a102),x63922),x63921))),f280(x63921,x63922))+P24(f332(f332(f247(a102),x63922),x63921)) % 165.28/165.05 [6990]~P91(x69901)+~P24(f332(f332(f334(x69901),x69902),f112(x69901)))+~E(f332(f332(f81(x69901),f332(f332(f81(x69901),f79(x69901)),x69902)),x69902),f2(x69901)) % 165.28/165.05 [7104]~P24(f332(f332(f246(a1),x71042),f2(a1)))+~P24(f332(f332(f247(a1),x71041),f2(a1)))+E(f332(f266(a1,a1),f332(a51,f47(f332(f80(a1),x71041),f332(f80(a1),x71042)))),f332(f332(f39(a1),x71041),x71042)) % 165.28/165.05 [7121]~P24(f332(f332(f246(a1),x71212),f2(a1)))+~P24(f332(f332(f247(a1),x71211),f2(a1)))+E(f332(f270(a1,a1),f332(a51,f47(f332(f80(a1),x71211),f332(f80(a1),x71212)))),f45(a1,x71211,x71212)) % 165.28/165.05 [7127]~P24(f332(f332(f247(a1),x71272),f2(a1)))+E(f332(f266(a1,a1),f332(a51,f50(f332(f80(a1),x71271),f332(f80(a1),x71272)))),f332(f332(f39(a1),x71271),x71272))+~P24(f332(f332(f247(a1),f2(a1)),x71271)) % 165.28/165.05 [7145]~P24(f332(f332(f247(a1),x71452),f2(a1)))+E(f332(f270(a1,a1),f332(a51,f50(f332(f80(a1),x71451),f332(f80(a1),x71452)))),f45(a1,x71451,x71452))+~P24(f332(f332(f247(a1),f2(a1)),x71451)) % 165.28/165.05 [7198]E(f332(f332(f39(a1),f332(f332(f257(a1),x71981),x71982)),x71981),f332(f332(f257(a1),x71981),f332(f332(f22(a868),x71982),f332(a115,f2(a868)))))+~P24(f332(f332(f247(a868),f2(a868)),x71982))+~P24(f332(f332(f247(a1),f2(a1)),x71981)) % 165.28/165.05 [7291]~P24(f332(f332(f247(a868),f2(a868)),x72911))+~P24(f332(f332(f247(a868),f2(a868)),x72912))+P24(f332(f332(f247(a868),f332(f332(f22(a868),x72911),x72912)),x72911)) % 165.28/165.05 [7292]~P24(f332(f332(f247(a868),f2(a868)),x72921))+~P24(f332(f332(f247(a868),f79(a868)),x72922))+P24(f332(f332(f247(a868),f332(f332(f39(a868),x72921),x72922)),x72921)) % 165.28/165.05 [7293]~P24(f332(f332(f247(a1),f2(a1)),x72931))+~P24(f332(f332(f247(a1),f79(a1)),x72932))+P24(f332(f332(f247(a1),f332(f332(f39(a1),x72931),x72932)),x72931)) % 165.28/165.05 [7438]E(x74381,f2(a868))+~E(x74382,f2(a1))+~P24(f332(f332(f247(a1),f2(a1)),f332(f332(f257(a1),f332(f76(a1),x74382)),x74381))) % 165.28/165.05 [7857]~E(x78572,f116(f869(x78571)))+E(f332(f197(f869(f869(x78571))),f182(x78571,x78572)),f2(a868))+~P32(a868,f332(f170(a868),f332(f332(f155(f869(x78571),a868),f197(f869(x78571))),x78572))) % 165.28/165.05 [8101]P24(f332(x81011,x81012))+~P24(f332(x81011,f332(a109,f686(x81011,x81012))))+~P24(f332(f332(f334(f875(f874(a868,a868),a862)),x81012),a101)) % 165.28/165.05 [8119]E(x81191,f116(f869(x81192)))+E(f332(f197(f869(x81192)),f332(f332(f166(f869(x81192)),x81191),f2(a868))),f332(f197(f869(f869(x81192))),f182(x81192,x81191)))+~P32(a868,f332(f170(a868),f332(f332(f155(f869(x81192),a868),f197(f869(x81192))),x81191))) % 165.28/165.05 [8803]~P24(f332(f62(x88031),f332(f252(x88031),x88032)))+~P24(f332(f62(x88031),f255(f875(x88031,a862))))+P24(f332(f62(x88031),f332(f252(x88031),f332(f332(f8(a862,a862,x88031),a327),x88032)))) % 165.28/165.05 [8865]E(f332(f332(f267(a868,a868),f332(a115,f332(f332(f39(a868),f332(f332(f22(a868),x88651),x88652)),x88652))),f45(a868,f332(f332(f22(a868),x88651),x88652),x88652)),f86(f874(a868,a868),f48(x88651,x88652)))+~P24(f332(f332(f247(a868),f2(a868)),x88652))+~P24(f332(f332(f246(a868),x88652),x88651)) % 165.28/165.05 [9145]~P24(f332(f62(x91451),f332(f252(x91451),x91452)))+P24(f332(f62(x91451),f255(f875(x91451,a862))))+~P24(f332(f62(x91451),f332(f252(x91451),f332(f332(f8(a862,a862,x91451),a327),x91452)))) % 165.28/165.05 [9849]P22(x98491,x98492)+~P41(x98491,f332(f266(f875(f874(x98491,x98491),a862),f875(f874(x98491,x98491),a862)),x98492))+~P24(f332(f332(f246(f875(f874(x98491,x98491),a862)),f332(f332(f289(x98491,x98491,x98491),f332(f266(f875(f874(x98491,x98491),a862),f875(f874(x98491,x98491),a862)),x98492)),f332(f270(f875(f874(x98491,x98491),a862),f875(f874(x98491,x98491),a862)),x98492))),f332(f266(f875(f874(x98491,x98491),a862),f875(f874(x98491,x98491),a862)),x98492))) % 165.28/165.05 [7224]~P24(f332(f332(f247(a868),f2(a868)),x72242))+P24(f332(f332(f247(a868),x72241),x72242))+E(f332(a115,f332(f332(f39(a868),f332(f332(f22(a868),x72241),x72242)),x72242)),f332(f332(f39(a868),x72241),x72242)) % 165.28/165.05 [7358]~P24(f332(f332(f247(a868),f2(a868)),x73582))+~P24(f332(f332(f246(a868),x73582),x73581))+E(f332(a115,f332(f332(f39(a868),f332(f332(f22(a868),x73581),x73582)),x73582)),f332(f332(f39(a868),x73581),x73582)) % 165.28/165.05 [8326]~P92(x83261)+~P91(x83261)+~P34(x83261,f332(f106(x83261),f332(f332(f22(a1),f332(f332(f81(a1),x83262),x83262)),a100))) % 165.28/165.05 [9054]E(x90541,f2(a868))+E(f332(f332(f271(a868,a868,f874(a868,a868)),f332(f332(f8(a868,f875(a868,f874(a868,a868)),a868),f267(a868,a868)),a115)),f86(f874(a868,a868),f48(f332(f332(f22(a868),x90542),x90541),x90541))),f86(f874(a868,a868),f48(x90542,x90541)))+P24(f332(f332(f247(a868),x90542),x90541)) % 165.28/165.05 [9460]P24(f332(x94602,f774(x94602,x94601)))+P24(f332(x94601,f774(x94602,x94601)))+E(f332(f252(a1),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f246(a1),f2(a1)))),x94601)),f332(f252(a1),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f246(a1),f2(a1)))),x94602))) % 165.28/165.05 [9464]~P24(f332(x94642,f774(x94642,x94641)))+~P24(f332(x94641,f774(x94642,x94641)))+E(f332(f252(a1),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f246(a1),f2(a1)))),x94641)),f332(f252(a1),f332(f332(f18(a1,a862,a862),f332(f332(f8(a862,f875(a862,a862),a1),a330),f332(f246(a1),f2(a1)))),x94642))) % 165.28/165.05 [7575]~P61(x75751)+~P92(x75751)+E(f332(f332(f290(x75751),x75752),f332(f106(x75751),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))),x75752) % 165.28/165.05 [9775]~P24(f332(f62(a865),x97752))+P20(a864,x97751,f332(f311(a865,f867(a864),f332(f332(f8(a863,f867(a864),a865),a94),a28)),x97752))+~P20(a864,f332(f332(f113(f875(f867(a864),a862)),x97751),f332(f311(a865,f867(a864),f332(f332(f8(a863,f867(a864),a865),a94),a28)),x97752)),f332(f311(a865,f867(a864),f332(f332(f8(a863,f867(a864),a865),a94),f332(f332(f8(f872(a863),a863,a865),f243(a863)),a26))),x97752)) % 165.28/165.05 [9175]~P92(x91751)+~E(f332(f106(x91751),x91752),f79(x91751))+P34(x91751,f332(f106(x91751),f332(f332(f81(a1),x91752),f332(f80(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))) % 165.28/165.05 [9345]~P137(x93451)+~E(x93452,f79(x93451))+E(f332(f332(f257(x93451),x93452),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f79(x93451)) % 165.28/165.05 [9346]~P137(x93461)+~E(x93462,f2(x93461))+E(f332(f332(f257(x93461),x93462),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f2(x93461)) % 165.28/165.05 [9359]~P137(x93591)+~E(x93592,f332(f80(x93591),f79(x93591)))+E(f332(f332(f257(x93591),x93592),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f79(x93591)) % 165.28/165.05 [9402]~P92(x94021)+E(f332(f106(x94021),x94022),f79(x94021))+~P34(x94021,f332(f106(x94021),f332(f332(f81(a1),x94022),f332(f80(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))) % 165.28/165.05 [9784]~P118(x97842)+E(x97841,f2(x97842))+P24(f332(f332(f247(x97842),f2(x97842)),f332(f332(f257(x97842),x97841),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))) % 165.28/165.05 [9848]~P118(x98482)+~E(x98481,f2(x98482))+~P24(f332(f332(f247(x98482),f2(x98482)),f332(f332(f257(x98482),x98481),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))) % 165.28/165.05 [9874]P24(f332(f332(f246(a1),x98741),f2(a1)))+P24(f332(f332(f247(a1),x98742),x98741))+E(f332(f44(x98741),f47(x98742,f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x98741))),f47(x98742,x98741)) % 165.28/165.05 [9875]~P24(f332(f332(f247(a1),f2(a1)),x98751))+P24(f332(f332(f247(a1),x98752),x98751))+E(f332(f44(x98751),f47(x98752,f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x98751))),f47(x98752,x98751)) % 165.28/165.05 [9876]P24(f332(f332(f246(a1),x98761),f2(a1)))+P24(f332(f332(f246(a1),f2(a1)),f332(f332(f81(a1),x98762),x98761)))+E(f332(f44(x98761),f50(x98762,f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x98761))),f50(x98762,x98761)) % 165.28/165.05 [9877]~P24(f332(f332(f247(a1),f2(a1)),x98771))+P24(f332(f332(f246(a1),f2(a1)),f332(f332(f81(a1),x98772),x98771)))+E(f332(f44(x98771),f50(x98772,f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x98771))),f50(x98772,x98771)) % 165.28/165.05 [9878]~P142(x98781)+~P24(f332(f332(f246(a1),f2(a1)),x98782))+E(f332(f103(x98781),f332(a107,f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x98782))),f332(f332(f81(x98781),f332(f103(x98781),f332(a107,x98782))),f332(f103(x98781),f332(a107,x98782)))) % 165.28/165.05 [5029]~P144(x50291,x50292,x50293)+~E(x50293,f2(a1))+P24(f332(x50291,x50292)) % 165.28/165.05 [5151]~P106(x51511)+~P32(x51511,x51513)+P32(x51511,f172(x51511,x51512,x51513)) % 165.28/165.05 [5152]~P106(x51521)+~P32(x51521,x51523)+P32(x51521,f179(x51521,x51522,x51523)) % 165.28/165.05 [4730]~P67(x47302)+~E(x47303,f332(f80(x47302),x47301))+E(x47301,f332(f80(x47302),x47303)) % 165.28/165.05 [4732]~P67(x47321)+~E(f332(f80(x47321),x47323),x47322)+E(f332(f80(x47321),x47322),x47323) % 165.28/165.05 [4807]~P67(x48073)+E(x48071,x48072)+~E(f332(f80(x48073),x48071),f332(f80(x48073),x48072)) % 165.28/165.05 [4808]~P81(x48083)+E(x48081,x48082)+~E(f332(f80(x48083),x48081),f332(f80(x48083),x48082)) % 165.28/165.05 [4809]~P106(x48093)+E(x48091,x48092)+~E(f332(f253(x48093),x48091),f332(f253(x48093),x48092)) % 165.28/165.05 [4810]~P101(x48103)+E(x48101,x48102)+~E(f332(f103(x48103),x48101),f332(f103(x48103),x48102)) % 165.28/165.05 [4811]~P106(x48113)+E(x48111,x48112)+~E(f332(f304(x48113),x48111),f332(f304(x48113),x48112)) % 165.28/165.05 [4812]~P91(x48123)+E(x48121,x48122)+~E(f332(f105(x48123),x48121),f332(f105(x48123),x48122)) % 165.28/165.05 [4813]~P106(x48133)+E(x48131,x48132)+~E(f332(f254(x48133),x48131),f332(f254(x48133),x48132)) % 165.28/165.05 [4814]~P106(x48143)+E(x48141,x48142)+~E(f332(f301(x48143),x48141),f332(f301(x48143),x48142)) % 165.28/165.05 [4915]~P59(x49151)+~P24(f332(x49152,x49153))+P24(f332(f58(x49151),x49152)) % 165.28/165.05 [4948]~P59(x49483)+P24(f332(x49481,x49482))+~P24(f332(f59(x49483),x49481)) % 165.28/165.05 [5048]~P145(x50481,x50483,x50482)+~E(x50482,f2(a1))+P24(f332(x50481,f2(a1))) % 165.28/165.05 [5086]~E(x50861,f2(a868))+E(f704(x50861,x50862,x50863),f196(f875(x50863,a862)))+~E(f332(f38(x50863),x50862),f332(a115,x50861)) % 165.28/165.05 [5241]~E(x52412,f2(a868))+E(f332(f266(a868,a868),x52411),f2(a868))+~P24(f332(f48(x52413,x52412),x52411)) % 165.28/165.05 [5290]P24(f332(x52901,x52902))+~E(x52903,f332(f103(a1),x52902))+~P24(f332(x52901,f332(a107,x52903))) % 165.28/165.05 [5763]~E(x57633,f2(a868))+~P24(f332(x57631,x57632))+P24(f332(x57631,f45(a868,x57632,x57633))) % 165.28/165.05 [5894]~P24(f332(a25,x58943))+~P24(f332(a25,x58942))+P24(f332(a25,f31(x58941,x58942,x58943))) % 165.28/165.05 [5926]~P59(x59263)+~P7(x59263,x59261,x59262)+P24(f332(x59261,f627(x59262,x59261,x59263))) % 165.28/165.05 [5985]~P102(x59852)+~P102(x59851)+E(f132(x59851,x59852,f133(x59851,x59853),f133(x59852,x59853)),f133(f874(x59851,x59852),x59853)) % 165.28/165.05 [6173]~E(x61733,f2(a868))+P24(f332(x61731,x61732))+~P24(f332(x61731,f45(a868,x61732,x61733))) % 165.28/165.05 [6321]~P59(x63211)+P8(x63211,x63212,x63213)+~P24(f332(x63212,f628(x63213,x63212,x63211))) % 165.28/165.05 [6849]E(x68491,f2(a868))+~P24(f332(x68492,f421(x68491,x68493,x68492)))+P24(f332(x68492,f45(a868,x68493,x68491))) % 165.28/165.05 [6955]~P30(x69551)+~P24(f332(f332(f246(x69551),x69552),f640(x69553,x69552,x69551)))+P24(f332(f332(f246(x69551),x69552),f41(x69551,x69553))) % 165.28/165.05 [6957]~P24(f332(x69571,x69572))+~P24(f332(x69571,f421(x69573,x69572,x69571)))+P24(f332(x69571,f45(a868,x69572,x69573))) % 165.28/165.05 [7059]E(x70591,f116(x70592))+E(f332(f332(f152(x70592),f592(x70593,x70591,x70592)),f596(x70593,x70591,x70592)),x70591)+~P24(f332(f332(f334(f869(x70592)),x70591),f162(x70592,x70593))) % 165.28/165.05 [7091]~P138(x70911)+~P24(f332(f332(f334(x70911),x70912),f112(x70911)))+P24(f332(f332(f334(x70911),f332(f332(f257(x70911),x70912),x70913)),f112(x70911))) % 165.28/165.05 [7408]P41(x74081,x74082)+~P24(f332(f332(f334(x74081),x74083),f738(x74082,x74081)))+P24(f332(f332(f334(x74081),f773(x74082,x74081,x74083)),f738(x74082,x74081))) % 165.28/165.05 [7679]E(x76791,f116(x76792))+~P24(f332(f332(f334(f869(x76792)),x76791),f162(x76792,x76793)))+P24(f332(f332(f334(f869(x76792)),f596(x76793,x76791,x76792)),f162(x76792,x76793))) % 165.28/165.05 [7732]E(x77321,f2(a868))+E(f332(f332(f81(a868),f332(f332(f82(a868),x77321),f422(x77321,x77322,x77323))),f421(x77321,x77322,x77323)),x77322)+P24(f332(x77323,f45(a868,x77322,x77321))) % 165.28/165.05 [7775]~P24(f332(x77753,x77752))+E(f332(f332(f81(a868),f332(f332(f82(a868),x77751),f422(x77751,x77752,x77753))),f421(x77751,x77752,x77753)),x77752)+P24(f332(x77753,f45(a868,x77752,x77751))) % 165.28/165.05 [7912]P24(f332(f332(f247(a1),x79121),f418(x79122,x79123,x79121)))+P24(f332(f332(x79123,f332(f332(f39(a1),x79122),x79121)),f45(a1,x79122,x79121)))+~P24(f332(f332(f247(a1),x79121),f2(a1))) % 165.28/165.05 [8180]P24(f332(f332(x81802,f332(f332(f39(a1),x81801),x81803)),f45(a1,x81801,x81803)))+~P24(f332(f332(f247(a1),x81803),f2(a1)))+P24(f332(f332(f246(a1),f418(x81801,x81802,x81803)),f2(a1))) % 165.28/165.05 [8359]E(f332(f332(f81(a1),f332(f332(f82(a1),x83591),f416(x83592,x83593,x83591))),f418(x83592,x83593,x83591)),x83592)+P24(f332(f332(x83593,f332(f332(f39(a1),x83592),x83591)),f45(a1,x83592,x83591)))+~P24(f332(f332(f247(a1),x83591),f2(a1))) % 165.28/165.05 [8586]~P24(f332(f332(x85861,f416(x85862,x85861,x85863)),f418(x85862,x85861,x85863)))+P24(f332(f332(x85861,f332(f332(f39(a1),x85862),x85863)),f45(a1,x85862,x85863)))+~P24(f332(f332(f247(a1),x85863),f2(a1))) % 165.28/165.05 [8813]~P106(x88131)+~P32(x88131,x88133)+P32(x88131,f150(x88131,x88131,f5(x88131),x88132,x88133)) % 165.28/165.05 [9297]~P122(x92972)+E(x92971,f2(x92972))+~P24(f332(f332(f246(x92972),f332(f332(f81(x92972),f332(f332(f82(x92972),x92973),x92973)),f332(f332(f82(x92972),x92971),x92971))),f2(x92972))) % 165.28/165.05 [9298]~P122(x92982)+E(x92981,f2(x92982))+~P24(f332(f332(f246(x92982),f332(f332(f81(x92982),f332(f332(f82(x92982),x92981),x92981)),f332(f332(f82(x92982),x92983),x92983))),f2(x92982))) % 165.28/165.05 [10063]~P118(x100631)+~P24(f332(f332(f247(x100631),x100632),f2(x100631)))+P24(f332(f332(f247(x100631),f332(f332(f257(x100631),x100632),f332(a115,f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x100633)))),f2(x100631))) % 165.28/165.05 [10071]~P118(x100712)+E(x100711,f2(x100712))+~P24(f332(f332(f246(x100712),f332(f332(f81(x100712),f332(f332(f257(x100712),x100713),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x100712),x100711),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))),f2(x100712))) % 165.28/165.05 [10072]~P118(x100722)+E(x100721,f2(x100722))+~P24(f332(f332(f246(x100722),f332(f332(f81(x100722),f332(f332(f257(x100722),x100721),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x100722),x100723),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))),f2(x100722))) % 165.28/165.05 [4764]~E(x47642,x47643)+~P66(x47641)+E(f332(f332(f22(x47641),x47642),x47643),f2(x47641)) % 165.28/165.05 [4765]~E(x47652,x47653)+~P67(x47651)+E(f332(f332(f22(x47651),x47652),x47653),f2(x47651)) % 165.28/165.05 [4778]~P123(x47781)+~E(x47783,f2(x47781))+E(f332(f332(f81(x47781),x47782),x47783),x47782) % 165.28/165.05 [4794]~P139(x47941)+~E(x47943,f2(x47941))+E(f332(f332(f82(x47941),x47942),x47943),f2(x47941)) % 165.28/165.05 [4795]~P139(x47951)+~E(x47952,f2(x47951))+E(f332(f332(f82(x47951),x47952),x47953),f2(x47951)) % 165.28/165.05 [4816]~E(x48163,f116(x48161))+~E(x48162,f116(x48161))+E(f332(f332(f135(x48161),x48162),x48163),f116(x48161)) % 165.28/165.05 [4905]~P123(x49052)+E(x49051,f2(x49052))+~E(f332(f332(f81(x49052),x49053),x49051),x49053) % 165.28/165.05 [4906]~P67(x49061)+~E(x49062,f332(f80(x49061),x49063))+E(f332(f332(f81(x49061),x49062),x49063),f2(x49061)) % 165.28/165.05 [4913]E(x49131,f116(x49132))+E(x49133,f2(a868))+~E(f332(f332(f177(x49132),x49133),x49131),f116(x49132)) % 165.28/165.05 [4919]~P66(x49193)+E(x49191,x49192)+~E(f332(f332(f22(x49193),x49191),x49192),f2(x49193)) % 165.28/165.05 [4920]~P67(x49203)+E(x49201,x49202)+~E(f332(f332(f22(x49203),x49201),x49202),f2(x49203)) % 165.28/165.05 [4929]~P137(x49292)+E(x49291,f2(x49292))+~E(f332(f332(f257(x49292),x49291),x49293),f2(x49292)) % 165.28/165.05 [4930]~P64(x49302)+E(x49301,f196(x49302))+~E(f332(f332(f113(x49302),x49303),x49301),f196(x49302)) % 165.28/165.05 [4931]~P64(x49312)+E(x49311,f196(x49312))+~E(f332(f332(f113(x49312),x49311),x49313),f196(x49312)) % 165.28/165.05 [4932]~P98(x49322)+E(x49321,f255(x49322))+~E(f332(f332(f104(x49322),x49323),x49321),f255(x49322)) % 165.28/165.05 [4933]~P98(x49332)+E(x49331,f255(x49332))+~E(f332(f332(f104(x49332),x49331),x49333),f255(x49332)) % 165.28/165.05 [4999]~P67(x49992)+E(x49991,f332(f80(x49992),x49993))+~E(f332(f332(f81(x49992),x49991),x49993),f2(x49992)) % 165.28/165.05 [5000]~P67(x50001)+E(f332(f80(x50001),x50002),x50003)+~E(f332(f332(f81(x50001),x50002),x50003),f2(x50001)) % 165.28/165.05 [5002]~E(x50022,x50023)+~P104(x50021)+P24(f332(f332(f246(x50021),x50022),x50023)) % 165.28/165.05 [5004]~E(x50042,x50043)+~P107(x50041)+P24(f332(f332(f246(x50041),x50042),x50043)) % 165.28/165.05 [5005]~E(x50052,x50053)+~P94(x50051)+P24(f332(f332(f92(x50051),x50052),x50053)) % 165.28/165.05 [5102]~P115(x51021)+~E(x51022,f332(f80(x51021),x51023))+E(f332(f332(f82(x51021),x51022),x51022),f332(f332(f82(x51021),x51023),x51023)) % 165.28/165.05 [5110]~P106(x51101)+~P32(x51101,x51103)+P32(x51101,f332(f332(f177(x51101),x51102),x51103)) % 165.28/165.05 [5111]~P106(x51111)+~P32(x51111,x51113)+P32(x51111,f332(f332(f139(x51111),x51112),x51113)) % 165.28/165.05 [5149]E(x51491,x51492)+E(x51493,f2(a868))+~E(f332(f332(f82(a868),x51493),x51491),f332(f332(f82(a868),x51493),x51492)) % 165.28/165.05 [5150]E(x51501,x51502)+E(x51503,f2(a868))+~E(f332(f332(f82(a868),x51501),x51503),f332(f332(f82(a868),x51502),x51503)) % 165.28/165.05 [5232]~E(x52322,x52323)+~P107(x52321)+E(f303(x52321,x52322,x52323),f332(f332(f310(x52321),x52322),f196(f875(x52321,a862)))) % 165.28/165.05 [5277]E(x52771,x52772)+~P94(x52773)+~P24(f332(f332(f92(x52773),x52771),x52772)) % 165.28/165.05 [5288]~E(x52881,x52882)+~P106(x52883)+~P24(f332(f332(f247(x52883),x52881),x52882)) % 165.28/165.05 [5289]~E(x52891,x52892)+~P107(x52893)+~P24(f332(f332(f247(x52893),x52891),x52892)) % 165.28/165.05 [5299]~P107(x52991)+E(f332(f302(x52991,x52992),x52993),f196(f875(x52991,a862)))+P24(f332(f332(f247(x52991),x52992),x52993)) % 165.28/165.05 [5346]~P107(x53461)+E(f305(x53461,x53462,x53463),f196(f875(x53461,a862)))+P24(f332(f332(f247(x53461),x53462),x53463)) % 165.28/165.05 [5347]~P107(x53471)+E(f303(x53471,x53472,x53473),f196(f875(x53471,a862)))+P24(f332(f332(f246(x53471),x53472),x53473)) % 165.28/165.05 [5348]~P107(x53481)+E(f196(f875(x53481,a862)),f305(x53481,x53482,x53483))+P24(f332(f332(f247(x53481),x53482),x53483)) % 165.28/165.05 [5349]~P107(x53491)+E(f196(f875(x53491,a862)),f303(x53491,x53492,x53493))+P24(f332(f332(f246(x53491),x53492),x53493)) % 165.28/165.05 [5357]~P99(x53571)+~E(f332(f332(f113(x53571),x53572),x53573),x53573)+P24(f332(f332(f246(x53571),x53572),x53573)) % 165.28/165.05 [5358]~P100(x53581)+~E(f332(f332(f104(x53581),x53582),x53583),x53582)+P24(f332(f332(f246(x53581),x53582),x53583)) % 165.28/165.05 [5359]~P106(x53591)+~E(f332(f332(f244(x53591),x53592),x53593),x53592)+P24(f332(f332(f246(x53591),x53592),x53593)) % 165.28/165.05 [5360]~P106(x53601)+~E(f332(f332(f245(x53601),x53602),x53603),x53603)+P24(f332(f332(f246(x53601),x53602),x53603)) % 165.28/165.05 [5380]~P106(x53801)+P32(x53801,x53802)+~P32(x53801,f332(f332(f152(x53801),x53803),x53802)) % 165.28/165.05 [5381]~P106(x53811)+P32(x53811,x53812)+~P32(x53811,f332(f332(f135(x53811),x53813),x53812)) % 165.28/165.05 [5382]~P106(x53821)+P32(x53821,x53822)+~P32(x53821,f332(f332(f135(x53821),x53822),x53823)) % 165.28/165.05 [5447]~P106(x54471)+P24(f332(f332(f246(x54471),x54473),x54472))+P24(f332(f332(f246(x54471),x54472),x54473)) % 165.28/165.05 [5452]~P106(x54521)+P24(f332(f332(f247(x54521),x54523),x54522))+P24(f332(f332(f246(x54521),x54522),x54523)) % 165.28/165.05 [5490]~P99(x54901)+E(f332(f332(f113(x54901),x54902),x54903),x54902)+~P24(f332(f332(f246(x54901),x54903),x54902)) % 165.28/165.05 [5492]~P99(x54921)+E(f332(f332(f113(x54921),x54922),x54923),x54923)+~P24(f332(f332(f246(x54921),x54922),x54923)) % 165.28/165.05 [5493]~P100(x54931)+E(f332(f332(f104(x54931),x54932),x54933),x54933)+~P24(f332(f332(f246(x54931),x54933),x54932)) % 165.28/165.05 [5495]~P100(x54951)+E(f332(f332(f104(x54951),x54952),x54953),x54952)+~P24(f332(f332(f246(x54951),x54952),x54953)) % 165.28/165.05 [5496]~P106(x54961)+E(f332(f332(f244(x54961),x54962),x54963),x54963)+~P24(f332(f332(f246(x54961),x54963),x54962)) % 165.28/165.05 [5498]~P106(x54981)+E(f332(f332(f244(x54981),x54982),x54983),x54982)+~P24(f332(f332(f246(x54981),x54982),x54983)) % 165.28/165.05 [5499]~P106(x54991)+E(f332(f332(f245(x54991),x54992),x54993),x54992)+~P24(f332(f332(f246(x54991),x54993),x54992)) % 165.28/165.05 [5501]~P106(x55011)+E(f332(f332(f245(x55011),x55012),x55013),x55013)+~P24(f332(f332(f246(x55011),x55012),x55013)) % 165.28/165.05 [5508]~P116(x55082)+E(x55081,f2(x55082))+E(f332(f332(f290(x55082),f332(f80(x55082),x55083)),f332(f80(x55082),x55081)),f332(f332(f290(x55082),x55083),x55081)) % 165.28/165.05 [5555]~P107(x55551)+E(f332(f302(x55551,x55552),x55553),f196(f875(x55551,a862)))+~P24(f332(f332(f246(x55551),x55553),x55552)) % 165.28/165.05 [5587]~P107(x55871)+E(f306(x55871,x55872,x55873),f196(f875(x55871,a862)))+~P24(f332(f332(f246(x55871),x55873),x55872)) % 165.28/165.05 [5588]~P107(x55881)+E(f305(x55881,x55882,x55883),f196(f875(x55881,a862)))+~P24(f332(f332(f246(x55881),x55883),x55882)) % 165.28/165.05 [5589]~P107(x55891)+E(f303(x55891,x55892,x55893),f196(f875(x55891,a862)))+~P24(f332(f332(f247(x55891),x55893),x55892)) % 165.28/165.05 [5640]~E(f332(f332(f22(a868),x56401),x56403),x56402)+E(x56401,f332(f332(f81(a868),x56402),x56403))+~P24(f332(f332(f246(a868),x56403),x56401)) % 165.28/165.05 [5641]~E(x56411,f332(f332(f81(a868),x56413),x56412))+E(f332(f332(f22(a868),x56411),x56412),x56413)+~P24(f332(f332(f246(a868),x56412),x56411)) % 165.28/165.05 [5687]~P24(f332(x56871,x56873))+P24(f332(x56871,f346(x56871,x56872)))+~P24(f332(f332(f247(a868),x56873),x56872)) % 165.28/165.05 [5688]~P24(f332(x56881,x56883))+P24(f332(x56881,f366(x56881,x56882)))+~P24(f332(f332(f246(a868),x56883),x56882)) % 165.28/165.05 [5696]~P107(x56961)+~E(f332(f302(x56961,x56962),x56963),f196(f875(x56961,a862)))+~P24(f332(f332(f247(x56961),x56962),x56963)) % 165.28/165.05 [5701]~P104(x57011)+~P24(f332(f332(f247(x57011),x57012),x57013))+P24(f332(f332(f246(x57011),x57012),x57013)) % 165.28/165.05 [5703]~P107(x57031)+~P24(f332(f332(f247(x57031),x57032),x57033))+P24(f332(f332(f246(x57031),x57032),x57033)) % 165.28/165.05 [5811]~P107(x58111)+~E(f305(x58111,x58112,x58113),f196(f875(x58111,a862)))+~P24(f332(f332(f247(x58111),x58112),x58113)) % 165.28/165.05 [5812]~P107(x58121)+~E(f303(x58121,x58122,x58123),f196(f875(x58121,a862)))+~P24(f332(f332(f246(x58121),x58122),x58123)) % 165.28/165.05 [5813]~P107(x58131)+~E(f196(f875(x58131,a862)),f305(x58131,x58132,x58133))+~P24(f332(f332(f247(x58131),x58132),x58133)) % 165.28/165.05 [5814]~P107(x58141)+~E(f196(f875(x58141,a862)),f303(x58141,x58142,x58143))+~P24(f332(f332(f246(x58141),x58142),x58143)) % 165.28/165.05 [5822]P24(f332(x58221,x58222))+~P24(f332(x58221,f347(x58221,x58223)))+~P24(f332(f332(f247(a868),x58222),x58223)) % 165.28/165.05 [5823]P24(f332(x58231,x58232))+~P24(f332(x58231,f367(x58231,x58233)))+~P24(f332(f332(f246(a868),x58232),x58233)) % 165.28/165.05 [5831]~E(x58311,f332(a115,x58313))+P24(f332(f332(f247(a868),x58311),f332(a115,x58312)))+~P24(f332(f332(f247(a868),x58313),x58312)) % 165.28/165.05 [5847]E(x58471,x58472)+~E(f332(f332(f82(a868),x58473),x58471),f332(f332(f82(a868),x58473),x58472))+~P24(f332(f332(f247(a868),f2(a868)),x58473)) % 165.28/165.05 [5905]E(f332(x59051,f848(x59051,x59052,x59053)),f79(a868))+~E(f332(f332(f6(x59053,a868),x59051),x59052),f79(a868))+~P24(f332(f62(x59053),x59052)) % 165.28/165.05 [5917]~P30(x59171)+P24(f332(f332(f246(x59171),x59172),f40(x59171,x59173)))+~P24(f332(f332(f334(x59171),x59172),x59173)) % 165.28/165.05 [5943]~P104(x59431)+~P24(f332(f332(f247(x59431),x59433),x59432))+~P24(f332(f332(f246(x59431),x59432),x59433)) % 165.28/165.05 [5947]~P104(x59471)+~P24(f332(f332(f247(x59471),x59473),x59472))+~P24(f332(f332(f247(x59471),x59472),x59473)) % 165.28/165.05 [5950]~P106(x59501)+~P24(f332(f332(f247(x59501),x59503),x59502))+~P24(f332(f332(f246(x59501),x59502),x59503)) % 165.28/165.05 [5951]~P106(x59511)+~P24(f332(f332(f247(x59511),x59513),x59512))+~P24(f332(f332(f247(x59511),x59512),x59513)) % 165.28/165.05 [5952]~P107(x59521)+~P24(f332(f332(f247(x59521),x59523),x59522))+~P24(f332(f332(f247(x59521),x59522),x59523)) % 165.28/165.05 [5977]~E(f332(x59772,f823(x59772,x59773,x59771)),f2(a868))+E(f332(f332(f6(x59771,a868),x59772),x59773),f2(a868))+~P24(f332(f62(x59771),x59773)) % 165.28/165.05 [5978]~E(f332(x59782,f845(x59782,x59783,x59781)),f79(a868))+E(f332(f332(f9(x59781,a868),x59782),x59783),f79(a868))+~P24(f332(f62(x59781),x59783)) % 165.28/165.05 [5996]~P105(x59961)+~P24(f332(f332(f247(x59961),x59963),x59962))+P24(f332(f332(f334(x59961),x59962),f332(f304(x59961),x59963))) % 165.28/165.05 [5997]~P105(x59971)+~P24(f332(f332(f246(x59971),x59973),x59972))+P24(f332(f332(f334(x59971),x59972),f332(f254(x59971),x59973))) % 165.28/165.05 [5998]~P105(x59981)+~P24(f332(f332(f247(x59981),x59982),x59983))+P24(f332(f332(f334(x59981),x59982),f332(f253(x59981),x59983))) % 165.28/165.05 [5999]~P105(x59991)+~P24(f332(f332(f246(x59991),x59992),x59993))+P24(f332(f332(f334(x59991),x59992),f332(f301(x59991),x59993))) % 165.28/165.05 [6011]E(f332(x60111,f846(x60111,x60112,x60113)),f332(a115,f2(a868)))+~E(f332(f332(f6(x60113,a868),x60111),x60112),f332(a115,f2(a868)))+~P24(f332(f62(x60113),x60112)) % 165.28/165.05 [6094]~P30(x60941)+~P24(f332(f332(f334(x60941),x60943),x60942))+P24(f332(f332(f246(x60941),f41(x60941,x60942)),x60943)) % 165.28/165.05 [6111]~P24(f332(f332(f246(a868),x61111),x61113))+P24(f332(f332(f246(a868),x61111),x61112))+~P24(f332(f332(f246(a868),x61113),x61112)) % 165.28/165.05 [6112]~P24(f332(f332(f246(a1),x61121),x61123))+P24(f332(f332(f246(a1),x61121),x61122))+~P24(f332(f332(f246(a1),x61123),x61122)) % 165.28/165.05 [6131]~P105(x61311)+~P24(f332(f332(f334(x61311),x61313),f332(f254(x61311),x61312)))+P24(f332(f332(f246(x61311),x61312),x61313)) % 165.28/165.05 [6132]~P105(x61321)+~P24(f332(f332(f334(x61321),x61322),f332(f301(x61321),x61323)))+P24(f332(f332(f246(x61321),x61322),x61323)) % 165.28/165.05 [6133]~P105(x61331)+~P24(f332(f332(f334(x61331),x61333),f332(f304(x61331),x61332)))+P24(f332(f332(f247(x61331),x61332),x61333)) % 165.28/165.05 [6134]~P105(x61341)+~P24(f332(f332(f334(x61341),x61342),f332(f253(x61341),x61343)))+P24(f332(f332(f247(x61341),x61342),x61343)) % 165.28/165.05 [6357]~P62(x63571)+P24(f332(f332(f247(x63571),f2(x63571)),f413(x63573,x63572,x63571)))+P24(f332(f332(f246(x63571),x63572),x63573)) % 165.28/165.05 [6358]~P63(x63581)+P24(f332(f332(f247(x63581),f2(x63581)),f796(x63583,x63582,x63581)))+P24(f332(f332(f246(x63581),x63582),x63583)) % 165.28/165.05 [6425]~P77(x64251)+~P24(f332(f332(f246(x64251),x64253),f332(f80(x64251),x64252)))+P24(f332(f332(f246(x64251),x64252),f332(f80(x64251),x64253))) % 165.28/165.05 [6427]~P77(x64271)+~P24(f332(f332(f247(x64271),x64273),f332(f80(x64271),x64272)))+P24(f332(f332(f247(x64271),x64272),f332(f80(x64271),x64273))) % 165.28/165.05 [6439]~P24(f332(f332(f247(a868),x64391),x64393))+~P24(f332(f332(f247(a868),x64393),x64392))+P24(f332(f332(f247(a868),f332(a115,x64391)),x64392)) % 165.28/165.05 [6465]~P112(x64651)+P24(f332(f332(f246(x64651),f332(f103(x64651),x64652)),f332(f103(x64651),x64653)))+~P24(f332(f332(f246(a868),x64652),x64653)) % 165.28/165.05 [6466]~P118(x64661)+P24(f332(f332(f246(x64661),f332(f105(x64661),x64662)),f332(f105(x64661),x64663)))+~P24(f332(f332(f246(a1),x64662),x64663)) % 165.28/165.05 [6468]~P118(x64681)+P24(f332(f332(f247(x64681),f332(f105(x64681),x64682)),f332(f105(x64681),x64683)))+~P24(f332(f332(f247(a1),x64682),x64683)) % 165.28/165.05 [6469]~P112(x64691)+P24(f332(f332(f247(x64691),f332(f103(x64691),x64692)),f332(f103(x64691),x64693)))+~P24(f332(f332(f247(a868),x64692),x64693)) % 165.28/165.05 [6475]~P106(x64751)+E(f332(f332(f113(f875(x64751,a862)),f332(f253(x64751),x64752)),f332(f302(x64751,x64752),x64753)),f332(f253(x64751),x64753))+~P24(f332(f332(f246(x64751),x64752),x64753)) % 165.28/165.05 [6506]~P77(x65061)+~P24(f332(f332(f246(x65061),x65063),x65062))+P24(f332(f332(f246(x65061),f332(f80(x65061),x65062)),f332(f80(x65061),x65063))) % 165.28/165.05 [6508]~P81(x65081)+~P24(f332(f332(f246(x65081),x65083),x65082))+P24(f332(f332(f246(x65081),f332(f80(x65081),x65082)),f332(f80(x65081),x65083))) % 165.28/165.05 [6509]~P77(x65091)+~P24(f332(f332(f247(x65091),x65093),x65092))+P24(f332(f332(f247(x65091),f332(f80(x65091),x65092)),f332(f80(x65091),x65093))) % 165.28/165.05 [6541]~P106(x65411)+E(f332(f332(f113(f875(x65411,a862)),f332(f253(x65411),x65412)),f303(x65411,x65412,x65413)),f332(f301(x65411),x65413))+~P24(f332(f332(f246(x65411),x65412),x65413)) % 165.28/165.05 [6542]~P106(x65421)+E(f332(f332(f113(f875(x65421,a862)),f332(f301(x65421),x65422)),f306(x65421,x65422,x65423)),f332(f253(x65421),x65423))+~P24(f332(f332(f247(x65421),x65422),x65423)) % 165.28/165.05 [6543]~P106(x65431)+E(f332(f332(f113(f875(x65431,a862)),f332(f301(x65431),x65432)),f305(x65431,x65432,x65433)),f332(f301(x65431),x65433))+~P24(f332(f332(f246(x65431),x65432),x65433)) % 165.28/165.05 [6577]~P106(x65771)+E(f332(f332(f113(f875(x65771,a862)),f332(f302(x65771,x65772),x65773)),f332(f254(x65771),x65773)),f332(f254(x65771),x65772))+~P24(f332(f332(f246(x65771),x65772),x65773)) % 165.28/165.05 [6731]~P106(x67311)+E(f332(f332(f113(f875(x67311,a862)),f306(x67311,x67312,x67313)),f332(f254(x67311),x67313)),f332(f304(x67311),x67312))+~P24(f332(f332(f247(x67311),x67312),x67313)) % 165.28/165.05 [6732]~P106(x67321)+E(f332(f332(f113(f875(x67321,a862)),f305(x67321,x67322,x67323)),f332(f304(x67321),x67323)),f332(f304(x67321),x67322))+~P24(f332(f332(f246(x67321),x67322),x67323)) % 165.28/165.05 [6733]~P106(x67331)+E(f332(f332(f113(f875(x67331,a862)),f303(x67331,x67332,x67333)),f332(f304(x67331),x67333)),f332(f254(x67331),x67332))+~P24(f332(f332(f246(x67331),x67332),x67333)) % 165.28/165.05 [6751]P24(f332(x67511,x67512))+~P24(f332(f332(f246(a868),x67512),x67513))+P24(f332(f332(f334(a868),f367(x67511,x67513)),f303(a868,f2(a868),x67513))) % 165.28/165.05 [6785]E(x67851,x67852)+~E(f332(f332(f166(x67853),x67851),f522(x67853,x67852,x67851)),f332(f332(f166(x67853),x67852),f522(x67853,x67852,x67851)))+~E(f332(f197(f869(x67853)),x67851),f332(f197(f869(x67853)),x67852)) % 165.28/165.05 [6790]~E(x67903,f332(f332(f39(a868),x67901),x67902))+~P24(f332(f332(f247(a868),f2(a868)),x67902))+P24(f332(f332(f247(a868),x67901),f332(f332(f82(a868),x67902),f332(a115,x67903)))) % 165.28/165.05 [6807]~P24(f332(x68071,x68073))+~P24(f332(f332(f246(a868),x68073),x68072))+P24(f332(f332(f334(a868),f366(x68071,x68072)),f303(a868,f2(a868),x68072))) % 165.28/165.05 [6846]~P24(f332(x68461,x68463))+P24(f332(x68461,f369(x68461,x68462)))+~P24(f332(f332(f334(a868),x68463),f303(a868,f2(a868),x68462))) % 165.28/165.05 [6865]~P112(x68653)+~P24(f332(f332(f246(x68653),f332(f103(x68653),x68651)),f332(f103(x68653),x68652)))+P24(f332(f332(f246(a868),x68651),x68652)) % 165.28/165.05 [6866]~P118(x68663)+~P24(f332(f332(f246(x68663),f332(f105(x68663),x68661)),f332(f105(x68663),x68662)))+P24(f332(f332(f246(a1),x68661),x68662)) % 165.28/165.05 [6868]~P112(x68683)+~P24(f332(f332(f247(x68683),f332(f103(x68683),x68681)),f332(f103(x68683),x68682)))+P24(f332(f332(f247(a868),x68681),x68682)) % 165.28/165.05 [6869]~P118(x68693)+~P24(f332(f332(f247(x68693),f332(f105(x68693),x68691)),f332(f105(x68693),x68692)))+P24(f332(f332(f247(a1),x68691),x68692)) % 165.28/165.05 [6886]~P112(x68861)+~P24(f332(f332(f247(x68861),f79(x68861)),x68862))+P24(f332(f332(f247(x68861),f79(x68861)),f332(f332(f257(x68861),x68862),f332(a115,x68863)))) % 165.28/165.05 [6888]~P77(x68881)+~P24(f332(f332(f246(x68881),f332(f80(x68881),x68883)),f332(f80(x68881),x68882)))+P24(f332(f332(f246(x68881),x68882),x68883)) % 165.28/165.05 [6889]~P81(x68891)+~P24(f332(f332(f246(x68891),f332(f80(x68891),x68893)),f332(f80(x68891),x68892)))+P24(f332(f332(f246(x68891),x68892),x68893)) % 165.28/165.05 [6890]~P77(x68901)+~P24(f332(f332(f247(x68901),f332(f80(x68901),x68903)),f332(f80(x68901),x68902)))+P24(f332(f332(f247(x68901),x68902),x68903)) % 165.28/165.05 [6914]P24(f332(x69141,x69142))+~P24(f332(x69141,f368(x69141,x69143)))+~P24(f332(f332(f334(a868),x69142),f303(a868,f2(a868),x69143))) % 165.28/165.05 [6933]~P62(x69331)+P24(f332(f332(f247(x69331),f413(x69333,x69332,x69331)),f79(x69331)))+P24(f332(f332(f246(x69331),x69332),x69333)) % 165.28/165.05 [6952]~E(f45(a868,x69523,x69522),f45(a868,x69521,x69522))+E(f332(f332(f81(a868),x69521),f332(f332(f82(a868),x69522),f451(x69521,x69522,x69523))),x69523)+~P24(f332(f332(f246(a868),x69521),x69523)) % 165.28/165.05 [6971]E(f332(x69711,f824(x69711,x69712,x69713)),f209(x69712))+~P24(f332(f62(x69713),f186(x69713,x69712,x69711)))+P24(f332(f62(x69713),f255(f875(x69713,a862)))) % 165.28/165.05 [7010]E(f332(f332(f6(x70101,a868),x70102),x70103),f2(a868))+~P24(f332(f62(x70101),x70103))+P24(f332(f332(f334(x70101),f823(x70102,x70103,x70101)),x70103)) % 165.28/165.05 [7011]E(f332(f332(f9(x70111,a868),x70112),x70113),f79(a868))+~P24(f332(f62(x70111),x70113))+P24(f332(f332(f334(x70111),f845(x70112,x70113,x70111)),x70113)) % 165.28/165.05 [7033]~P106(x70331)+~P24(f332(f332(f246(x70331),x70332),x70333))+P24(f332(f332(f246(f875(x70331,a862)),f332(f253(x70331),x70332)),f332(f253(x70331),x70333))) % 165.28/165.05 [7034]~P106(x70341)+~P24(f332(f332(f246(x70341),x70343),x70342))+P24(f332(f332(f246(f875(x70341,a862)),f332(f304(x70341),x70342)),f332(f304(x70341),x70343))) % 165.28/165.05 [7035]~P107(x70351)+~P24(f332(f332(f246(x70351),x70353),x70352))+P24(f332(f332(f246(f875(x70351,a862)),f332(f254(x70351),x70352)),f332(f254(x70351),x70353))) % 165.28/165.05 [7036]~P107(x70361)+~P24(f332(f332(f246(x70361),x70362),x70363))+P24(f332(f332(f246(f875(x70361,a862)),f332(f301(x70361),x70362)),f332(f301(x70361),x70363))) % 165.28/165.05 [7037]~P106(x70371)+~P24(f332(f332(f247(x70371),x70372),x70373))+P24(f332(f332(f247(f875(x70371,a862)),f332(f253(x70371),x70372)),f332(f253(x70371),x70373))) % 165.28/165.05 [7045]~P30(x70451)+P24(f332(f332(f246(x70451),x70452),f41(x70451,x70453)))+P24(f332(f332(f334(x70451),f640(x70453,x70452,x70451)),x70453)) % 165.28/165.05 [7051]~P77(x70511)+P24(f332(f332(f246(x70511),f332(f332(f22(x70511),x70512),x70513)),f2(x70511)))+~P24(f332(f332(f246(x70511),x70512),x70513)) % 165.28/165.05 [7052]~P77(x70521)+P24(f332(f332(f247(x70521),f332(f332(f22(x70521),x70522),x70523)),f2(x70521)))+~P24(f332(f332(f247(x70521),x70522),x70523)) % 165.28/165.05 [7094]P24(f332(x70941,x70942))+P24(f332(f332(f246(a868),f368(x70941,x70943)),x70943))+~P24(f332(f332(f334(a868),x70942),f303(a868,f2(a868),x70943))) % 165.28/165.05 [7134]~E(f332(f332(f6(x71341,a868),x71342),x71343),f79(a868))+~P24(f332(f62(x71341),x71343))+P24(f332(f332(f334(x71341),f848(x71342,x71343,x71341)),x71343)) % 165.28/165.05 [7135]~P24(f332(x71351,x71353))+P24(f332(f332(f246(a868),f369(x71351,x71352)),x71352))+~P24(f332(f332(f334(a868),x71353),f303(a868,f2(a868),x71352))) % 165.28/165.05 [7175]~P30(x71751)+P24(f332(f332(f334(x71751),f638(x71753,x71752,x71751)),x71752))+P24(f332(f332(f246(x71751),f40(x71751,x71752)),x71753)) % 165.28/165.05 [7206]~E(f332(f332(f6(x72061,a868),x72062),x72063),f332(a115,f2(a868)))+~P24(f332(f62(x72061),x72063))+P24(f332(f332(f334(x72061),f846(x72062,x72063,x72061)),x72063)) % 165.28/165.05 [7217]E(x72171,f2(a868))+P24(f332(x72172,f45(a868,x72173,x72171)))+P24(f332(f332(f247(a868),f421(x72171,x72173,x72172)),x72171)) % 165.28/165.05 [7322]~P24(f332(x73221,x73222))+P24(f332(x73221,f45(a868,x73222,x73223)))+P24(f332(f332(f247(a868),f421(x73223,x73222,x73221)),x73223)) % 165.28/165.05 [7442]E(x74421,f116(x74422))+~P24(f332(f332(f334(f869(x74422)),x74421),f162(x74422,x74423)))+P24(f332(f332(f334(x74422),f592(x74423,x74421,x74422)),x74423)) % 165.28/165.05 [7464]~P106(x74641)+E(f332(f332(f113(f875(x74641,a862)),f332(f332(f310(x74641),x74642),f196(f875(x74641,a862)))),f306(x74641,x74642,x74643)),f332(f302(x74641,x74642),x74643))+~P24(f332(f332(f247(x74641),x74642),x74643)) % 165.28/165.05 [7490]~P106(x74901)+E(f332(f332(f113(f875(x74901,a862)),f332(f332(f310(x74901),x74902),f196(f875(x74901,a862)))),f305(x74901,x74902,x74903)),f303(x74901,x74902,x74903))+~P24(f332(f332(f246(x74901),x74902),x74903)) % 165.28/165.05 [7597]~P106(x75971)+P24(f332(f332(f246(x75971),x75972),x75973))+~P24(f332(f332(f246(f875(x75971,a862)),f332(f304(x75971),x75973)),f332(f304(x75971),x75972))) % 165.28/165.05 [7598]~P107(x75981)+P24(f332(f332(f246(x75981),x75982),x75983))+~P24(f332(f332(f246(f875(x75981,a862)),f332(f254(x75981),x75983)),f332(f254(x75981),x75982))) % 165.28/165.05 [7599]~P106(x75991)+P24(f332(f332(f246(x75991),x75992),x75993))+~P24(f332(f332(f246(f875(x75991,a862)),f332(f253(x75991),x75992)),f332(f253(x75991),x75993))) % 165.28/165.05 [7600]~P107(x76001)+P24(f332(f332(f246(x76001),x76002),x76003))+~P24(f332(f332(f246(f875(x76001,a862)),f332(f301(x76001),x76002)),f332(f301(x76001),x76003))) % 165.28/165.05 [7601]~P106(x76011)+P24(f332(f332(f247(x76011),x76012),x76013))+~P24(f332(f332(f247(f875(x76011,a862)),f332(f253(x76011),x76012)),f332(f253(x76011),x76013))) % 165.28/165.05 [7624]~P77(x76241)+~P24(f332(f332(f246(x76241),f332(f332(f22(x76241),x76242),x76243)),f2(x76241)))+P24(f332(f332(f246(x76241),x76242),x76243)) % 165.28/165.05 [7625]~P77(x76251)+~P24(f332(f332(f247(x76251),f332(f332(f22(x76251),x76252),x76253)),f2(x76251)))+P24(f332(f332(f247(x76251),x76252),x76253)) % 165.28/165.05 [7782]E(x77821,f2(a868))+~E(f332(f143(a868,a868,f81(a868),x77822),x77823),f2(a868))+~P24(f332(f332(f334(a868),x77821),f332(f174(a868),x77823))) % 165.28/165.05 [7786]~P30(x77861)+~P24(f332(f332(f246(x77861),f638(x77863,x77862,x77861)),x77863))+P24(f332(f332(f246(x77861),f40(x77861,x77862)),x77863)) % 165.28/165.05 [7938]P24(f332(f332(f246(a1),f2(a1)),f419(x79381,x79382,x79383)))+P24(f332(f332(x79382,f332(f332(f39(a1),x79381),x79383)),f45(a1,x79381,x79383)))+~P24(f332(f332(f247(a1),f2(a1)),x79383)) % 165.28/165.05 [8025]E(x80251,x80252)+~E(f332(f197(f869(x80253)),x80251),f332(f197(f869(x80253)),x80252))+~P24(f332(f332(f271(x80253,x80253,a862),a329),f545(x80253,x80251,x80252))) % 165.28/165.05 [8092]~P41(x80922,x80923)+E(x80921,f196(f875(x80922,a862)))+~P24(f332(f332(f246(f875(x80922,a862)),x80921),f332(f286(x80922,x80922,x80923),x80921))) % 165.28/165.05 [8121]~P63(x81211)+~P24(f332(f332(f246(x81211),x81212),f332(f332(f81(x81211),x81213),f796(x81213,x81212,x81211))))+P24(f332(f332(f246(x81211),x81212),x81213)) % 165.28/165.05 [8161]P43(x81611,x81612,x81613)+P24(f332(f332(f334(x81611),f548(x81613,x81612,x81611)),x81612))+P24(f332(f332(f334(f874(x81611,x81611)),f549(x81613,x81612,x81611)),x81613)) % 165.28/165.05 [8184]P24(f332(f332(x81842,f332(f332(f39(a1),x81841),x81843)),f45(a1,x81841,x81843)))+~P24(f332(f332(f247(a1),f2(a1)),x81843))+P24(f332(f332(f247(a1),f419(x81841,x81842,x81843)),x81843)) % 165.28/165.05 [8208]E(f332(f311(a868,a868,f332(f332(f7(a868,a868,a868),f22(a868)),x82081)),f332(f302(a868,x82082),x82083)),f196(f875(a868,a862)))+P24(f332(f332(f247(a868),x82081),x82083))+P24(f332(f332(f247(a868),x82082),x82083)) % 165.28/165.05 [8312]E(f332(f311(a868,a868,f332(f332(f7(a868,a868,a868),f22(a868)),x83121)),f332(f302(a868,x83122),x83123)),f332(f332(f310(a868),f2(a868)),f196(f875(a868,a862))))+P24(f332(f332(f247(a868),x83121),x83123))+~P24(f332(f332(f247(a868),x83122),x83123)) % 165.28/165.05 [8329]~P106(x83291)+E(f150(x83291,x83291,f5(x83291),x83292,x83293),x83293)+~P24(f332(f332(f334(x83291),x83292),f332(f174(x83291),x83293))) % 165.28/165.05 [8343]P21(x83431,x83431,x83432,x83433)+~P24(f332(f62(x83431),x83433))+~P24(f332(f332(f246(f875(x83431,a862)),x83433),f332(f311(x83431,x83431,x83432),x83433))) % 165.28/165.05 [8366]E(f332(f332(f81(a1),f332(f332(f82(a1),x83661),f420(x83662,x83663,x83661))),f419(x83662,x83663,x83661)),x83662)+P24(f332(f332(x83663,f332(f332(f39(a1),x83662),x83661)),f45(a1,x83662,x83661)))+~P24(f332(f332(f247(a1),f2(a1)),x83661)) % 165.28/165.05 [8592]~P24(f332(f332(x85921,f420(x85922,x85921,x85923)),f419(x85922,x85921,x85923)))+P24(f332(f332(x85921,f332(f332(f39(a1),x85922),x85923)),f45(a1,x85922,x85923)))+~P24(f332(f332(f247(a1),f2(a1)),x85923)) % 165.28/165.05 [9430]~P24(f332(f62(x94301),x94302))+~P24(f332(f332(f334(x94301),x94303),x94302))+P24(f332(f332(f247(a868),f332(f38(x94301),f332(f332(f22(f875(x94301,a862)),x94302),f332(f332(f310(x94301),x94303),f196(f875(x94301,a862)))))),f332(f38(x94301),x94302))) % 165.28/165.05 [10024]P43(x100241,x100242,x100243)+~P24(f332(f332(f271(x100241,x100241,a862),f332(f332(f7(x100241,f875(x100241,a862),f875(x100241,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x100241,a862),f875(x100241,a862)),x100241),f8(a862,a862,x100241)),f332(f332(f8(a862,f875(a862,a862),x100241),a330),f332(f332(f7(x100241,f875(x100241,a862),a862),f334(x100241)),x100242)))),f332(f332(f7(x100241,f875(x100241,a862),a862),f334(x100241)),x100242))),f549(x100243,x100242,x100241)))+P24(f332(f332(f334(x100241),f548(x100243,x100242,x100241)),x100242)) % 165.28/165.05 [5469]~P116(x54692)+E(x54691,f2(x54692))+E(f332(f332(f290(x54692),x54693),f332(f80(x54692),x54691)),f332(f80(x54692),f332(f332(f290(x54692),x54693),x54691))) % 165.28/165.05 [5603]~E(x56033,f196(f875(x56031,a862)))+~E(x56032,f196(f875(x56031,a862)))+E(f332(f332(f113(f875(x56031,a862)),x56032),x56033),f196(f875(x56031,a862))) % 165.28/165.05 [5661]~E(x56613,f2(a868))+~P24(f332(x56611,f2(a868)))+P24(f332(x56611,f332(f332(f39(a868),x56612),x56613))) % 165.28/165.05 [5803]~P63(x58032)+E(x58031,f2(x58032))+E(f332(f332(f290(x58032),f332(f76(x58032),x58033)),f332(f76(x58032),x58031)),f332(f76(x58032),f332(f332(f290(x58032),x58033),x58031))) % 165.28/165.05 [5967]~P24(f332(f62(x59671),x59673))+E(f332(f38(x59671),f332(f332(f310(x59671),x59672),x59673)),f332(a115,f332(f38(x59671),x59673)))+P24(f332(f332(f334(x59671),x59672),x59673)) % 165.28/165.05 [6043]~E(x60432,f2(a868))+P24(f332(x60431,f2(a868)))+~P24(f332(x60431,f332(f332(f39(a868),x60433),x60432))) % 165.28/165.05 [6062]~P24(f332(f62(x60621),x60623))+E(f332(f38(x60621),f332(f332(f310(x60621),x60622),x60623)),f332(f38(x60621),x60623))+~P24(f332(f332(f334(x60621),x60622),x60623)) % 165.28/165.05 [6096]~P24(f332(f62(x60961),x60963))+E(f332(f38(x60961),f332(f332(f310(x60961),x60962),x60963)),f332(f332(f81(a868),f79(a868)),f332(f38(x60961),x60963)))+P24(f332(f332(f334(x60961),x60962),x60963)) % 165.28/165.05 [6219]E(f332(f332(f81(a868),x62191),f849(x62191,x62192,x62193)),x62192)+~P24(f332(x62193,f2(a868)))+P24(f332(x62193,f332(f332(f22(a868),x62192),x62191))) % 165.28/165.05 [6220]E(f332(f332(f81(a868),x62201),f851(x62201,x62202,x62203)),x62202)+~P24(f332(x62203,f2(a868)))+P24(f332(x62203,f332(f332(f22(a868),x62202),x62201))) % 165.28/165.05 [6266]~P30(x62661)+~P24(f332(f62(x62661),x62663))+E(f332(f332(f65(x62661,x62661,f113(x62661)),x62662),x62663),f332(f332(f113(x62661),x62662),f40(x62661,x62663))) % 165.28/165.05 [6267]~P30(x62671)+~P24(f332(f62(x62671),x62673))+E(f332(f332(f65(x62671,x62671,f104(x62671)),x62672),x62673),f332(f332(f104(x62671),x62672),f41(x62671,x62673))) % 165.28/165.05 [6273]~P92(x62731)+~E(f332(f106(x62731),x62732),f332(f106(x62731),x62733))+P34(x62731,f332(f106(x62731),f332(f332(f81(a1),x62732),f332(f80(a1),x62733)))) % 165.28/165.05 [6280]~P138(x62801)+E(f332(f332(f22(x62801),f332(f103(x62801),x62802)),f332(f103(x62801),x62803)),f332(f103(x62801),f332(f332(f22(a868),x62802),x62803)))+~P24(f332(f332(f246(a868),x62803),x62802)) % 165.28/165.05 [6368]E(f332(f332(f81(a868),x63681),f849(x63681,x63682,x63683)),x63682)+P24(f332(f332(f247(a868),x63682),x63681))+P24(f332(x63683,f332(f332(f22(a868),x63682),x63681))) % 165.28/165.05 [6369]E(f332(f332(f81(a868),x63691),f851(x63691,x63692,x63693)),x63692)+P24(f332(f332(f247(a868),x63692),x63691))+P24(f332(x63693,f332(f332(f22(a868),x63692),x63691))) % 165.28/165.05 [6384]~P118(x63841)+E(f332(f332(f82(x63841),f332(f76(x63841),x63842)),x63843),f332(f76(x63841),f332(f332(f82(x63841),x63842),x63843)))+~P24(f332(f332(f246(x63841),f2(x63841)),x63843)) % 165.28/165.05 [6385]~P62(x63851)+E(f332(f332(f290(x63851),f332(f76(x63851),x63852)),x63853),f332(f76(x63851),f332(f332(f290(x63851),x63852),x63853)))+~P24(f332(f332(f247(x63851),f2(x63851)),x63853)) % 165.28/165.05 [6393]~P26(x63931)+~P24(f332(f62(x63931),x63933))+E(f332(f332(f65(x63931,x63931,f113(x63931)),x63932),x63933),f10(x63931,f332(f332(f310(x63931),x63932),x63933))) % 165.28/165.05 [6394]~P26(x63941)+~P24(f332(f62(x63941),x63943))+E(f332(f332(f65(x63941,x63941,f104(x63941)),x63942),x63943),f11(x63941,f332(f332(f310(x63941),x63942),x63943))) % 165.28/165.05 [6395]~P106(x63951)+~P24(f332(f62(x63951),x63953))+E(f332(f332(f65(x63951,x63951,f245(x63951)),x63952),x63953),f14(x63951,f332(f332(f310(x63951),x63952),x63953))) % 165.28/165.05 [6396]~P106(x63961)+~P24(f332(f62(x63961),x63963))+E(f332(f332(f65(x63961,x63961,f244(x63961)),x63962),x63963),f15(x63961,f332(f332(f310(x63961),x63962),x63963))) % 165.28/165.05 [6441]E(x64411,f116(x64412))+~E(f182(x64412,x64413),f116(f869(x64412)))+~P24(f332(f332(f334(f869(x64412)),x64411),f332(f174(f869(x64412)),x64413))) % 165.28/165.05 [6483]~P24(f332(f138(x64831),x64833))+P24(f332(f332(f334(x64831),x64832),f332(f174(x64831),x64833)))+P24(f332(f138(x64831),f332(f332(f152(x64831),x64832),x64833))) % 165.28/165.05 [6494]~P95(x64941)+~P24(f332(f62(x64941),x64943))+E(f332(f64(x64941,f82(x64941)),f332(f332(f310(x64941),x64942),x64943)),f332(f332(f65(x64941,x64941,f82(x64941)),x64942),x64943)) % 165.28/165.05 [6517]~P106(x65171)+~P24(f332(f62(x65171),x65173))+E(f12(x65171,f244(x65171),f332(f332(f310(x65171),x65172),x65173)),f332(f332(f65(x65171,x65171,f244(x65171)),x65172),x65173)) % 165.28/165.05 [6518]~P106(x65181)+~P24(f332(f62(x65181),x65183))+E(f13(x65181,f245(x65181),f332(f332(f310(x65181),x65182),x65183)),f332(f332(f65(x65181,x65181,f245(x65181)),x65182),x65183)) % 165.28/165.05 [6520]P24(f332(x65201,f2(a868)))+~P24(f332(f332(f247(a868),x65202),x65203))+~P24(f332(x65201,f332(f332(f22(a868),x65202),x65203))) % 165.28/165.05 [6539]~P85(x65391)+P24(f332(f332(f246(x65391),x65392),x65393))+~P24(f332(f332(f246(x65391),f332(f76(x65391),x65392)),x65393)) % 165.28/165.05 [6540]~P118(x65401)+P24(f332(f332(f247(x65401),x65402),x65403))+~P24(f332(f332(f247(x65401),f332(f76(x65401),x65402)),x65403)) % 165.28/165.05 [6557]E(x65571,f116(x65572))+E(f332(f142(x65572),f332(f332(f139(x65572),x65573),x65571)),f332(f332(f166(x65572),x65571),x65573))+~P24(f332(f332(f247(a868),x65573),f332(f197(f869(x65572)),x65571))) % 165.28/165.05 [6608]~P24(f332(x66081,x66083))+P24(f332(x66081,f351(x66081,x66082)))+~P24(f332(f332(f334(a868),x66083),f332(f302(a868,f2(a868)),x66082))) % 165.28/165.05 [6629]P24(f332(x66291,x66292))+~P24(f332(f332(f247(a868),x66292),x66293))+P24(f332(f332(f334(a868),f347(x66291,x66293)),f332(f302(a868,f2(a868)),x66293))) % 165.28/165.05 [6644]~P112(x66441)+~P24(f332(f332(f246(x66441),f79(x66441)),x66442))+P24(f332(f332(f246(x66441),f79(x66441)),f332(f332(f257(x66441),x66442),x66443))) % 165.28/165.05 [6646]~P112(x66461)+~P24(f332(f332(f246(x66461),f2(x66461)),x66462))+P24(f332(f332(f246(x66461),f2(x66461)),f332(f332(f257(x66461),x66462),x66463))) % 165.28/165.05 [6648]~P112(x66481)+~P24(f332(f332(f247(x66481),f2(x66481)),x66482))+P24(f332(f332(f247(x66481),f2(x66481)),f332(f332(f257(x66481),x66482),x66483))) % 165.28/165.05 [6672]~P24(f332(x66721,x66723))+~P24(f332(f332(f247(a868),x66723),x66722))+P24(f332(f332(f334(a868),f346(x66721,x66722)),f332(f302(a868,f2(a868)),x66722))) % 165.28/165.05 [6679]P24(f332(f62(x66791),x66792))+~P24(f332(f62(x66791),x66793))+~P24(f332(f332(f246(f875(x66791,a862)),x66792),x66793)) % 165.28/165.05 [6687]P24(f332(x66871,x66872))+~P24(f332(x66871,f349(x66871,x66873)))+~P24(f332(f332(f334(a868),x66872),f332(f302(a868,f2(a868)),x66873))) % 165.28/165.05 [6698]E(x66981,f2(a868))+P24(f332(x66982,f353(x66981,x66983,x66982)))+~P24(f332(x66982,f332(f332(f39(a868),x66983),x66981))) % 165.28/165.05 [6706]~P122(x67062)+E(x67061,f2(x67062))+~E(f332(f332(f81(x67062),f332(f332(f82(x67062),x67063),x67063)),f332(f332(f82(x67062),x67061),x67061)),f2(x67062)) % 165.28/165.05 [6707]~P122(x67072)+E(x67071,f2(x67072))+~E(f332(f332(f81(x67072),f332(f332(f82(x67072),x67071),x67071)),f332(f332(f82(x67072),x67073),x67073)),f2(x67072)) % 165.28/165.05 [6752]E(x67521,f2(a868))+~P24(f332(x67522,f354(x67521,x67523,x67522)))+P24(f332(x67522,f332(f332(f39(a868),x67523),x67521))) % 165.28/165.05 [6757]~P106(x67571)+~P32(x67571,x67573)+P32(x67571,f332(f332(f149(x67571,x67571,f5(x67571)),x67572),x67573)) % 165.28/165.05 [6800]P24(f332(x68001,f353(x68002,x68003,x68001)))+P24(f332(x68001,f2(a868)))+~P24(f332(x68001,f332(f332(f39(a868),x68003),x68002))) % 165.28/165.05 [6806]~P92(x68061)+E(f332(f106(x68061),x68062),f332(f106(x68061),x68063))+~P34(x68061,f332(f106(x68061),f332(f332(f81(a1),x68062),f332(f80(a1),x68063)))) % 165.28/165.05 [6872]E(x68721,f2(a1))+E(x68722,f2(a1))+~P24(f332(f49(x68722,x68722),f332(f332(f267(a1,a1),x68723),x68721))) % 165.28/165.05 [6873]E(x68731,f79(a1))+E(x68732,f2(a1))+~P24(f332(f49(x68732,x68732),f332(f332(f267(a1,a1),x68731),x68733))) % 165.28/165.05 [6887]P24(f332(x68871,x68872))+P24(f332(f332(f247(a868),f349(x68871,x68873)),x68873))+~P24(f332(f332(f334(a868),x68872),f332(f302(a868,f2(a868)),x68873))) % 165.28/165.05 [6909]~P24(f332(x69091,f849(x69093,x69092,x69091)))+~P24(f332(x69091,f2(a868)))+P24(f332(x69091,f332(f332(f22(a868),x69092),x69093))) % 165.28/165.05 [6910]~P24(f332(x69101,f851(x69103,x69102,x69101)))+~P24(f332(x69101,f2(a868)))+P24(f332(x69101,f332(f332(f22(a868),x69102),x69103))) % 165.28/165.05 [6911]~P24(f332(x69111,f354(x69113,x69112,x69111)))+~P24(f332(x69111,f2(a868)))+P24(f332(x69111,f332(f332(f39(a868),x69112),x69113))) % 165.28/165.05 [6929]~P24(f332(x69291,x69293))+P24(f332(f332(f247(a868),f351(x69291,x69292)),x69292))+~P24(f332(f332(f334(a868),x69293),f332(f302(a868,f2(a868)),x69292))) % 165.28/165.05 [6930]E(f332(f332(f22(a868),f332(f332(f22(a868),x69301),x69302)),f332(f332(f22(a868),x69303),x69302)),f332(f332(f22(a868),x69301),x69303))+~P24(f332(f332(f246(a868),x69302),x69301))+~P24(f332(f332(f246(a868),x69302),x69303)) % 165.28/165.05 [6965]~P77(x69651)+~P24(f332(f332(f246(x69651),f332(f80(x69651),x69653)),x69652))+P24(f332(f332(f246(x69651),f332(f80(x69651),x69652)),x69653)) % 165.28/165.05 [6967]~P85(x69671)+~P24(f332(f332(f246(x69671),f332(f76(x69671),x69672)),x69673))+P24(f332(f332(f246(x69671),f332(f80(x69671),x69672)),x69673)) % 165.28/165.05 [6969]~P77(x69691)+~P24(f332(f332(f247(x69691),f332(f80(x69691),x69693)),x69692))+P24(f332(f332(f247(x69691),f332(f80(x69691),x69692)),x69693)) % 165.28/165.05 [6970]~P118(x69701)+~P24(f332(f332(f247(x69701),f332(f76(x69701),x69702)),x69703))+P24(f332(f332(f247(x69701),f332(f80(x69701),x69702)),x69703)) % 165.28/165.05 [7004]~P24(f332(x70043,f849(x70042,x70041,x70043)))+P24(f332(f332(f247(a868),x70041),x70042))+P24(f332(x70043,f332(f332(f22(a868),x70041),x70042))) % 165.28/165.05 [7005]~P24(f332(x70053,f851(x70052,x70051,x70053)))+P24(f332(f332(f247(a868),x70051),x70052))+P24(f332(x70053,f332(f332(f22(a868),x70051),x70052))) % 165.28/165.05 [7055]~E(f641(x70553,x70552,x70551),f642(x70553,x70552,x70551))+E(f332(f332(f104(f875(x70551,a862)),x70552),f40(f875(x70551,a862),x70553)),f196(f875(x70551,a862)))+P24(f332(f332(f334(f875(x70551,a862)),x70552),x70553)) % 165.28/165.05 [7064]~P24(f332(f62(x70641),x70643))+P24(f332(f62(x70641),f41(f875(x70641,a862),x70642)))+~P24(f332(f332(f334(f875(x70641,a862)),x70643),x70642)) % 165.28/165.05 [7123]~P106(x71231)+E(f332(f332(f113(f875(x71231,a862)),f332(f302(x71231,x71232),x71233)),f332(f332(f310(x71231),x71233),f196(f875(x71231,a862)))),f303(x71231,x71232,x71233))+~P24(f332(f332(f246(x71231),x71232),x71233)) % 165.28/165.05 [7124]E(x71241,f2(a868))+P24(f332(f332(f247(a868),f355(x71241,x71243,x71242)),x71241))+P24(f332(x71242,f332(f332(f39(a868),x71243),x71241))) % 165.28/165.05 [7159]E(x71591,x71592)+~P24(f332(f332(f246(f875(x71593,a862)),x71591),x71592))+P24(f332(f332(f247(f875(x71593,a862)),x71591),x71592)) % 165.28/165.05 [7172]E(x71721,x71722)+~E(f332(f197(f869(x71723)),x71721),f332(f197(f869(x71723)),x71722))+P24(f332(f332(f247(a868),f522(x71723,x71721,x71722)),f332(f197(f869(x71723)),x71722))) % 165.28/165.05 [7218]P6(x72181,x72182,x72183)+~E(f332(f265(x72181,x72181),x72183),x72182)+~E(f332(f332(f289(x72181,x72181,x72181),f332(f287(x72181,x72181),x72183)),x72183),x72183) % 165.28/165.05 [7290]~P24(f332(x72901,f2(a868)))+P24(f332(f332(f247(a868),f355(x72903,x72902,x72901)),x72903))+P24(f332(x72901,f332(f332(f39(a868),x72902),x72903))) % 165.28/165.05 [7299]~P106(x72991)+E(f332(f332(f113(f875(x72991,a862)),f306(x72991,x72992,x72993)),f332(f332(f310(x72991),x72993),f196(f875(x72991,a862)))),f305(x72991,x72992,x72993))+~P24(f332(f332(f247(x72991),x72992),x72993)) % 165.28/165.05 [7397]~P24(f332(f62(x73971),x73973))+P24(f332(f332(f246(a868),f332(f38(x73971),x73972)),f332(f38(x73971),x73973)))+~P24(f332(f332(f246(f875(x73971,a862)),x73972),x73973)) % 165.28/165.05 [7398]~P24(f332(f62(x73981),x73983))+P24(f332(f332(f247(a868),f332(f38(x73981),x73982)),f332(f38(x73981),x73983)))+~P24(f332(f332(f247(f875(x73981,a862)),x73982),x73983)) % 165.28/165.05 [7535]E(x75351,x75352)+~P24(f332(f332(f246(f875(x75353,a862)),x75352),x75351))+~P24(f332(f332(f246(f875(x75353,a862)),x75351),x75352)) % 165.28/165.05 [7538]~P106(x75381)+P32(x75381,x75382)+~P32(x75381,f332(f332(f149(x75381,x75381,f5(x75381)),x75383),x75382)) % 165.28/165.05 [7606]~P24(f332(f332(f247(a868),x76063),x76062))+~P24(f332(f332(f247(a868),x76063),x76061))+P24(f332(f332(f247(a868),f332(f332(f22(a868),x76061),x76062)),f332(f332(f22(a868),x76061),x76063))) % 165.28/165.05 [7607]~P24(f332(f332(f246(a868),x76072),x76071))+~P24(f332(f332(f247(a868),x76071),x76073))+P24(f332(f332(f247(a868),f332(f332(f22(a868),x76071),x76072)),f332(f332(f22(a868),x76073),x76072))) % 165.28/165.05 [7622]~P24(f332(f332(f247(a1),x76222),f2(a1)))+~P24(f332(f332(f246(a1),x76223),x76221))+P24(f332(f332(f246(a1),f332(f332(f39(a1),x76221),x76222)),f332(f332(f39(a1),x76223),x76222))) % 165.28/165.05 [7640]~P24(f332(f332(f247(a868),f2(a868)),x76403))+~P24(f332(f332(f246(a868),x76403),x76402))+P24(f332(f332(f246(a868),f332(f332(f39(a868),x76401),x76402)),f332(f332(f39(a868),x76401),x76403))) % 165.28/165.05 [7641]~P24(f332(f332(f247(a1),f2(a1)),x76412))+~P24(f332(f332(f246(a1),x76411),x76413))+P24(f332(f332(f246(a1),f332(f332(f39(a1),x76411),x76412)),f332(f332(f39(a1),x76413),x76412))) % 165.28/165.05 [7645]~P24(f332(f332(f247(a868),f2(a868)),x76452))+~P24(f332(f332(f247(a868),x76451),x76453))+P24(f332(f332(f247(a868),f332(f332(f82(a868),x76451),x76452)),f332(f332(f82(a868),x76453),x76452))) % 165.28/165.05 [7646]~P24(f332(f332(f247(a868),f2(a868)),x76461))+~P24(f332(f332(f247(a868),x76462),x76463))+P24(f332(f332(f247(a868),f332(f332(f82(a868),x76461),x76462)),f332(f332(f82(a868),x76461),x76463))) % 165.28/165.05 [7647]~P24(f332(f332(f247(a1),f2(a1)),x76471))+~P24(f332(f332(f247(a1),x76472),x76473))+P24(f332(f332(f247(a1),f332(f332(f82(a1),x76471),x76472)),f332(f332(f82(a1),x76471),x76473))) % 165.28/165.05 [7697]E(x76971,f2(a868))+E(f332(f332(f81(a868),f332(f332(f82(a868),x76971),f354(x76971,x76972,x76973))),f355(x76971,x76972,x76973)),x76972)+P24(f332(x76973,f332(f332(f39(a868),x76972),x76971))) % 165.28/165.05 [7755]E(f332(f332(f81(a868),f332(f332(f82(a868),x77551),f354(x77551,x77552,x77553))),f355(x77551,x77552,x77553)),x77552)+~P24(f332(x77553,f2(a868)))+P24(f332(x77553,f332(f332(f39(a868),x77552),x77551))) % 165.28/165.05 [7773]~P24(f332(f62(x77731),x77733))+P24(f332(f332(f334(x77731),f843(x77732,x77733,x77731)),x77733))+P24(f332(f332(f247(a868),f2(a868)),f332(f332(f9(x77731,a868),x77732),x77733))) % 165.28/165.05 [7774]~P24(f332(f62(x77741),x77743))+P24(f332(f332(f334(x77741),f423(x77742,x77743,x77741)),x77743))+P24(f332(f332(f247(a868),f2(a868)),f332(f332(f9(x77741,a868),x77742),x77743))) % 165.28/165.05 [8058]E(x80581,f196(f875(x80582,a862)))+E(x80581,f332(f332(f310(x80582),x80583),f196(f875(x80582,a862))))+~P24(f332(f332(f246(f875(x80582,a862)),x80581),f332(f332(f310(x80582),x80583),f196(f875(x80582,a862))))) % 165.28/165.05 [8075]~P59(x80751)+P8(x80751,x80752,x80753)+P24(f332(f332(f334(f869(x80751)),f628(x80753,x80752,x80751)),f332(f174(f869(x80751)),f55(x80751,x80753,f56(x80751))))) % 165.28/165.05 [8094]~P24(f332(f332(f247(a868),f2(a868)),x80943))+P24(f332(f332(f246(a868),x80941),x80942))+~P24(f332(f332(f246(a868),f332(f332(f82(a868),x80943),x80941)),f332(f332(f82(a868),x80943),x80942))) % 165.28/165.05 [8095]~P24(f332(f332(f247(a868),f2(a868)),x80953))+P24(f332(f332(f246(a868),x80951),x80952))+~P24(f332(f332(f246(a868),f332(f332(f82(a868),x80951),x80953)),f332(f332(f82(a868),x80952),x80953))) % 165.28/165.05 [8097]~P24(f332(f332(f247(a868),f2(a868)),x80973))+P24(f332(f332(f247(a868),x80971),x80972))+~P24(f332(f332(f247(a868),f332(f332(f257(a868),x80973),x80971)),f332(f332(f257(a868),x80973),x80972))) % 165.28/165.05 [8123]~P59(x81231)+~P7(x81231,x81233,x81232)+P24(f332(f332(f334(f869(x81231)),f627(x81232,x81233,x81231)),f332(f174(f869(x81231)),f55(x81231,x81232,f56(x81231))))) % 165.28/165.05 [8139]~E(f332(f332(f104(f875(x81391,a862)),f642(x81393,x81392,x81391)),f641(x81393,x81392,x81391)),f196(f875(x81391,a862)))+E(f332(f332(f104(f875(x81391,a862)),x81392),f40(f875(x81391,a862),x81393)),f196(f875(x81391,a862)))+P24(f332(f332(f334(f875(x81391,a862)),x81392),x81393)) % 165.28/165.05 [8156]E(x81561,f116(x81562))+~E(f332(f143(f869(x81562),f869(x81562),f135(x81562),f116(x81562)),x81563),f116(x81562))+~P24(f332(f332(f334(f869(x81562)),x81561),f332(f174(f869(x81562)),x81563))) % 165.28/165.05 [8213]E(x82131,f196(f875(f875(x82132,a862),a862)))+P24(f332(f332(f334(f875(x82132,a862)),f679(x82133,x82131,x82132)),x82131))+P24(f332(f332(f246(f875(x82132,a862)),f41(f875(x82132,a862),x82131)),x82133)) % 165.28/165.05 [8220]~P73(x82201)+~P74(x82201)+E(f332(f332(f6(a1,x82201),f332(f332(f8(a868,x82201,a1),x82202),a107)),f332(f311(a868,a1,f103(a1)),x82203)),f332(f332(f6(a868,x82201),x82202),x82203)) % 165.28/165.05 [8221]~P73(x82211)+~P74(x82211)+E(f332(f332(f9(a1,x82211),f332(f332(f8(a868,x82211,a1),x82212),a107)),f332(f311(a868,a1,f103(a1)),x82213)),f332(f332(f9(a868,x82211),x82212),x82213)) % 165.28/165.05 [8260]~P24(f332(f62(x82601),x82603))+~P24(f332(f332(f247(a868),f2(a868)),f332(x82602,f843(x82602,x82603,x82601))))+P24(f332(f332(f247(a868),f2(a868)),f332(f332(f9(x82601,a868),x82602),x82603))) % 165.28/165.05 [8261]~P24(f332(f62(x82611),x82613))+~P24(f332(f332(f247(a868),f2(a868)),f332(x82612,f423(x82612,x82613,x82611))))+P24(f332(f332(f247(a868),f2(a868)),f332(f332(f9(x82611,a868),x82612),x82613))) % 165.28/165.05 [8294]~P61(x82942)+E(x82941,f79(x82942))+E(f332(f332(f290(x82942),f332(f332(f22(x82942),f332(f332(f257(x82942),x82941),x82943)),f79(x82942))),f332(f332(f22(x82942),x82941),f79(x82942))),f332(f332(f6(a868,x82942),f332(f257(x82942),x82941)),f332(f302(a868,f2(a868)),x82943))) % 165.28/165.05 [8352]E(x83521,f2(a868))+~P24(f332(x83523,f332(f332(f39(a868),x83522),x83521)))+P24(f332(f332(f247(a868),x83522),f332(f332(f82(a868),x83521),f332(a115,f353(x83521,x83522,x83523))))) % 165.28/165.05 [8369]P24(f332(x83691,f2(a868)))+~P24(f332(x83691,f332(f332(f39(a868),x83692),x83693)))+P24(f332(f332(f247(a868),x83692),f332(f332(f82(a868),x83693),f332(a115,f353(x83693,x83692,x83691))))) % 165.28/165.05 [8408]E(x84081,f2(a868))+~P24(f332(x84083,f332(f332(f39(a868),x84082),x84081)))+P24(f332(f332(f246(a868),f332(f332(f82(a868),x84081),f353(x84081,x84082,x84083))),x84082)) % 165.28/165.05 [8441]P24(f332(x84411,f2(a868)))+~P24(f332(x84411,f332(f332(f39(a868),x84413),x84412)))+P24(f332(f332(f246(a868),f332(f332(f82(a868),x84412),f353(x84412,x84413,x84411))),x84413)) % 165.28/165.05 [8444]~P106(x84441)+E(f332(f332(f149(x84441,x84441,f5(x84441)),x84442),x84443),f150(x84441,x84441,f5(x84441),x84442,x84443))+P24(f332(f332(f334(x84441),x84442),f332(f174(x84441),x84443))) % 165.28/165.05 [8479]~E(f332(x84793,f692(x84792,x84793,x84791)),f332(x84793,f694(x84792,x84793,x84791)))+~P58(x84791,f332(x84793,f693(x84792,x84793,x84791)))+P58(x84791,f332(f332(f42(x84792,f875(x84791,f875(x84791,a862))),f255(f875(x84792,a862))),x84793)) % 165.28/165.05 [8487]E(x84871,f196(f875(f875(x84872,a862),a862)))+~P24(f332(f332(f246(f875(x84872,a862)),f679(x84873,x84871,x84872)),x84873))+P24(f332(f332(f246(f875(x84872,a862)),f41(f875(x84872,a862),x84871)),x84873)) % 165.28/165.05 [8545]~P63(x85451)+~P24(f332(f332(f247(x85451),x85452),x85453))+P24(f332(f332(f247(x85451),x85452),f332(f332(f290(x85451),f332(f332(f81(x85451),x85452),x85453)),f332(f332(f81(x85451),f79(x85451)),f79(x85451))))) % 165.28/165.05 [8598]~P24(f332(f332(x85981,f503(x85981,x85983,x85982)),f504(x85981,x85983,x85982)))+P24(f332(f332(x85981,x85982),x85983))+~P24(f332(f320(f874(a1,a1),a52),f332(f332(f267(a1,a1),x85982),x85983))) % 165.28/165.05 [8599]~P24(f332(f332(x85991,f505(x85991,x85993,x85992)),f507(x85991,x85993,x85992)))+P24(f332(f332(x85991,x85992),x85993))+~P24(f332(f320(f874(a1,a1),a57),f332(f332(f267(a1,a1),x85992),x85993))) % 165.28/165.05 [8600]~P24(f332(f332(x86001,f511(x86001,x86003,x86002)),f512(x86001,x86003,x86002)))+P24(f332(f332(x86001,x86002),x86003))+~P24(f332(f320(f874(a1,a1),a236),f332(f332(f267(a1,a1),x86002),x86003))) % 165.28/165.05 [8601]~P24(f332(f332(x86011,f513(x86011,x86013,x86012)),f514(x86011,x86013,x86012)))+P24(f332(f332(x86011,x86012),x86013))+~P24(f332(f320(f874(a868,a868),a231),f332(f332(f267(a868,a868),x86012),x86013))) % 165.28/165.05 [8602]~P24(f332(f332(x86021,f580(x86021,x86023,x86022)),f581(x86021,x86023,x86022)))+P24(f332(f332(x86021,x86022),x86023))+~P24(f332(f320(f874(a1,a1),a185),f332(f332(f267(a1,a1),x86022),x86023))) % 165.28/165.05 [8603]~P24(f332(f332(x86031,f802(x86031,x86033,x86032)),f803(x86031,x86033,x86032)))+P24(f332(f332(x86031,x86032),x86033))+~P24(f332(f320(f874(a1,a1),a134),f332(f332(f267(a1,a1),x86032),x86033))) % 165.28/165.05 [8854]P24(f332(f332(x88541,x88542),x88543))+P24(f332(f320(f874(a868,a868),a231),f332(f332(f267(a868,a868),f513(x88541,x88543,x88542)),f514(x88541,x88543,x88542))))+~P24(f332(f320(f874(a868,a868),a231),f332(f332(f267(a868,a868),x88542),x88543))) % 165.28/165.05 [8855]P24(f332(f332(x88551,x88552),x88553))+P24(f332(f320(f874(a1,a1),a52),f332(f332(f267(a1,a1),f503(x88551,x88553,x88552)),f504(x88551,x88553,x88552))))+~P24(f332(f320(f874(a1,a1),a52),f332(f332(f267(a1,a1),x88552),x88553))) % 165.28/165.05 [8856]P24(f332(f332(x88561,x88562),x88563))+P24(f332(f320(f874(a1,a1),a57),f332(f332(f267(a1,a1),f505(x88561,x88563,x88562)),f507(x88561,x88563,x88562))))+~P24(f332(f320(f874(a1,a1),a57),f332(f332(f267(a1,a1),x88562),x88563))) % 165.28/165.05 [8857]P24(f332(f332(x88571,x88572),x88573))+P24(f332(f320(f874(a1,a1),a236),f332(f332(f267(a1,a1),f511(x88571,x88573,x88572)),f512(x88571,x88573,x88572))))+~P24(f332(f320(f874(a1,a1),a236),f332(f332(f267(a1,a1),x88572),x88573))) % 165.28/165.05 [8858]P24(f332(f332(x88581,x88582),x88583))+P24(f332(f320(f874(a1,a1),a185),f332(f332(f267(a1,a1),f580(x88581,x88583,x88582)),f581(x88581,x88583,x88582))))+~P24(f332(f320(f874(a1,a1),a185),f332(f332(f267(a1,a1),x88582),x88583))) % 165.28/165.05 [8859]P24(f332(f332(x88591,x88592),x88593))+P24(f332(f320(f874(a1,a1),a134),f332(f332(f267(a1,a1),f802(x88591,x88593,x88592)),f803(x88591,x88593,x88592))))+~P24(f332(f320(f874(a1,a1),a134),f332(f332(f267(a1,a1),x88592),x88593))) % 165.28/165.05 [9186]~P24(f332(f62(x91861),x91863))+P24(f332(f332(f334(f874(f875(x91861,a862),f875(x91861,a862))),f332(f332(f267(f875(x91861,a862),f875(x91861,a862)),x91862),x91863)),f307(x91861)))+~P24(f332(f332(f247(f875(x91861,a862)),x91862),x91863)) % 165.28/165.05 [9194]~P23(a864,f196(f875(f867(a864),a862)),f332(f332(f310(f867(a864)),f332(f332(f332(f93(a864),x91941),x91942),x91943)),f196(f875(f867(a864),a862))))+P20(a864,f196(f875(f867(a864),a862)),f332(f332(f310(f867(a864)),f332(f332(f332(f93(a864),x91941),x91942),x91943)),f196(f875(f867(a864),a862))))+~P20(a864,f196(f875(f867(a864),a862)),f332(f332(f310(f867(a864)),f332(a94,x91942)),f196(f875(f867(a864),a862)))) % 165.28/165.05 [9253]~P58(x92531,f332(x92533,f693(x92532,x92533,x92531)))+P58(x92531,f332(f332(f42(x92532,f875(x92531,f875(x92531,a862))),f255(f875(x92532,a862))),x92533))+~E(f332(f332(f104(f875(x92531,a862)),f261(x92531,x92531,f332(x92533,f692(x92532,x92533,x92531)))),f262(x92531,x92531,f332(x92533,f694(x92532,x92533,x92531)))),f196(f875(x92531,a862))) % 165.28/165.05 [9442]P43(x94421,x94422,x94423)+P24(f332(f332(f334(f874(x94421,x94421)),f549(x94423,x94422,x94421)),x94423))+~P24(f332(f332(f334(f874(x94421,x94421)),f332(f332(f267(x94421,x94421),f548(x94423,x94422,x94421)),f548(x94423,x94422,x94421))),x94423)) % 165.28/165.05 [10025]P43(x100251,x100252,x100253)+~P24(f332(f332(f271(x100251,x100251,a862),f332(f332(f7(x100251,f875(x100251,a862),f875(x100251,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x100251,a862),f875(x100251,a862)),x100251),f8(a862,a862,x100251)),f332(f332(f8(a862,f875(a862,a862),x100251),a330),f332(f332(f7(x100251,f875(x100251,a862),a862),f334(x100251)),x100252)))),f332(f332(f7(x100251,f875(x100251,a862),a862),f334(x100251)),x100252))),f549(x100253,x100252,x100251)))+~P24(f332(f332(f334(f874(x100251,x100251)),f332(f332(f267(x100251,x100251),f548(x100253,x100252,x100251)),f548(x100253,x100252,x100251))),x100253)) % 165.28/165.05 [5642]~P28(x56422)+E(x56421,f2(x56422))+E(f332(f332(f39(x56422),f332(f332(f82(x56422),x56423),x56421)),x56421),x56423) % 165.28/165.05 [5643]~P28(x56432)+E(x56431,f2(x56432))+E(f332(f332(f39(x56432),f332(f332(f82(x56432),x56431),x56433)),x56431),x56433) % 165.28/165.05 [6440]~P74(x64401)+~E(f332(x64402,f2(a868)),f2(x64401))+E(f332(f332(f6(a868,x64401),x64402),f332(f302(a868,f332(a115,f2(a868))),x64403)),f332(f332(f6(a868,x64401),x64402),f332(f302(a868,f2(a868)),x64403))) % 165.28/165.05 [6569]~P28(x65692)+E(x65691,f2(x65692))+E(f332(f332(f39(x65692),f332(f332(f81(x65692),x65693),x65691)),x65691),f332(f332(f81(x65692),f332(f332(f39(x65692),x65693),x65691)),f79(x65692))) % 165.28/165.05 [6570]~P28(x65702)+E(x65701,f2(x65702))+E(f332(f332(f39(x65702),f332(f332(f81(x65702),x65701),x65703)),x65701),f332(f332(f81(x65702),f332(f332(f39(x65702),x65703),x65701)),f79(x65702))) % 165.28/165.05 [6788]~P24(f332(x67883,f2(a1)))+P24(f332(f332(f246(a868),x67881),x67882))+P24(f332(x67883,f332(f103(a1),f332(f332(f22(a868),x67882),x67881)))) % 165.28/165.05 [6893]P24(f332(f332(f247(a868),x68932),x68931))+P24(f332(f332(f246(a868),x68931),x68932))+P24(f332(x68933,f332(f103(a1),f332(f332(f22(a868),x68932),x68931)))) % 165.28/165.05 [6963]E(f332(f332(f81(a868),f332(f106(a868),x69631)),f332(f332(f81(a868),f332(f106(a868),x69632)),x69633)),f332(f332(f81(a868),f332(f106(a868),x69631)),x69633))+P24(f332(a201,f332(f106(a1),x69631)))+~P24(f332(a201,f332(f106(a1),x69632))) % 165.28/165.05 [7042]~E(x70422,f332(f332(f39(a868),x70423),x70421))+~P24(f332(f332(f247(a868),f2(a868)),x70421))+P24(f332(f332(f246(a868),f332(f332(f82(a868),x70421),x70422)),x70423)) % 165.28/165.05 [7156]~P24(f332(f62(x71561),x71563))+~P24(f332(f62(x71561),x71562))+P24(f332(f62(x71561),f332(f332(f113(f875(x71561,a862)),x71562),x71563))) % 165.28/165.05 [7448]~P106(x74481)+~P24(f332(f62(x74481),x74482))+E(f140(x74481,f332(f332(f22(f875(x74481,a862)),x74482),f332(f332(f310(x74481),x74483),f196(f875(x74481,a862))))),f172(x74481,x74483,f140(x74481,x74482))) % 165.28/165.05 [7514]P24(f332(x75141,f2(a1)))+~P24(f332(f332(f247(a868),x75142),x75143))+~P24(f332(x75141,f332(f103(a1),f332(f332(f22(a868),x75142),x75143)))) % 165.28/165.05 [7532]~P24(f332(f62(x75321),x75322))+E(f332(f38(x75321),f332(f332(f22(f875(x75321,a862)),x75322),f332(f332(f310(x75321),x75323),f196(f875(x75321,a862))))),f332(f38(x75321),x75322))+P24(f332(f332(f334(x75321),x75323),x75322)) % 165.28/165.05 [7662]~P112(x76621)+~P24(f332(f332(f247(x76621),f79(x76621)),x76622))+P24(f332(f332(f247(x76621),f79(x76621)),f332(f332(f82(x76621),x76622),f332(f332(f257(x76621),x76622),x76623)))) % 165.28/165.05 [7707]~P24(f332(f62(x77071),x77073))+E(f332(f332(f22(a868),f332(f38(x77071),x77072)),f332(f38(x77071),x77073)),f332(f38(x77071),f332(f332(f22(f875(x77071,a862)),x77072),x77073)))+~P24(f332(f332(f246(f875(x77071,a862)),x77073),x77072)) % 165.28/165.05 [7764]~P24(f332(f332(f246(a868),x77642),x77643))+~P24(f332(f332(f246(a868),x77641),f332(f332(f22(a868),x77643),x77642)))+P24(f332(f332(f246(a868),f332(f332(f81(a868),x77641),x77642)),x77643)) % 165.28/165.05 [7815]P24(f332(f62(x78151),x78152))+~P24(f332(f62(x78151),x78153))+~P24(f332(f62(x78151),f332(f332(f22(f875(x78151,a862)),x78152),x78153))) % 165.28/165.05 [7821]~P24(f332(f62(x78211),x78212))+E(f332(f38(x78211),f332(f332(f22(f875(x78211,a862)),x78212),f332(f332(f310(x78211),x78213),f196(f875(x78211,a862))))),f332(f332(f22(a868),f332(f38(x78211),x78212)),f79(a868)))+~P24(f332(f332(f334(x78211),x78213),x78212)) % 165.28/165.05 [7896]P58(x78961,x78962)+~P58(x78961,x78963)+~P24(f332(f332(f246(f875(x78961,f875(x78961,a862))),x78962),x78963)) % 165.28/165.05 [7937]~P24(f332(f332(f246(a868),x79373),x79372))+P24(f332(f332(f246(a868),x79371),f332(f332(f22(a868),x79372),x79373)))+~P24(f332(f332(f246(a868),f332(f332(f81(a868),x79371),x79373)),x79372)) % 165.28/165.05 [7955]P41(x79551,x79552)+~P41(x79551,x79553)+~P24(f332(f332(f246(f875(f874(x79551,x79551),a862)),x79552),x79553)) % 165.28/165.05 [7956]P56(x79561,x79562)+~P56(x79561,x79563)+~P24(f332(f332(f246(f875(f874(x79561,x79561),a862)),x79562),x79563)) % 165.28/165.05 [8191]~P112(x81911)+~P24(f332(f332(f247(x81911),f79(x81911)),x81912))+P24(f332(f332(f247(x81911),f332(f332(f257(x81911),x81912),x81913)),f332(f332(f82(x81911),x81912),f332(f332(f257(x81911),x81912),x81913)))) % 165.28/165.05 [8278]~P24(f332(x82781,f2(a1)))+~P24(f332(x82781,f332(f332(f22(a1),f332(f103(a1),x82782)),f332(f103(a1),x82783))))+P24(f332(x82781,f332(f103(a1),f332(f332(f22(a868),x82782),x82783)))) % 165.28/165.05 [8291]~P24(f332(f332(f246(a868),x82913),x82912))+P24(f332(x82911,f332(f332(f22(a1),f332(f103(a1),x82912)),f332(f103(a1),x82913))))+~P24(f332(x82911,f332(f103(a1),f332(f332(f22(a868),x82912),x82913)))) % 165.28/165.05 [8309]P24(f332(f332(f247(a868),x83091),x83092))+~P24(f332(x83093,f332(f332(f22(a1),f332(f103(a1),x83091)),f332(f103(a1),x83092))))+P24(f332(x83093,f332(f103(a1),f332(f332(f22(a868),x83091),x83092)))) % 165.28/165.05 [8363]~P122(x83632)+E(x83631,f2(x83632))+P24(f332(f332(f247(x83632),f2(x83632)),f332(f332(f81(x83632),f332(f332(f82(x83632),x83633),x83633)),f332(f332(f82(x83632),x83631),x83631)))) % 165.28/165.05 [8364]~P122(x83642)+E(x83641,f2(x83642))+P24(f332(f332(f247(x83642),f2(x83642)),f332(f332(f81(x83642),f332(f332(f82(x83642),x83641),x83641)),f332(f332(f82(x83642),x83643),x83643)))) % 165.28/165.05 [8462]~P24(f332(f332(f247(a868),f2(a868)),x84621))+~P24(f332(f332(f247(a1),x84622),x84623))+P24(f332(f332(f247(a1),f332(f332(f82(a1),f332(f103(a1),x84621)),x84622)),f332(f332(f82(a1),f332(f103(a1),x84621)),x84623))) % 165.28/165.05 [8515]E(f332(f332(f104(f875(x85151,a862)),x85152),f40(f875(x85151,a862),x85153)),f196(f875(x85151,a862)))+P24(f332(f332(f334(f875(x85151,a862)),x85152),x85153))+P24(f332(f332(f334(f875(x85151,a862)),f642(x85153,x85152,x85151)),f332(f332(f310(f875(x85151,a862)),x85152),x85153))) % 165.28/165.05 [8516]E(f332(f332(f104(f875(x85161,a862)),x85162),f40(f875(x85161,a862),x85163)),f196(f875(x85161,a862)))+P24(f332(f332(f334(f875(x85161,a862)),x85162),x85163))+P24(f332(f332(f334(f875(x85161,a862)),f641(x85163,x85162,x85161)),f332(f332(f310(f875(x85161,a862)),x85162),x85163))) % 165.28/165.05 [8544]E(x85441,x85442)+~E(f332(f197(f869(x85443)),x85441),f332(f197(f869(x85443)),x85442))+P24(f332(f332(f334(f874(x85443,x85443)),f545(x85443,x85441,x85442)),f332(f174(f874(x85443,x85443)),f332(f332(f184(x85443,x85443),x85442),x85441)))) % 165.28/165.05 [8774]E(f308(x87741,x87742),f308(x87741,x87743))+~P24(f332(f332(f246(f875(f874(x87741,x87741),a862)),x87743),f308(x87741,x87742)))+~P24(f332(f332(f246(f875(f874(x87741,x87741),a862)),x87742),x87743)) % 165.28/165.05 [8834]~P43(x88341,f255(f875(x88341,a862)),x88343)+P24(f332(f332(f246(f875(f874(f869(x88341),f869(x88341)),a862)),f158(x88341,x88342)),f159(x88341,x88343)))+~P24(f332(f332(f246(f875(f874(x88341,x88341),a862)),x88342),x88343)) % 165.28/165.05 [9030]P41(x90301,x90302)+~P24(f332(f332(f334(x90301),x90303),f738(x90302,x90301)))+P24(f332(f332(f334(f874(x90301,x90301)),f332(f332(f267(x90301,x90301),f773(x90302,x90301,x90303)),x90303)),x90302)) % 165.28/165.05 [9065]~P24(f332(f62(x90651),x90652))+P24(f332(f62(f875(x90651,a862)),f332(f332(f61(x90651),x90652),x90653)))+~P24(f332(f332(f246(f875(f874(x90651,x90651),a862)),x90653),f332(f332(f269(x90651,x90651),x90652),f332(f16(f875(x90651,a862),x90651),x90652)))) % 165.28/165.05 [9099]P43(x90991,x90992,x90993)+P24(f332(f332(f334(x90991),f561(x90993,x90992,x90991)),x90992))+~P24(f332(f332(f246(f875(f874(x90991,x90991),a862)),x90993),f332(f332(f269(x90991,x90991),x90992),f332(f16(f875(x90991,a862),x90991),x90992)))) % 165.28/165.05 [9100]P43(x91001,x91002,x91003)+P24(f332(f332(f334(x91001),f574(x91002,x91003,x91001)),x91002))+~P24(f332(f332(f246(f875(f874(x91001,x91001),a862)),x91003),f332(f332(f269(x91001,x91001),x91002),f332(f16(f875(x91001,a862),x91001),x91002)))) % 165.28/165.05 [9133]~P63(x91331)+~P24(f332(f332(f247(x91331),x91332),x91333))+P24(f332(f332(f247(x91331),f332(f332(f290(x91331),f332(f332(f81(x91331),x91332),x91333)),f332(f332(f81(x91331),f79(x91331)),f79(x91331)))),x91333)) % 165.28/165.05 [9162]~P62(x91621)+P24(f332(f332(f246(x91621),x91622),x91623))+~P24(f332(f332(f246(x91621),f332(f332(f82(x91621),f413(x91623,x91622,x91621)),x91622)),x91623)) % 165.28/165.05 [9288]E(f332(f197(f869(f869(x92881))),f332(f137(f869(x92881),f332(f332(f8(a868,a862,f869(x92881)),f332(f247(a868),x92882)),f197(f869(x92881)))),f182(x92881,x92883))),f332(f197(f869(x92881)),f332(f332(f166(f869(x92881)),x92883),x92882)))+~P32(a868,f332(f170(a868),f332(f332(f155(f869(x92881),a868),f197(f869(x92881))),x92883)))+~P24(f332(f332(f247(a868),x92882),f332(f197(f869(f869(x92881))),x92883))) % 165.28/165.05 [9392]~P41(x93921,x93922)+P22(x93921,f332(f332(f267(f875(f874(x93921,x93921),a862),f875(f874(x93921,x93921),a862)),x93922),x93923))+~P24(f332(f332(f246(f875(f874(x93921,x93921),a862)),f332(f332(f289(x93921,x93921,x93921),x93922),x93923)),x93922)) % 165.28/165.05 [9399]E(f332(f332(f155(f869(x93991),x93991),f332(f332(f7(f869(x93991),a868,x93991),f166(x93991)),x93992)),f332(f137(f869(x93991),f332(f332(f8(a868,a862,f869(x93991)),f332(f247(a868),x93992)),f197(f869(x93991)))),f182(x93991,x93993))),f332(f332(f166(f869(x93991)),x93993),x93992))+~P32(a868,f332(f170(a868),f332(f332(f155(f869(x93991),a868),f197(f869(x93991))),x93993)))+~P24(f332(f332(f247(a868),x93992),f332(f197(f869(f869(x93991))),x93993))) % 165.28/165.05 [9529]P43(x95291,x95292,x95293)+~P24(f332(f332(f334(f874(x95291,x95291)),f332(f332(f267(x95291,x95291),f561(x95293,x95292,x95291)),f561(x95293,x95292,x95291))),x95293))+~P24(f332(f332(f246(f875(f874(x95291,x95291),a862)),x95293),f332(f332(f269(x95291,x95291),x95292),f332(f16(f875(x95291,a862),x95291),x95292)))) % 165.28/165.05 [9530]P43(x95301,x95302,x95303)+~P24(f332(f332(f334(f874(x95301,x95301)),f332(f332(f267(x95301,x95301),f574(x95302,x95303,x95301)),f574(x95302,x95303,x95301))),x95303))+~P24(f332(f332(f246(f875(f874(x95301,x95301),a862)),x95303),f332(f332(f269(x95301,x95301),x95302),f332(f16(f875(x95301,a862),x95301),x95302)))) % 165.28/165.05 [9705]~P138(x97051)+~P120(x97051)+E(f332(f332(f290(x97051),f332(f105(x97051),f332(f332(f74(f874(a1,a1),a1,x97052,f266(a1,a1)),f224(x97052)),x97053))),f332(f105(x97051),f332(f332(f74(f874(a1,a1),a1,x97052,f270(a1,a1)),f224(x97052)),x97053))),f237(x97052,x97051,x97053)) % 165.28/165.05 [9906]~E(x99063,f2(a868))+~E(f332(f197(f869(x99061)),f332(f332(f166(f869(x99061)),x99062),f620(x99063,x99061,x99062))),x99063)+E(f332(f332(f155(a868,f869(x99061)),f332(f332(f7(a868,f869(a868),f869(x99061)),f332(f332(f8(f875(a868,x99061),f875(f869(a868),f869(x99061)),a868),f155(a868,x99061)),f332(f7(a868,a868,x99061),f332(f332(f8(f869(x99061),f875(a868,x99061),a868),f166(x99061)),f332(f166(f869(x99061)),x99062))))),f140(a868,f332(f302(a868,f2(a868)),f332(f197(f869(f869(x99061))),x99062))))),f140(a868,f332(f302(a868,f2(a868)),x99063))),f182(x99061,x99062)) % 165.28/165.05 [9907]E(x99071,f116(f869(x99072)))+~E(f332(f197(f869(x99072)),f332(f332(f166(f869(x99072)),x99071),f620(x99073,x99072,x99071))),x99073)+E(f332(f332(f155(a868,f869(x99072)),f332(f332(f7(a868,f869(a868),f869(x99072)),f332(f332(f8(f875(a868,x99072),f875(f869(a868),f869(x99072)),a868),f155(a868,x99072)),f332(f7(a868,a868,x99072),f332(f332(f8(f869(x99072),f875(a868,x99072),a868),f166(x99072)),f332(f166(f869(x99072)),x99071))))),f140(a868,f332(f302(a868,f2(a868)),f332(f197(f869(f869(x99072))),x99071))))),f140(a868,f332(f302(a868,f2(a868)),x99073))),f182(x99072,x99071)) % 165.28/165.05 [9908]~E(x99083,f2(a868))+E(f332(f332(f155(a868,f869(x99081)),f332(f332(f7(a868,f869(a868),f869(x99081)),f332(f332(f8(f875(a868,x99081),f875(f869(a868),f869(x99081)),a868),f155(a868,x99081)),f332(f7(a868,a868,x99081),f332(f332(f8(f869(x99081),f875(a868,x99081),a868),f166(x99081)),f332(f166(f869(x99081)),x99082))))),f140(a868,f332(f302(a868,f2(a868)),f332(f197(f869(f869(x99081))),x99082))))),f140(a868,f332(f302(a868,f2(a868)),x99083))),f182(x99081,x99082))+P24(f332(f332(f247(a868),f620(x99083,x99081,x99082)),f332(f197(f869(f869(x99081))),x99082))) % 165.28/165.05 [9909]E(x99091,f116(f869(x99092)))+E(f332(f332(f155(a868,f869(x99092)),f332(f332(f7(a868,f869(a868),f869(x99092)),f332(f332(f8(f875(a868,x99092),f875(f869(a868),f869(x99092)),a868),f155(a868,x99092)),f332(f7(a868,a868,x99092),f332(f332(f8(f869(x99092),f875(a868,x99092),a868),f166(x99092)),f332(f166(f869(x99092)),x99091))))),f140(a868,f332(f302(a868,f2(a868)),f332(f197(f869(f869(x99092))),x99091))))),f140(a868,f332(f302(a868,f2(a868)),x99093))),f182(x99092,x99091))+P24(f332(f332(f247(a868),f620(x99093,x99092,x99091)),f332(f197(f869(f869(x99092))),x99091))) % 165.28/165.05 [7704]E(f332(f332(f81(a868),f332(f106(a868),x77041)),f332(f332(f81(a868),f332(f106(a868),x77042)),x77043)),f332(f332(f81(a868),f332(f106(a868),f332(f332(f81(a1),x77041),x77042))),x77043))+P24(f332(a201,f332(f106(a1),x77041)))+P24(f332(a201,f332(f106(a1),x77042))) % 165.28/165.05 [8453]~P24(f332(f62(x84531),x84532))+~P24(f332(f332(f334(x84531),x84533),x84532))+E(f332(a115,f332(f38(x84531),f332(f332(f22(f875(x84531,a862)),x84532),f332(f332(f310(x84531),x84533),f196(f875(x84531,a862)))))),f332(f38(x84531),x84532)) % 165.28/165.05 [8469]~P24(f332(f62(x84691),x84692))+~P24(f332(f332(f334(x84691),x84693),x84692))+E(f332(f332(f81(a868),f79(a868)),f332(f38(x84691),f332(f332(f22(f875(x84691,a862)),x84692),f332(f332(f310(x84691),x84693),f196(f875(x84691,a862)))))),f332(f38(x84691),x84692)) % 165.28/165.05 [8553]~P106(x85531)+~P24(f332(f62(x85531),x85533))+E(f332(f332(f149(x85531,x85531,f5(x85531)),x85532),f140(x85531,f332(f332(f22(f875(x85531,a862)),x85533),f332(f332(f310(x85531),x85532),f196(f875(x85531,a862)))))),f140(x85531,f332(f332(f310(x85531),x85532),x85533))) % 165.28/165.05 [8704]~P24(f332(f62(x87041),x87043))+~P24(f332(f62(x87041),x87042))+E(f332(f332(f81(a868),f332(f38(x87041),f332(f332(f113(f875(x87041,a862)),x87042),x87043))),f332(f38(x87041),f332(f332(f104(f875(x87041,a862)),x87042),x87043))),f332(f332(f81(a868),f332(f38(x87041),x87042)),f332(f38(x87041),x87043))) % 165.28/165.05 [9854]~P21(x98541,f875(f875(x98541,a862),a862),f332(f332(f7(x98541,f875(f874(x98541,x98541),a862),f875(f875(x98541,a862),a862)),f332(f332(f8(f875(x98541,a862),f875(f875(f874(x98541,x98541),a862),f875(f875(x98541,a862),a862)),x98541),f61(x98541)),f332(f332(f7(x98541,f875(x98541,a862),f875(x98541,a862)),f310(x98541)),f196(f875(x98541,a862))))),x98543),x98542)+~P24(f332(f62(x98541),x98542))+E(f332(f38(f875(x98541,a862)),f332(f332(f61(x98541),x98542),x98543)),f332(f38(x98541),x98542)) % 165.28/165.05 [7969]~P92(x79691)+P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x79693)))+E(f332(f332(f257(x79691),x79692),f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),x79693),x79693)),a100))),f79(x79691)) % 165.28/165.05 [9376]~P92(x93761)+~P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x93763)))+E(f332(f332(f257(x93761),x93762),f332(f106(a868),f332(f332(f22(a1),f332(f332(f81(a1),x93763),x93763)),a100))),f332(f332(f87(x93761,x93761),f332(f332(f257(x93761),x93762),f332(f106(a868),x93763))),f332(f332(f18(x93761,x93761,x93761),f332(f332(f8(x93761,f875(x93761,x93761),x93761),f82(x93761)),f332(f82(x93761),x93762))),f5(x93761)))) % 165.28/165.05 [9765]~P24(f332(f138(x97651),x97653))+~P24(f332(f332(f334(x97651),x97652),f332(f174(x97651),x97653)))+E(f332(f332(f139(x97651),f332(f197(f869(x97651)),f179(x97651,f332(f332(f8(a862,a862,x97651),a327),f332(f332(f7(x97651,x97651,a862),a329),x97652)),f332(f170(x97651),x97653)))),f332(f170(x97651),x97653)),f332(f332(f152(x97651),x97652),f332(f170(x97651),f179(x97651,f332(f332(f8(a862,a862,x97651),a327),f332(f332(f7(x97651,x97651,a862),a329),x97652)),x97653)))) % 165.28/165.05 [9835]P24(f332(f332(f246(f875(f874(x98351,x98351),a862)),f308(x98351,x98352)),x98353))+~P24(f332(f332(f246(f875(f874(x98351,x98351),a862)),f308(x98351,f196(f875(f874(x98351,x98351),a862)))),x98353))+~P24(f332(f332(f246(f875(f874(x98351,x98351),a862)),f332(f332(f289(x98351,x98351,x98351),f332(f332(f104(f875(f874(x98351,x98351),a862)),f308(x98351,x98352)),x98353)),x98352)),x98353)) % 165.28/165.05 [9676]~P24(f332(f62(x96761),f332(f252(x96761),x96763)))+~P24(f332(f62(x96761),f332(f252(x96761),x96762)))+P24(f332(f62(x96761),f332(f252(x96761),f332(f332(f18(x96761,a862,a862),f332(f332(f8(a862,f875(a862,a862),x96761),a331),x96762)),x96763)))) % 165.28/165.05 [9969]P24(f332(f332(f246(f875(f874(x99691,x99691),a862)),f332(f332(f289(x99691,x99691,x99691),x99692),f308(x99691,x99692))),x99693))+~P24(f332(f332(f246(f875(f874(x99691,x99691),a862)),x99692),x99693))+~P24(f332(f332(f246(f875(f874(x99691,x99691),a862)),f332(f332(f289(x99691,x99691,x99691),f332(f332(f104(f875(f874(x99691,x99691),a862)),f332(f332(f289(x99691,x99691,x99691),x99692),f308(x99691,x99692))),x99693)),x99692)),x99693)) % 165.28/165.05 [9922]~P118(x99222)+E(x99221,f2(x99222))+~E(f332(f332(f81(x99222),f332(f332(f257(x99222),x99223),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x99222),x99221),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f2(x99222)) % 165.28/165.05 [9923]~P118(x99232)+E(x99231,f2(x99232))+~E(f332(f332(f81(x99232),f332(f332(f257(x99232),x99231),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x99232),x99233),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f2(x99232)) % 165.28/165.05 [9928]~P24(f332(f138(x99281),x99283))+~P24(f332(f332(f334(x99281),x99282),f332(f174(x99281),x99283)))+E(f332(f170(x99281),f332(f173(x99281),f332(f332(f139(x99281),f332(f197(f869(x99281)),f179(x99281,f332(f332(f8(a862,a862,x99281),a327),f332(f332(f7(x99281,x99281,a862),a329),x99282)),x99283))),x99283))),f179(x99281,f332(f332(f8(a862,a862,x99281),a327),f332(f332(f7(x99281,x99281,a862),a329),x99282)),f332(f170(x99281),x99283))) % 165.28/165.05 [10013]~P118(x100132)+E(x100131,f2(x100132))+P24(f332(f332(f247(x100132),f2(x100132)),f332(f332(f81(x100132),f332(f332(f257(x100132),x100133),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x100132),x100131),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))))) % 165.28/165.05 [10014]~P118(x100142)+E(x100141,f2(x100142))+P24(f332(f332(f247(x100142),f2(x100142)),f332(f332(f81(x100142),f332(f332(f257(x100142),x100141),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x100142),x100143),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))))) % 165.28/165.05 [10055]~P118(x100551)+P24(f332(f332(f246(x100551),f2(x100551)),x100552))+~P24(f332(f332(f246(x100551),f2(x100551)),f332(f332(f257(x100551),x100552),f332(a115,f332(f332(f82(a868),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),x100553))))) % 165.28/165.05 [5482]~P20(x54821,x54824,x54823)+P20(x54821,x54822,x54823)+~P20(x54821,x54822,x54824) % 165.28/165.05 [4939]~E(x49392,f91(x49393,x49391))+P24(f332(x49391,x49392))+~P24(f332(x49391,x49394)) % 165.28/165.05 [6699]~P41(x66992,x66994)+~P41(x66991,x66993)+P41(f874(x66991,x66992),f324(x66991,x66992,x66993,x66994)) % 165.28/165.05 [5121]~P5(x51214,x51211)+~E(f332(x51211,x51212),f332(x51211,x51213))+P24(f332(f332(x51211,x51212),x51213)) % 165.28/165.05 [5297]~P5(x52974,x52971)+E(f332(x52971,x52972),f332(x52971,x52973))+~P24(f332(f332(x52971,x52972),x52973)) % 165.28/165.05 [5389]~P14(x53893,x53894,x53891)+E(f332(x53891,x53892),f332(f64(x53893,x53894),x53892))+~P24(f332(f62(x53893),x53892)) % 165.28/165.05 [5390]~P2(x53903,x53904,x53901)+E(f332(x53901,x53902),f332(f64(x53903,x53904),x53902))+~P24(f332(f62(x53903),x53902)) % 165.28/165.05 [5515]~P5(x55154,x55151)+~P24(f332(f332(x55151,x55153),x55152))+P24(f332(f332(x55151,x55152),x55153)) % 165.28/165.05 [5585]E(x55851,x55852)+~E(f332(f266(x55853,x55854),x55851),f332(f266(x55853,x55854),x55852))+~E(f332(f270(x55853,x55854),x55851),f332(f270(x55853,x55854),x55852)) % 165.28/165.05 [5610]E(x56101,x56102)+~P24(f332(f48(x56103,x56104),x56102))+~P24(f332(f48(x56103,x56104),x56101)) % 165.28/165.05 [5802]~P74(x58022)+E(f238(x58021,x58022,x58023,x58024),f2(x58022))+P24(f332(f62(x58021),x58024)) % 165.28/165.05 [5938]~P24(f332(f320(x59381,x59382),x59384))+P24(f332(f320(x59381,x59382),x59383))+~P24(f332(f332(x59382,x59383),x59384)) % 165.28/165.05 [7810]E(x78101,f2(a868))+~P24(f332(x78102,x78103))+P24(f332(x78102,f798(x78102,x78103,x78101,x78104))) % 165.28/165.05 [7891]~P106(x78912)+~P24(f332(f138(x78911),x78914))+P24(f332(f138(x78911),f151(x78911,x78912,x78913,x78914))) % 165.28/165.05 [8110]~P24(f332(f62(x81102),x81104))+~P24(f332(f62(x81101),x81103))+P24(f332(f62(f876(x81101,x81102)),f319(x81101,x81102,x81103,x81104))) % 165.28/165.05 [8111]~P24(f332(f138(x81112),x81114))+~P24(f332(f138(x81111),x81113))+P24(f332(f138(f874(x81111,x81112)),f60(x81111,x81112,x81113,x81114))) % 165.28/165.05 [8115]P24(f332(f332(f334(f869(x81151)),f332(f332(f135(x81151),x81152),x81153)),f162(x81151,x81154)))+~P24(f332(f332(f334(f869(x81151)),x81153),f162(x81151,x81154)))+~P24(f332(f332(f334(f869(x81151)),x81152),f162(x81151,x81154))) % 165.28/165.05 [8393]E(x83931,f2(a868))+P24(f332(x83932,x83933))+~P24(f332(x83932,f799(x83932,x83933,x83931,x83934))) % 165.28/165.05 [8432]~P106(x84323)+~P24(f332(f138(x84321),f151(x84321,x84323,x84324,x84322)))+P24(f332(f138(x84321),x84322)) % 165.28/165.05 [8695]~P24(f332(f332(f334(f874(x86951,x86951)),f332(f332(f267(x86951,x86951),x86952),x86954)),f308(x86951,x86953)))+P24(f332(f332(f334(x86951),x86952),f321(x86951,x86953)))+~P24(f332(f332(f334(x86951),x86954),f321(x86951,x86953))) % 165.28/165.05 [5105]~P74(x51052)+E(f332(f332(f6(x51051,x51052),x51053),x51054),f2(x51052))+P24(f332(f62(x51051),x51054)) % 165.28/165.05 [5108]~P73(x51082)+E(f332(f332(f9(x51081,x51082),x51083),x51084),f79(x51082))+P24(f332(f62(x51081),x51084)) % 165.28/165.05 [5260]~P68(x52603)+E(x52601,x52602)+~E(f332(f332(f81(x52603),x52604),x52601),f332(f332(f81(x52603),x52604),x52602)) % 165.28/165.05 [5261]~P69(x52613)+E(x52611,x52612)+~E(f332(f332(f81(x52613),x52614),x52611),f332(f332(f81(x52613),x52614),x52612)) % 165.28/165.05 [5263]~P68(x52633)+E(x52631,x52632)+~E(f332(f332(f81(x52633),x52631),x52634),f332(f332(f81(x52633),x52632),x52634)) % 165.28/165.05 [5385]~P30(x53853)+E(x53851,f196(f875(x53852,a862)))+E(f332(f332(f42(x53852,x53853),x53851),f332(f16(x53853,x53852),x53854)),x53854) % 165.28/165.05 [5386]~P30(x53863)+E(x53861,f196(f875(x53862,a862)))+E(f332(f332(f43(x53862,x53863),x53861),f332(f16(x53863,x53862),x53864)),x53864) % 165.28/165.05 [5598]~P107(x55983)+E(x55981,x55982)+~E(f303(x55983,x55984,x55981),f332(f332(f310(x55983),x55982),f196(f875(x55983,a862)))) % 165.28/165.05 [5599]~P107(x55993)+E(x55991,x55992)+~E(f303(x55993,x55991,x55992),f332(f332(f310(x55993),x55994),f196(f875(x55993,a862)))) % 165.28/165.05 [5659]~P39(x56593,x56591,x56594)+P39(x56593,x56591,f332(f332(f152(x56593),x56592),x56594))+P24(f332(x56591,x56592)) % 165.28/165.05 [5762]~P35(x57621,x57622,x57624)+~P24(f332(x57622,x57623))+P35(x57621,x57622,f332(f332(f152(x57621),x57623),x57624)) % 165.28/165.05 [5895]P24(f332(x58951,x58952))+~P24(f332(f260(x58953,x58951),x58954))+~P24(f332(f332(f334(x58953),x58952),x58954)) % 165.28/165.05 [5904]~P35(x59041,x59042,x59044)+~P35(x59041,x59042,x59043)+P35(x59041,x59042,f332(f332(f135(x59041),x59043),x59044)) % 165.28/165.05 [5914]P37(x59141,x59142,x59143)+~P37(x59141,x59142,f332(f332(f152(x59141),x59144),x59143))+P24(f332(x59142,x59144)) % 165.28/165.05 [5915]P39(x59151,x59152,x59153)+~P39(x59151,x59152,f332(f332(f152(x59151),x59154),x59153))+P24(f332(x59152,x59154)) % 165.28/165.05 [5993]P37(x59931,x59932,x59933)+P37(x59931,x59932,x59934)+~P37(x59931,x59932,f332(f332(f135(x59931),x59934),x59933)) % 165.28/165.05 [6012]~P74(x60121)+E(f332(f332(f6(a868,x60121),x60122),f332(f302(a868,x60123),f332(a115,x60124))),f2(x60121))+~P24(f332(f332(f247(a868),x60124),x60123)) % 165.28/165.05 [6017]~P29(x60171)+~E(f45(x60171,x60172,x60173),f45(x60171,x60174,x60173))+E(f45(x60171,f332(f80(x60171),x60172),x60173),f45(x60171,f332(f80(x60171),x60174),x60173)) % 165.28/165.05 [6085]P24(f332(x60851,x60852))+~E(f332(f137(x60853,x60851),x60854),x60854)+~P24(f332(f332(f334(x60853),x60852),f332(f174(x60853),x60854))) % 165.28/165.05 [6104]~E(f332(f332(f81(a868),x61043),x61042),f332(f332(f81(a868),x61041),x61044))+~P24(f332(f332(f247(a868),x61043),x61044))+P24(f332(f332(f247(a868),x61041),x61042)) % 165.28/165.05 [6108]P37(x61081,x61082,x61083)+~P24(f332(x61082,x61084))+~P24(f332(f332(f334(x61081),x61084),f332(f174(x61081),x61083))) % 165.28/165.05 [6146]~P35(x61463,x61461,x61464)+P24(f332(x61461,x61462))+~P24(f332(f332(f334(x61463),x61462),f332(f174(x61463),x61464))) % 165.28/165.05 [6148]~E(f332(f137(x61481,x61482),x61483),f116(x61481))+~P24(f332(x61482,x61484))+~P24(f332(f332(f334(x61481),x61484),f332(f174(x61481),x61483))) % 165.28/165.05 [6149]~E(f179(x61493,x61491,x61494),x61494)+P24(f332(x61491,x61492))+~P24(f332(f332(f334(x61493),x61492),f332(f174(x61493),x61494))) % 165.28/165.05 [6184]~E(x61844,f196(f875(x61842,a862)))+~E(x61843,f196(f875(x61841,a862)))+E(f319(x61841,x61842,x61843,x61844),f196(f875(f876(x61841,x61842),a862))) % 165.28/165.05 [6328]P24(f332(x63281,x63282))+~P24(f332(f161(x63283,x63281),x63284))+~P24(f332(f332(f334(x63283),x63282),f332(f174(x63283),x63284))) % 165.28/165.05 [6598]~P74(x65981)+E(f332(f332(f6(a868,x65981),x65982),f303(a868,x65983,f332(a115,x65984))),f2(x65981))+~P24(f332(f332(f247(a868),f332(a115,x65984)),x65983)) % 165.28/165.05 [6738]~P106(x67381)+E(f332(f332(f22(f875(x67381,a862)),f332(f302(x67381,x67382),x67383)),f332(f302(x67381,x67382),x67384)),f332(f302(x67381,x67384),x67383))+~P24(f332(f332(f246(x67381),x67382),x67384)) % 165.28/165.05 [6810]~E(x68103,x68104)+E(x68101,f2(a868))+P24(f332(f332(f334(x68102),x68103),f332(f174(x68102),f171(x68102,x68101,x68104)))) % 165.28/165.05 [7088]~P24(f332(f332(f334(f869(x70881)),x70884),f162(x70881,x70883)))+P24(f332(f332(f334(x70881),x70882),x70883))+~P24(f332(f332(f334(x70881),x70882),f332(f174(x70881),x70884))) % 165.28/165.05 [7095]~P41(x70951,x70952)+P24(f332(f332(f334(x70951),f739(x70952,x70951,x70953)),x70953))+~P24(f332(f332(f334(x70951),x70954),x70953)) % 165.28/165.05 [7151]~P74(x71511)+E(f332(f332(f332(f66(x71511,x71512,f81(x71511)),x71513),f2(x71511)),x71514),f332(f332(f6(x71512,x71511),x71513),x71514))+~P24(f332(f62(x71512),x71514)) % 165.28/165.05 [7153]~P73(x71531)+E(f332(f332(f332(f66(x71531,x71532,f82(x71531)),x71533),f79(x71531)),x71534),f332(f332(f9(x71532,x71531),x71533),x71534))+~P24(f332(f62(x71532),x71534)) % 165.28/165.05 [7181]P21(x71811,x71812,x71813,x71814)+~E(f332(f38(x71812),f332(f311(x71811,x71812,x71813),x71814)),f332(f38(x71811),x71814))+~P24(f332(f62(x71811),x71814)) % 165.28/165.05 [7364]~P74(x73641)+E(f332(f332(f81(x73641),f332(x73642,x73643)),f332(f332(f6(a868,x73641),x73642),f305(a868,x73643,x73644))),f332(f332(f6(a868,x73641),x73642),f303(a868,x73643,x73644)))+~P24(f332(f332(f246(a868),x73643),x73644)) % 165.28/165.05 [7374]~P74(x73741)+~P21(x73742,x73741,x73743,x73744)+E(f332(f332(f6(x73741,x73741),f35(x73741)),f332(f311(x73742,x73741,x73743),x73744)),f332(f332(f6(x73742,x73741),x73743),x73744)) % 165.28/165.05 [7375]~P73(x73751)+~P21(x73752,x73751,x73753,x73754)+E(f332(f332(f9(x73751,x73751),f35(x73751)),f332(f311(x73752,x73751,x73753),x73754)),f332(f332(f9(x73752,x73751),x73753),x73754)) % 165.28/165.05 [7429]E(f332(f38(f876(x74291,x74292)),f319(x74291,x74292,x74293,x74294)),f332(f332(f81(a868),f332(f38(x74291),x74293)),f332(f38(x74292),x74294)))+~P24(f332(f62(x74292),x74294))+~P24(f332(f62(x74291),x74293)) % 165.28/165.05 [7515]E(x75151,x75152)+P24(f332(f332(f334(x75153),x75151),f332(f174(x75153),f172(x75153,x75152,x75154))))+~P24(f332(f332(f334(x75153),x75151),f332(f174(x75153),x75154))) % 165.28/165.05 [7741]~P74(x77411)+E(f332(f332(f81(x77411),f332(f332(f6(a868,x77411),x77412),f332(f302(a868,x77413),x77414))),f332(x77412,x77414)),f332(f332(f6(a868,x77411),x77412),f332(f302(a868,x77413),f332(a115,x77414))))+P24(f332(f332(f247(a868),x77414),x77413)) % 165.28/165.05 [7792]~P21(x77921,x77922,x77923,f255(f875(x77921,a862)))+~P24(f332(f62(x77922),x77924))+P24(f332(f62(x77921),f332(f312(x77921,x77922,x77923),x77924))) % 165.28/165.05 [7904]P24(f332(f332(f334(f869(x79041)),f332(f332(f152(x79041),x79042),x79043)),f162(x79041,x79044)))+~P24(f332(f332(f334(f869(x79041)),x79043),f162(x79041,x79044)))+~P24(f332(f332(f334(x79041),x79042),x79044)) % 165.28/165.05 [7993]~E(f332(f311(x79933,x79931,x79934),f255(f875(x79933,a862))),f255(f875(x79931,a862)))+P24(f332(f62(x79931),x79932))+~P24(f332(f62(x79933),f332(f312(x79933,x79931,x79934),x79932))) % 165.28/165.05 [8083]~P21(x80831,x80833,x80834,x80832)+P24(f332(f62(x80831),x80832))+~P24(f332(f62(x80833),f332(f311(x80831,x80833,x80834),x80832))) % 165.28/165.05 [8104]~E(x81042,x81043)+P24(f332(f332(f334(f874(x81041,x81041)),f332(f332(f267(x81041,x81041),x81042),x81043)),f264(x81041,x81044)))+~P24(f332(f332(f334(x81041),x81042),x81044)) % 165.28/165.05 [8141]~P74(x81411)+E(f332(f332(f81(x81411),f332(f332(f6(a868,x81411),x81412),f303(a868,x81413,x81414))),f332(x81412,f332(a115,x81414))),f332(f332(f6(a868,x81411),x81412),f303(a868,x81413,f332(a115,x81414))))+P24(f332(f332(f247(a868),f332(a115,x81414)),x81413)) % 165.28/165.05 [8205]P24(f332(x82051,x82052))+~P24(f332(x82051,f332(f332(f166(x82053),x82054),f531(x82051,x82054,x82053))))+~P24(f332(f332(f334(x82053),x82052),f332(f174(x82053),x82054))) % 165.28/165.05 [8342]~P24(f332(f332(f334(x83421),x83422),f321(x83421,x83424)))+P24(f332(f332(f334(f869(x83421)),f332(f332(f152(x83421),x83422),x83423)),f321(f869(x83421),f158(x83421,x83424))))+~P24(f332(f332(f334(f869(x83421)),x83423),f321(f869(x83421),f158(x83421,x83424)))) % 165.28/165.05 [8355]~P21(x83552,x83553,x83554,f676(x83554,x83553,x83552,x83551))+P21(x83552,x83553,x83554,f41(f875(x83552,a862),x83551))+E(x83551,f196(f875(f875(x83552,a862),a862))) % 165.28/165.05 [8613]E(x86131,x86132)+~P24(f332(f332(f334(f874(x86133,x86133)),f332(f332(f267(x86133,x86133),x86131),x86132)),f308(x86133,x86134)))+P24(f332(f332(f334(x86133),x86131),f332(f265(x86133,x86133),x86134))) % 165.28/165.05 [8876]E(x88761,f2(a868))+P24(f332(x88762,x88763))+P24(f332(f332(f334(x88764),f799(x88762,x88763,x88761,x88764)),f332(f174(x88764),f171(x88764,x88761,x88763)))) % 165.28/165.05 [8886]E(x88861,f2(a868))+~P24(f332(x88863,x88864))+P24(f332(f332(f334(x88862),f798(x88863,x88864,x88861,x88862)),f332(f174(x88862),f171(x88862,x88861,x88864)))) % 165.28/165.05 [8891]P21(x88912,x88913,x88914,f41(f875(x88912,a862),x88911))+E(x88911,f196(f875(f875(x88912,a862),a862)))+P24(f332(f332(f334(f875(x88912,a862)),f676(x88914,x88913,x88912,x88911)),x88911)) % 165.28/165.05 [9021]P24(f332(f62(x90211),x90212))+~P24(f332(f62(x90214),f332(f311(x90211,x90214,x90213),x90212)))+P24(f332(f332(f334(x90211),f466(x90213,x90214,x90212,x90211)),x90212)) % 165.28/165.05 [9111]~P30(x91112)+E(f332(f332(f65(x91111,x91112,f332(f332(f8(x91112,f875(x91112,x91112),x91111),f113(x91112)),x91113)),f196(x91112)),x91114),f332(f332(f42(x91111,x91112),x91114),x91113))+~P24(f332(f62(x91111),x91114)) % 165.28/165.05 [9112]~P30(x91122)+E(f332(f332(f65(x91121,x91122,f332(f332(f8(x91122,f875(x91122,x91122),x91121),f104(x91122)),x91123)),f255(x91122)),x91124),f332(f332(f43(x91121,x91122),x91124),x91123))+~P24(f332(f62(x91121),x91124)) % 165.28/165.05 [9189]P24(f332(x91891,x91892))+~P24(f332(x91891,f332(f332(f166(x91893),x91894),f538(x91892,x91891,x91894,x91893))))+~P24(f332(f332(f334(x91893),x91892),f332(f174(x91893),x91894))) % 165.28/165.05 [9210]E(x92101,x92102)+~P24(f332(f332(f334(f874(x92103,x92103)),f332(f332(f267(x92103,x92103),x92101),x92102)),f308(x92103,x92104)))+P24(f332(f332(f334(f874(x92103,x92103)),f332(f332(f267(x92103,x92103),x92101),x92102)),f332(f332(f289(x92103,x92103,x92103),x92104),f308(x92103,x92104)))) % 165.28/165.05 [9254]~E(f332(f197(f869(x92541)),x92542),f332(f197(f869(x92541)),x92543))+~P24(f332(f332(f334(f874(f869(x92541),f869(x92541))),f332(f332(f267(f869(x92541),f869(x92541)),x92542),x92543)),f148(x92541,x92544)))+P24(f332(f332(f334(f874(f869(x92541),f869(x92541))),f332(f332(f267(f869(x92541),f869(x92541)),x92542),x92543)),f146(x92541,x92544))) % 165.28/165.05 [9476]P35(x94761,f332(f332(f18(x94761,a862,a862),f332(f332(f8(a862,f875(a862,a862),x94761),a331),f332(f332(f8(a862,a862,x94761),a327),x94762))),f332(a329,x94763)),x94764)+~P24(f332(x94762,x94763))+~P39(x94761,x94762,f332(f332(f152(x94761),x94763),x94764)) % 165.28/165.05 [9638]~P35(x96381,f332(f332(f18(x96381,a862,a862),f332(f332(f8(a862,f875(a862,a862),x96381),a331),f332(f332(f8(a862,a862,x96381),a327),x96382))),f332(a329,x96383)),x96384)+~P24(f332(x96382,x96383))+P39(x96381,x96382,f332(f332(f152(x96381),x96383),x96384)) % 165.28/165.05 [9642]~P39(x96421,x96422,x96424)+~P35(x96421,f332(f332(f18(x96421,a862,a862),f332(f332(f8(a862,f875(a862,a862),x96421),a331),f332(f332(f8(a862,a862,x96421),a327),x96422))),f332(a329,x96423)),x96424)+P39(x96421,x96422,f332(f332(f152(x96421),x96423),x96424)) % 165.28/165.05 [9679]~P66(x96791)+E(f332(f332(f6(a868,x96791),f332(f332(f18(a868,x96791,x96791),f332(f332(f8(x96791,f875(x96791,x96791),a868),f22(x96791)),x96792)),f332(f332(f8(a868,x96791,a868),x96792),f332(f332(f7(a868,a868,a868),f81(a868)),f79(a868))))),f303(a868,x96793,x96794)),f2(x96791))+P24(f332(f332(f246(a868),x96793),x96794)) % 165.28/165.05 [9921]~P41(x99212,x99214)+~P21(x99212,x99211,x99213,f255(f875(x99212,a862)))+P41(x99211,f332(f311(f874(x99212,x99212),f874(x99211,x99211),f272(x99212,x99211,x99212,x99211,x99213,x99213)),x99214)) % 165.28/165.05 [10081]~E(f332(f197(f869(x100811)),x100813),f332(f197(f869(x100811)),x100812))+P24(f332(f332(f334(f874(f869(x100811),f869(x100811))),f332(f332(f267(f869(x100811),f869(x100811)),x100812),x100813)),f159(x100811,x100814)))+~P24(f332(f332(f271(x100811,x100811,a862),f332(f332(f7(x100811,f875(f874(x100811,x100811),a862),f875(x100811,a862)),f332(f332(f8(f875(x100811,f875(f875(f874(x100811,x100811),a862),a862)),f875(f875(f874(x100811,x100811),a862),f875(x100811,a862)),x100811),f7(x100811,f875(f874(x100811,x100811),a862),a862)),f332(f332(f8(f875(x100811,f874(x100811,x100811)),f875(x100811,f875(f875(f874(x100811,x100811),a862),a862)),x100811),f332(f8(f874(x100811,x100811),f875(f875(f874(x100811,x100811),a862),a862),x100811),f334(f874(x100811,x100811)))),f267(x100811,x100811)))),x100814)),f543(x100814,x100813,x100812,x100811))) % 165.28/165.05 [6069]~P28(x60691)+~E(x60692,f2(x60691))+E(f332(f332(f39(x60691),f332(f332(f82(x60691),x60692),x60693)),f332(f332(f82(x60691),x60692),x60694)),f2(x60691)) % 165.28/165.05 [6107]E(x61071,f116(x61072))+E(x61073,f332(f332(f22(a868),f332(f197(f869(x61072)),x61071)),f79(a868)))+E(f145(x61072,f332(f332(f160(x61072,x61071),x61073),x61074)),f145(x61072,x61071)) % 165.28/165.05 [6137]E(x61371,x61372)+P24(f332(x61373,x61372))+~P24(f332(f332(f332(f310(x61374),x61371),x61373),x61372)) % 165.28/165.05 [6153]~P74(x61531)+~P24(f332(f138(x61532),x61534))+E(f332(f167(x61531),f332(f332(f155(x61532,x61531),x61533),x61534)),f332(f332(f6(x61532,x61531),x61533),f332(f174(x61532),x61534))) % 165.28/165.05 [6177]~P73(x61772)+~P24(f332(f62(x61771),x61774))+E(f332(f332(f9(x61771,x61772),f332(f16(x61772,x61771),x61773)),x61774),f332(f332(f257(x61772),x61773),f332(f38(x61771),x61774))) % 165.28/165.05 [6232]~P28(x62322)+E(x62321,f2(x62322))+E(f332(f332(f39(x62322),f332(f332(f82(x62322),x62323),x62321)),f332(f332(f82(x62322),x62324),x62321)),f332(f332(f39(x62322),x62323),x62324)) % 165.28/165.05 [6234]~P60(x62342)+E(x62341,f2(x62342))+E(f332(f332(f290(x62342),f332(f332(f82(x62342),x62343),x62341)),f332(f332(f82(x62342),x62344),x62341)),f332(f332(f290(x62342),x62343),x62344)) % 165.28/165.05 [6235]~P60(x62352)+E(x62351,f2(x62352))+E(f332(f332(f290(x62352),f332(f332(f82(x62352),x62351),x62353)),f332(f332(f82(x62352),x62351),x62354)),f332(f332(f290(x62352),x62353),x62354)) % 165.28/165.05 [6236]~P28(x62362)+E(x62361,f2(x62362))+E(f332(f332(f39(x62362),f332(f332(f82(x62362),x62361),x62363)),f332(f332(f82(x62362),x62361),x62364)),f332(f332(f39(x62362),x62363),x62364)) % 165.28/165.05 [6298]P24(f332(x62981,x62982))+~E(x62983,f332(f332(f81(a868),x62984),x62982))+~P24(f332(x62981,f332(f332(f22(a868),x62983),x62984))) % 165.28/165.05 [6381]P23(x63811,x63812,x63813)+P33(x63811,f536(x63813,x63812,x63811),x63814)+~P24(f332(f332(f334(f867(x63811)),x63814),x63812)) % 165.28/165.05 [6383]~P24(f332(x63832,x63833))+~P24(f332(f161(x63831,x63832),x63834))+P24(f332(f161(x63831,x63832),f332(f332(f152(x63831),x63833),x63834))) % 165.28/165.05 [6423]E(x64231,f116(x64232))+~E(x64233,f332(f332(f22(a868),f332(f197(f869(x64232)),x64231)),f79(a868)))+E(f145(x64232,f332(f332(f160(x64232,x64231),x64233),x64234)),x64234) % 165.28/165.05 [6446]~P99(x64461)+~P24(f332(f332(f246(x64461),x64462),x64464))+P24(f332(f332(f246(x64461),x64462),f332(f332(f113(x64461),x64463),x64464))) % 165.28/165.05 [6447]~P99(x64471)+~P24(f332(f332(f246(x64471),x64472),x64473))+P24(f332(f332(f246(x64471),x64472),f332(f332(f113(x64471),x64473),x64474))) % 165.28/165.05 [6449]~P106(x64491)+~P24(f332(f332(f246(x64491),x64492),x64494))+P24(f332(f332(f246(x64491),x64492),f332(f332(f245(x64491),x64493),x64494))) % 165.28/165.05 [6451]~P106(x64511)+~P24(f332(f332(f246(x64511),x64512),x64513))+P24(f332(f332(f246(x64511),x64512),f332(f332(f245(x64511),x64513),x64514))) % 165.28/165.05 [6452]~P99(x64521)+~P24(f332(f332(f247(x64521),x64522),x64524))+P24(f332(f332(f247(x64521),x64522),f332(f332(f113(x64521),x64523),x64524))) % 165.28/165.05 [6453]~P99(x64531)+~P24(f332(f332(f247(x64531),x64532),x64533))+P24(f332(f332(f247(x64531),x64532),f332(f332(f113(x64531),x64533),x64534))) % 165.28/165.05 [6455]~P106(x64551)+~P24(f332(f332(f247(x64551),x64552),x64554))+P24(f332(f332(f247(x64551),x64552),f332(f332(f245(x64551),x64553),x64554))) % 165.28/165.05 [6457]~P106(x64571)+~P24(f332(f332(f247(x64571),x64572),x64573))+P24(f332(f332(f247(x64571),x64572),f332(f332(f245(x64571),x64573),x64574))) % 165.28/165.05 [6544]~E(f332(f332(f166(x65441),x65442),x65443),x65444)+E(f332(f332(f160(x65441,x65442),x65443),x65444),x65442)+~P24(f332(f332(f247(a868),x65443),f332(f197(f869(x65441)),x65442))) % 165.28/165.05 [6584]P24(f332(x65841,x65842))+~P24(f332(x65843,x65842))+~P24(f332(f332(f246(f875(x65844,a862)),x65843),x65841)) % 165.28/165.05 [6615]~E(f332(f332(f160(x66151,x66152),x66153),x66154),x66152)+E(f332(f332(f166(x66151),x66152),x66153),x66154)+~P24(f332(f332(f247(a868),x66153),f332(f197(f869(x66151)),x66152))) % 165.28/165.05 [6630]~P24(f332(f161(x66301,x66302),x66304))+~P24(f332(f161(x66301,x66302),x66303))+P24(f332(f161(x66301,x66302),f332(f332(f135(x66301),x66303),x66304))) % 165.28/165.05 [6726]P33(x67261,x67262,x67263)+~P33(x67261,f332(a115,x67262),f547(x67262,x67264,x67261))+~P24(f332(f332(f334(f867(x67261)),x67263),x67264)) % 165.28/165.05 [6735]E(x67351,f196(f875(x67352,a862)))+E(x67353,f196(f875(x67354,a862)))+~E(f332(f332(f269(x67354,x67352),x67353),f332(f16(f875(x67352,a862),x67354),x67351)),f196(f875(f874(x67354,x67352),a862))) % 165.28/165.05 [6754]E(x67541,x67542)+P24(f332(f332(f334(x67543),x67541),x67544))+~P24(f332(f332(f334(x67543),x67541),f332(f332(f310(x67543),x67542),x67544))) % 165.28/165.05 [6771]~P106(x67711)+P24(f332(f332(f246(x67711),x67712),x67713))+~P24(f332(f332(f246(x67711),x67712),f332(f332(f244(x67711),x67714),x67713))) % 165.28/165.05 [6773]~P106(x67731)+P24(f332(f332(f246(x67731),x67732),x67733))+~P24(f332(f332(f246(x67731),x67732),f332(f332(f244(x67731),x67733),x67734))) % 165.28/165.05 [6775]~P100(x67751)+P24(f332(f332(f246(x67751),x67752),x67753))+~P24(f332(f332(f246(x67751),x67752),f332(f332(f104(x67751),x67754),x67753))) % 165.28/165.05 [6777]~P100(x67771)+P24(f332(f332(f246(x67771),x67772),x67773))+~P24(f332(f332(f246(x67771),x67772),f332(f332(f104(x67771),x67773),x67774))) % 165.28/165.05 [6778]~P106(x67781)+P24(f332(f332(f247(x67781),x67782),x67783))+~P24(f332(f332(f247(x67781),x67782),f332(f332(f244(x67781),x67784),x67783))) % 165.28/165.05 [6779]~P106(x67791)+P24(f332(f332(f247(x67791),x67792),x67793))+~P24(f332(f332(f247(x67791),x67792),f332(f332(f244(x67791),x67793),x67794))) % 165.28/165.05 [6801]~E(f332(f332(f166(x68011),x68013),x68014),x68012)+P24(f332(f332(f334(x68011),x68012),f332(f174(x68011),x68013)))+~P24(f332(f332(f247(a868),x68014),f332(f197(f869(x68011)),x68013))) % 165.28/165.05 [6813]~P106(x68131)+~P32(x68131,f332(f332(f152(x68131),x68132),f332(f332(f152(x68131),x68133),x68134)))+P24(f332(f332(f246(x68131),x68132),x68133)) % 165.28/165.05 [6953]~P35(x69532,x69531,x69533)+P24(f332(x69531,f332(f332(f166(x69532),x69533),x69534)))+~P24(f332(f332(f247(a868),x69534),f332(f197(f869(x69532)),x69533))) % 165.28/165.05 [6972]E(x69721,f2(a1))+E(f332(f332(f39(a1),x69722),x69721),x69723)+~P24(f332(f49(x69722,x69721),f332(f332(f267(a1,a1),x69723),x69724))) % 165.28/165.05 [6993]E(f45(a1,x69932,x69931),x69933)+E(x69931,f2(a1))+~P24(f332(f49(x69932,x69931),f332(f332(f267(a1,a1),x69934),x69933))) % 165.28/165.05 [7112]P24(f332(f332(f334(x71121),x71122),x71123))+~P24(f332(f332(f334(x71121),x71122),x71124))+~P24(f332(f332(f247(f875(x71121,a862)),x71124),x71123)) % 165.28/165.05 [7113]P24(f332(f332(f334(x71131),x71132),x71133))+~P24(f332(f332(f334(x71131),x71132),x71134))+~P24(f332(f332(f246(f875(x71131,a862)),x71134),x71133)) % 165.28/165.05 [7221]P37(x72211,x72212,x72213)+~P24(f332(x72212,f332(f332(f166(x72211),x72213),x72214)))+~P24(f332(f332(f247(a868),x72214),f332(f197(f869(x72211)),x72213))) % 165.28/165.05 [7330]~P105(x73302)+~P24(f332(f332(f247(f875(x73301,x73302)),x73303),x73304))+P24(f332(f332(f246(f875(x73301,x73302)),x73303),x73304)) % 165.28/165.05 [7417]~P20(x74171,x74172,x74174)+P20(x74171,x74172,f332(f332(f310(f867(x74171)),x74173),x74174))+~P20(x74171,x74172,f332(f332(f310(f867(x74171)),x74173),f196(f875(f867(x74171),a862)))) % 165.28/165.05 [7461]~P24(f332(f332(f334(x74611),x74612),x74614))+P24(f332(f332(f334(x74611),x74612),f40(f875(x74611,a862),x74613)))+~P24(f332(f332(f334(f875(x74611,a862)),x74614),x74613)) % 165.28/165.05 [7473]P33(x74731,x74732,x74733)+P24(f332(f332(f334(f867(x74731)),f547(x74732,x74734,x74731)),x74734))+~P24(f332(f332(f334(f867(x74731)),x74733),x74734)) % 165.28/165.05 [7493]~P83(x74931)+~P24(f332(f332(f246(x74931),x74933),x74934))+P24(f332(f332(f246(x74931),f332(f332(f81(x74931),x74932),x74933)),f332(f332(f81(x74931),x74932),x74934))) % 165.28/165.05 [7494]~P84(x74941)+~P24(f332(f332(f246(x74941),x74943),x74944))+P24(f332(f332(f246(x74941),f332(f332(f81(x74941),x74942),x74943)),f332(f332(f81(x74941),x74942),x74944))) % 165.28/165.05 [7495]~P83(x74951)+~P24(f332(f332(f246(x74951),x74952),x74954))+P24(f332(f332(f246(x74951),f332(f332(f81(x74951),x74952),x74953)),f332(f332(f81(x74951),x74954),x74953))) % 165.28/165.05 [7496]~P84(x74961)+~P24(f332(f332(f246(x74961),x74962),x74964))+P24(f332(f332(f246(x74961),f332(f332(f81(x74961),x74962),x74963)),f332(f332(f81(x74961),x74964),x74963))) % 165.28/165.05 [7497]~P83(x74971)+~P24(f332(f332(f247(x74971),x74973),x74974))+P24(f332(f332(f247(x74971),f332(f332(f81(x74971),x74972),x74973)),f332(f332(f81(x74971),x74972),x74974))) % 165.28/165.05 [7498]~P86(x74981)+~P24(f332(f332(f247(x74981),x74983),x74984))+P24(f332(f332(f247(x74981),f332(f332(f81(x74981),x74982),x74983)),f332(f332(f81(x74981),x74982),x74984))) % 165.28/165.05 [7499]~P83(x74991)+~P24(f332(f332(f247(x74991),x74992),x74994))+P24(f332(f332(f247(x74991),f332(f332(f81(x74991),x74992),x74993)),f332(f332(f81(x74991),x74994),x74993))) % 165.28/165.05 [7500]~P86(x75001)+~P24(f332(f332(f247(x75001),x75002),x75004))+P24(f332(f332(f247(x75001),f332(f332(f81(x75001),x75002),x75003)),f332(f332(f81(x75001),x75004),x75003))) % 165.28/165.05 [7509]~P125(x75091)+~P93(x75091)+E(f332(f332(f22(x75091),f332(f332(f82(x75091),x75092),f332(f106(x75091),x75093))),f332(f332(f82(x75091),x75094),f332(f106(x75091),x75093))),f332(f332(f82(x75091),f332(f332(f22(x75091),x75092),x75094)),f332(f106(x75091),x75093))) % 165.28/165.05 [7510]~P124(x75101)+~P93(x75101)+E(f332(f332(f81(x75101),f332(f332(f82(x75101),x75102),f332(f106(x75101),x75103))),f332(f332(f82(x75101),x75104),f332(f106(x75101),x75103))),f332(f332(f82(x75101),f332(f332(f81(x75101),x75102),x75104)),f332(f106(x75101),x75103))) % 165.28/165.05 [7546]~P74(x75461)+E(f332(f332(f81(x75461),f332(x75462,x75463)),f332(f332(f6(a868,x75461),x75462),f303(a868,f332(a115,x75463),x75464))),f332(f332(f6(a868,x75461),x75462),f303(a868,x75463,x75464)))+~P24(f332(f332(f246(a868),x75463),x75464)) % 165.28/165.05 [7557]~P21(x75572,x75571,x75573,f332(f174(x75572),x75574))+~P24(f332(f138(x75572),x75574))+P24(f332(f138(x75571),f332(f332(f155(x75572,x75571),x75573),x75574))) % 165.28/165.05 [7604]~P24(f332(f332(f246(a868),x76042),x76044))+~P24(f332(f332(f246(a868),x76041),x76043))+P24(f332(f332(f246(a868),f332(f332(f81(a868),x76041),x76042)),f332(f332(f81(a868),x76043),x76044))) % 165.28/165.05 [7605]~P24(f332(f332(f246(a868),x76052),x76054))+~P24(f332(f332(f246(a868),x76051),x76053))+P24(f332(f332(f246(a868),f332(f332(f82(a868),x76051),x76052)),f332(f332(f82(a868),x76053),x76054))) % 165.28/165.05 [7608]~P24(f332(f332(f247(a868),x76082),x76084))+~P24(f332(f332(f247(a868),x76081),x76083))+P24(f332(f332(f247(a868),f332(f332(f81(a868),x76081),x76082)),f332(f332(f81(a868),x76083),x76084))) % 165.28/165.05 [7609]~P24(f332(f332(f246(a1),x76092),x76094))+~P24(f332(f332(f247(a1),x76091),x76093))+P24(f332(f332(f247(a1),f332(f332(f81(a1),x76091),x76092)),f332(f332(f81(a1),x76093),x76094))) % 165.28/165.05 [7657]P24(f332(f332(f334(x76571),x76572),x76573))+~P24(f332(f332(f334(x76571),x76572),f41(f875(x76571,a862),x76574)))+~P24(f332(f332(f334(f875(x76571,a862)),x76573),x76574)) % 165.28/165.05 [7673]~P24(f332(x76731,f530(x76731,x76733,x76732)))+P24(f332(x76731,f332(f332(f166(x76732),x76733),x76734)))+~P24(f332(f332(f247(a868),x76734),f332(f197(f869(x76732)),x76733))) % 165.28/165.05 [7678]P24(f332(x76781,x76782))+~P24(f332(f332(f334(x76784),x76782),f332(f174(x76784),x76783)))+P24(f332(f332(f247(a868),f531(x76781,x76783,x76784)),f332(f197(f869(x76784)),x76783))) % 165.28/165.05 [7726]~P105(x77261)+~P24(f332(f332(f247(f875(x77262,x77261)),x77264),x77263))+~P24(f332(f332(f246(f875(x77262,x77261)),x77263),x77264)) % 165.28/165.05 [7771]~P24(f332(x77714,x77712))+~P24(f332(f332(f334(x77711),x77712),x77713))+P24(f332(f332(f334(x77711),x77712),f332(f332(f104(f875(x77711,a862)),x77713),f332(f252(x77711),x77714)))) % 165.28/165.05 [7913]~P24(f332(f332(f334(x79131),x79133),x79134))+~P24(f332(f332(f247(f875(x79131,a862)),x79132),x79134))+P24(f332(f332(f247(f875(x79131,a862)),x79132),f332(f332(f310(x79131),x79133),x79134))) % 165.28/165.05 [7915]E(f332(f332(f104(f875(x79151,a862)),x79152),x79153),f196(f875(x79151,a862)))+~E(f332(f332(f104(f875(x79151,a862)),f40(f875(x79151,a862),x79154)),x79153),f196(f875(x79151,a862)))+~P24(f332(f332(f334(f875(x79151,a862)),x79152),x79154)) % 165.28/165.05 [7989]P24(f332(f332(f334(x79891),x79892),x79893))+~P24(f332(f332(f246(f875(x79891,a862)),x79893),f332(f332(f310(x79891),x79892),x79894)))+P24(f332(f332(f246(f875(x79891,a862)),x79893),x79894)) % 165.28/165.05 [8006]P24(f332(f332(f334(x80062),f530(x80061,x80063,x80062)),f332(f174(x80062),x80063)))+P24(f332(x80061,f332(f332(f166(x80062),x80063),x80064)))+~P24(f332(f332(f247(a868),x80064),f332(f197(f869(x80062)),x80063))) % 165.28/165.05 [8014]~P24(f332(f332(f246(f875(x80141,a862)),x80142),x80144))+P24(f332(f332(f246(f875(x80141,a862)),x80142),x80143))+~P24(f332(f332(f246(f875(x80141,a862)),x80144),x80143)) % 165.28/165.05 [8015]~P24(f332(f332(f247(f875(x80151,a862)),x80152),x80154))+~P24(f332(f332(f246(f875(x80151,a862)),x80154),x80153))+P24(f332(f332(f247(f875(x80151,a862)),x80152),x80153)) % 165.28/165.05 [8016]~P24(f332(f332(f246(f875(x80161,a862)),x80162),x80164))+~P24(f332(f332(f247(f875(x80161,a862)),x80164),x80163))+P24(f332(f332(f247(f875(x80161,a862)),x80162),x80163)) % 165.28/165.05 [8017]~P24(f332(f332(f247(f875(x80171,a862)),x80172),x80174))+P24(f332(f332(f247(f875(x80171,a862)),x80172),x80173))+~P24(f332(f332(f247(f875(x80171,a862)),x80174),x80173)) % 165.28/165.05 [8057]~P24(f332(f332(f334(x80571),x80574),x80573))+~P24(f332(f332(f247(f875(x80571,a862)),x80572),f332(f332(f310(x80571),x80574),x80573)))+P24(f332(f332(f247(f875(x80571,a862)),x80572),x80573)) % 165.28/165.05 [8068]~P83(x80681)+P24(f332(f332(f246(x80681),x80682),x80683))+~P24(f332(f332(f246(x80681),f332(f332(f81(x80681),x80684),x80682)),f332(f332(f81(x80681),x80684),x80683))) % 165.28/165.05 [8070]~P83(x80701)+P24(f332(f332(f246(x80701),x80702),x80703))+~P24(f332(f332(f246(x80701),f332(f332(f81(x80701),x80702),x80704)),f332(f332(f81(x80701),x80703),x80704))) % 165.28/165.05 [8072]~P83(x80721)+P24(f332(f332(f247(x80721),x80722),x80723))+~P24(f332(f332(f247(x80721),f332(f332(f81(x80721),x80724),x80722)),f332(f332(f81(x80721),x80724),x80723))) % 165.28/165.05 [8074]~P83(x80741)+P24(f332(f332(f247(x80741),x80742),x80743))+~P24(f332(f332(f247(x80741),f332(f332(f81(x80741),x80742),x80744)),f332(f332(f81(x80741),x80743),x80744))) % 165.28/165.05 [8122]P24(f332(x81221,x81222))+~E(f332(f332(f139(x81223),f332(f197(f869(x81223)),f179(x81223,x81221,x81224))),x81224),f116(x81223))+~P24(f332(f332(f334(x81223),x81222),f332(f174(x81223),x81224))) % 165.28/165.05 [8247]P24(f332(x82471,x82472))+~P24(f332(f332(f334(x82473),x82472),f332(f174(x82473),x82474)))+P24(f332(f332(f247(a868),f332(f197(f869(x82473)),f332(f137(x82473,x82471),x82474))),f332(f197(f869(x82473)),x82474))) % 165.28/165.05 [8706]~P24(f332(x87061,f720(x87061,x87063,x87062,x87064)))+P24(f332(x87061,f332(f332(f166(x87062),x87063),x87064)))+~P24(f332(f332(f247(a868),x87064),f332(f197(f869(x87062)),x87063))) % 165.28/165.05 [8729]~P21(x87294,x87293,x87291,f255(f875(x87294,a862)))+E(f332(x87291,f826(x87292,x87291,x87293,x87294)),x87292)+~P24(f332(f332(f334(x87293),x87292),f332(f311(x87294,x87293,x87291),f255(f875(x87294,a862))))) % 165.28/165.05 [8794]E(f179(x87941,x87942,x87943),f332(f332(f177(x87941),x87944),x87943))+P24(f332(f332(f247(a868),f644(x87942,x87943,x87941,x87944)),x87944))+P24(f332(f332(f247(a868),x87944),f332(f197(f869(x87941)),x87943))) % 165.28/165.05 [8797]E(f179(x87971,x87972,x87973),f332(f332(f177(x87971),x87974),x87973))+P24(f332(f332(f247(a868),f644(x87972,x87973,x87971,x87974)),x87974))+P24(f332(x87972,f332(f332(f166(x87971),x87973),x87974))) % 165.28/165.05 [8826]P24(f332(x88261,x88262))+~P24(f332(f332(f334(x88264),x88262),f332(f174(x88264),x88263)))+P24(f332(f332(f247(a868),f538(x88262,x88261,x88263,x88264)),f332(f197(f869(x88264)),x88263))) % 165.28/165.05 [8829]E(f179(x88291,x88292,x88293),f332(f332(f177(x88291),x88294),x88293))+P24(f332(f332(f247(a868),x88294),f332(f197(f869(x88291)),x88293)))+P24(f332(f332(f247(a868),f644(x88292,x88293,x88291,x88294)),f332(f197(f869(x88291)),x88293))) % 165.28/165.05 [8836]E(f179(x88361,x88362,x88363),f332(f332(f177(x88361),x88364),x88363))+P24(f332(x88362,f332(f332(f166(x88361),x88363),x88364)))+P24(f332(f332(f247(a868),f644(x88362,x88363,x88361,x88364)),f332(f197(f869(x88361)),x88363))) % 165.28/165.05 [8862]~P112(x88624)+P24(f332(f332(f334(x88621),f784(x88622,x88623,x88621,x88624)),x88623))+P24(f332(f332(f247(x88624),f2(x88624)),f332(f332(f9(x88621,x88624),x88622),x88623))) % 165.28/165.05 [8863]~P112(x88634)+P24(f332(f332(f334(x88631),f789(x88632,x88633,x88631,x88634)),x88633))+P24(f332(f332(f246(x88634),f2(x88634)),f332(f332(f9(x88631,x88634),x88632),x88633))) % 165.28/165.05 [8893]~P24(f332(f62(x88931),x88934))+P24(f332(f332(f334(x88931),f573(x88932,x88933,x88934,x88931)),x88934))+P24(f332(f62(f874(x88931,x88933)),f332(f332(f269(x88931,x88933),x88934),x88932))) % 165.28/165.05 [8921]P24(f332(f332(f334(x89212),f720(x89211,x89213,x89212,x89214)),f332(f174(x89212),x89213)))+P24(f332(x89211,f332(f332(f166(x89212),x89213),x89214)))+~P24(f332(f332(f247(a868),x89214),f332(f197(f869(x89212)),x89213))) % 165.28/165.05 [9050]P24(f332(f332(f246(a868),x90504),f332(f197(f869(x90502)),f179(x90502,x90503,x90501))))+P24(f332(f332(f247(a868),f645(x90501,x90502,x90503,x90504)),x90504))+~P24(f332(f332(f246(a868),x90504),f332(f197(f869(x90502)),x90501))) % 165.28/165.05 [9152]~E(f332(f332(f180(x91521,x91522),x91523),f687(x91524,x91523,x91522,x91521)),f332(f332(f180(x91521,x91522),x91524),f687(x91524,x91523,x91522,x91521)))+E(f332(f180(x91521,x91522),x91523),f332(f180(x91521,x91522),x91524))+~E(f332(f174(x91521),f332(f332(f155(f874(x91521,x91522),x91521),f266(x91521,x91522)),x91523)),f332(f174(x91521),f332(f332(f155(f874(x91521,x91522),x91521),f266(x91521,x91522)),x91524))) % 165.28/165.05 [9192]E(f179(x91921,x91922,x91923),f332(f332(f177(x91921),x91924),x91923))+~P24(f332(x91922,f332(f332(f166(x91921),x91923),f644(x91922,x91923,x91921,x91924))))+P24(f332(f332(f247(a868),x91924),f332(f197(f869(x91921)),x91923))) % 165.28/165.05 [9197]E(f179(x91971,x91972,x91973),f332(f332(f177(x91971),x91974),x91973))+~P24(f332(x91972,f332(f332(f166(x91971),x91973),f644(x91972,x91973,x91971,x91974))))+P24(f332(x91972,f332(f332(f166(x91971),x91973),x91974))) % 165.28/165.05 [9204]~P24(f332(f62(x92041),x92043))+~P24(f332(f62(x92042),f332(x92044,f573(x92044,x92042,x92043,x92041))))+P24(f332(f62(f874(x92041,x92042)),f332(f332(f269(x92041,x92042),x92043),x92044))) % 165.28/165.05 [9212]~P112(x92121)+~P24(f332(f332(f246(x92121),f2(x92121)),f332(x92123,f789(x92123,x92124,x92122,x92121))))+P24(f332(f332(f246(x92121),f2(x92121)),f332(f332(f9(x92122,x92121),x92123),x92124))) % 165.28/165.05 [9213]~P112(x92131)+~P24(f332(f332(f247(x92131),f2(x92131)),f332(x92133,f784(x92133,x92134,x92132,x92131))))+P24(f332(f332(f247(x92131),f2(x92131)),f332(f332(f9(x92132,x92131),x92133),x92134))) % 165.28/165.05 [9219]~E(f332(f197(f869(x92194)),x92192),f332(f197(f869(x92194)),x92193))+P24(f332(f332(f334(f874(f869(x92194),f869(x92194))),f332(f332(f267(f869(x92194),f869(x92194)),x92193),x92192)),f159(x92194,x92191)))+P24(f332(f332(f247(a868),f541(x92191,x92192,x92193,x92194)),f332(f197(f869(x92194)),x92193))) % 165.28/165.05 [9268]~P24(f332(x92683,f332(f332(f166(x92682),x92684),f645(x92684,x92682,x92683,x92681))))+P24(f332(f332(f246(a868),x92681),f332(f197(f869(x92682)),f179(x92682,x92683,x92684))))+~P24(f332(f332(f246(a868),x92681),f332(f197(f869(x92682)),x92684))) % 165.28/165.05 [9342]E(f332(f332(f177(x93421),f542(x93422,x93423,x93424,x93421)),x93423),f332(f332(f177(x93421),f542(x93422,x93423,x93424,x93421)),x93424))+~P24(f332(f332(f334(f874(f869(x93421),f869(x93421))),f332(f332(f267(f869(x93421),f869(x93421)),x93424),x93423)),f148(x93421,x93422)))+P24(f332(f332(f247(a868),f332(f197(f869(x93421)),x93424)),f332(f197(f869(x93421)),x93423))) % 165.28/165.05 [9395]~P24(f332(f332(f247(a868),f2(a868)),x93953))+~P24(f332(f332(f247(a868),x93954),x93951))+P24(f332(f332(f247(a868),f332(f332(f81(a868),f332(f332(f82(a868),x93951),f45(a868,x93952,x93953))),x93954)),f332(f332(f82(a868),x93951),x93953))) % 165.28/165.05 [9582]~P105(x95822)+~P24(f332(f332(f246(x95822),f332(x95823,f821(x95824,x95823,x95821,x95822))),f332(x95824,f821(x95824,x95823,x95821,x95822))))+P24(f332(f332(f246(f875(x95821,x95822)),x95823),x95824)) % 165.28/165.05 [9686]~P66(x96861)+E(f332(f332(f6(a868,x96861),f332(f332(f18(a868,x96861,x96861),f332(f332(f8(x96861,f875(x96861,x96861),a868),f22(x96861)),x96862)),f332(f332(f8(a868,x96861,a868),x96862),f332(f332(f7(a868,a868,a868),f81(a868)),f79(a868))))),f303(a868,x96863,x96864)),f332(f332(f22(x96861),f332(x96862,x96863)),f332(x96862,f332(f332(f81(a868),x96864),f79(a868)))))+~P24(f332(f332(f246(a868),x96863),x96864)) % 165.28/165.05 [6805]E(f332(f332(f135(x68051),x68052),x68053),x68054)+~E(x68053,f332(f332(f139(x68051),f332(f197(f869(x68051)),x68052)),x68054))+~E(f332(f332(f177(x68051),f332(f197(f869(x68051)),x68052)),x68054),x68052) % 165.28/165.05 [6861]~P61(x68612)+E(x68611,f2(x68612))+E(f332(f332(f290(x68612),f332(f332(f257(x68612),x68613),x68614)),f332(f332(f257(x68612),x68611),x68614)),f332(f332(f257(x68612),f332(f332(f290(x68612),x68613),x68611)),x68614)) % 165.28/165.05 [6995]~E(f332(f197(f869(x69951)),x69953),f332(f197(f869(x69952)),x69954))+~P24(f332(f138(x69951),x69953))+E(f186(x69951,x69952,f332(f180(x69951,x69952),f332(f332(f184(x69951,x69952),x69953),x69954))),f332(f174(x69951),x69953)) % 165.28/165.05 [7012]~P100(x70121)+~P24(f332(f332(f246(x70121),x70123),x70124))+P24(f332(f332(f246(x70121),f332(f332(f104(x70121),x70122),x70123)),x70124)) % 165.28/165.05 [7013]~P100(x70131)+~P24(f332(f332(f246(x70131),x70132),x70134))+P24(f332(f332(f246(x70131),f332(f332(f104(x70131),x70132),x70133)),x70134)) % 165.28/165.05 [7015]~P106(x70151)+~P24(f332(f332(f246(x70151),x70153),x70154))+P24(f332(f332(f246(x70151),f332(f332(f244(x70151),x70152),x70153)),x70154)) % 165.28/165.05 [7017]~P106(x70171)+~P24(f332(f332(f246(x70171),x70172),x70174))+P24(f332(f332(f246(x70171),f332(f332(f244(x70171),x70172),x70173)),x70174)) % 165.28/165.05 [7018]~P100(x70181)+~P24(f332(f332(f247(x70181),x70183),x70184))+P24(f332(f332(f247(x70181),f332(f332(f104(x70181),x70182),x70183)),x70184)) % 165.28/165.05 [7019]~P100(x70191)+~P24(f332(f332(f247(x70191),x70192),x70194))+P24(f332(f332(f247(x70191),f332(f332(f104(x70191),x70192),x70193)),x70194)) % 165.28/165.05 [7021]~P106(x70211)+~P24(f332(f332(f247(x70211),x70213),x70214))+P24(f332(f332(f247(x70211),f332(f332(f244(x70211),x70212),x70213)),x70214)) % 165.28/165.05 [7023]~P106(x70231)+~P24(f332(f332(f247(x70231),x70232),x70234))+P24(f332(f332(f247(x70231),f332(f332(f244(x70231),x70232),x70233)),x70234)) % 165.28/165.05 [7043]~P24(f332(x70433,x70434))+~P24(f332(x70432,x70434))+P24(f332(f332(f332(f104(f875(x70431,a862)),x70432),x70433),x70434)) % 165.28/165.05 [7167]P20(x71671,x71672,x71673)+~P20(x71671,x71674,x71673)+~P24(f332(f332(f246(f875(f867(x71671),a862)),x71674),x71672)) % 165.28/165.05 [7168]P20(x71681,x71682,x71683)+~P20(x71681,x71682,x71684)+~P24(f332(f332(f246(f875(f867(x71681),a862)),x71683),x71684)) % 165.28/165.05 [7536]~P74(x75361)+E(f332(f332(f81(x75361),f332(x75362,x75363)),f332(f332(f6(a868,x75361),x75362),f332(f302(a868,f332(a115,x75363)),x75364))),f332(f332(f6(a868,x75361),x75362),f332(f302(a868,x75363),x75364)))+~P24(f332(f332(f247(a868),x75363),x75364)) % 165.28/165.05 [7565]~P106(x75651)+P24(f332(f332(f246(x75651),x75652),x75653))+~P24(f332(f332(f246(x75651),f332(f332(f245(x75651),x75654),x75652)),x75653)) % 165.28/165.05 [7567]~P106(x75671)+P24(f332(f332(f246(x75671),x75672),x75673))+~P24(f332(f332(f246(x75671),f332(f332(f245(x75671),x75672),x75674)),x75673)) % 165.28/165.05 [7569]~P99(x75691)+P24(f332(f332(f246(x75691),x75692),x75693))+~P24(f332(f332(f246(x75691),f332(f332(f113(x75691),x75694),x75692)),x75693)) % 165.28/165.05 [7571]~P99(x75711)+P24(f332(f332(f246(x75711),x75712),x75713))+~P24(f332(f332(f246(x75711),f332(f332(f113(x75711),x75712),x75714)),x75713)) % 165.28/165.05 [7572]~P106(x75721)+P24(f332(f332(f247(x75721),x75722),x75723))+~P24(f332(f332(f247(x75721),f332(f332(f245(x75721),x75724),x75722)),x75723)) % 165.28/165.05 [7573]~P106(x75731)+P24(f332(f332(f247(x75731),x75732),x75733))+~P24(f332(f332(f247(x75731),f332(f332(f245(x75731),x75732),x75734)),x75733)) % 165.28/165.05 [7649]~P24(f332(f332(f334(x76491),x76492),x76494))+P24(f332(f332(f334(x76491),x76492),x76493))+P24(f332(f332(f334(x76491),x76492),f332(f332(f22(f875(x76491,a862)),x76494),x76493))) % 165.28/165.05 [7733]P24(f332(x77331,x77332))+P24(f332(x77333,x77332))+~P24(f332(f332(f332(f113(f875(x77334,a862)),x77333),x77331),x77332)) % 165.28/165.05 [7744]~P24(f332(f332(f334(x77441),x77442),x77444))+~P24(f332(f332(f334(x77441),x77442),x77443))+P24(f332(f332(f334(x77441),x77442),f332(f332(f104(f875(x77441,a862)),x77443),x77444))) % 165.28/165.05 [7793]~P99(x77931)+~P24(f332(f62(x77931),x77934))+E(f332(f332(f65(x77931,x77931,f113(x77931)),x77932),f332(f332(f310(x77931),x77933),x77934)),f332(f332(f113(x77931),x77933),f332(f332(f65(x77931,x77931,f113(x77931)),x77932),x77934))) % 165.28/165.05 [7794]~P100(x77941)+~P24(f332(f62(x77941),x77944))+E(f332(f332(f65(x77941,x77941,f104(x77941)),x77942),f332(f332(f310(x77941),x77943),x77944)),f332(f332(f104(x77941),x77943),f332(f332(f65(x77941,x77941,f104(x77941)),x77942),x77944))) % 165.28/165.05 [7795]~P106(x77951)+~P24(f332(f62(x77951),x77954))+E(f332(f332(f65(x77951,x77951,f244(x77951)),x77952),f332(f332(f310(x77951),x77953),x77954)),f332(f332(f244(x77951),x77953),f332(f332(f65(x77951,x77951,f244(x77951)),x77952),x77954))) % 165.28/165.05 [7796]~P106(x77961)+~P24(f332(f62(x77961),x77964))+E(f332(f332(f65(x77961,x77961,f245(x77961)),x77962),f332(f332(f310(x77961),x77963),x77964)),f332(f332(f245(x77961),x77963),f332(f332(f65(x77961,x77961,f245(x77961)),x77962),x77964))) % 165.28/165.05 [7797]~P125(x77971)+~P93(x77971)+E(f332(f332(f22(x77971),f332(f332(f82(x77971),f332(f106(x77971),x77972)),x77973)),f332(f332(f82(x77971),f332(f106(x77971),x77972)),x77974)),f332(f332(f82(x77971),f332(f106(x77971),x77972)),f332(f332(f22(x77971),x77973),x77974))) % 165.28/165.05 [7798]~P124(x77981)+~P93(x77981)+E(f332(f332(f81(x77981),f332(f332(f82(x77981),f332(f106(x77981),x77982)),x77983)),f332(f332(f82(x77981),f332(f106(x77981),x77982)),x77984)),f332(f332(f82(x77981),f332(f106(x77981),x77982)),f332(f332(f81(x77981),x77983),x77984))) % 165.28/165.05 [7911]E(x79111,x79112)+P24(f332(f332(f334(x79113),x79111),f332(f174(x79113),x79114)))+~P24(f332(f332(f334(x79113),x79111),f332(f174(x79113),f332(f332(f152(x79113),x79112),x79114)))) % 165.28/165.05 [7936]~P59(x79361)+~E(f332(f197(f869(x79362)),x79363),f332(f197(f869(x79361)),f56(x79361)))+E(f332(f332(f180(x79361,x79362),f332(f332(f184(x79361,x79362),f56(x79361)),x79363)),x79364),f332(f208(x79362),f633(x79364,x79363,x79362,x79361))) % 165.28/165.05 [8081]P53(x80811,x80812,x80813)+~P53(x80811,x80812,x80814)+~P24(f332(f332(f246(f875(f874(x80811,x80812),a862)),x80813),x80814)) % 165.28/165.05 [8125]P24(f332(f332(f334(x81251),x81252),x81253))+P24(f332(f332(f334(x81251),x81252),x81254))+~P24(f332(f332(f334(x81251),x81252),f332(f332(f113(f875(x81251,a862)),x81254),x81253))) % 165.28/165.05 [8135]~P43(x81351,x81354,x81353)+~P24(f332(f332(f334(x81351),x81352),x81354))+P24(f332(f332(f334(f874(x81351,x81351)),f332(f332(f267(x81351,x81351),x81352),x81352)),x81353)) % 165.28/165.05 [8150]~P24(f332(f62(x81502),x81504))+~P24(f332(f62(x81501),x81503))+P24(f332(f62(f874(x81501,x81502)),f332(f332(f269(x81501,x81502),x81503),f332(f16(f875(x81502,a862),x81501),x81504)))) % 165.28/165.05 [8151]~P24(f332(f332(f334(x81511),x81512),x81514))+~P24(f332(f332(f246(f875(x81511,a862)),x81513),x81514))+P24(f332(f332(f246(f875(x81511,a862)),f332(f332(f310(x81511),x81512),x81513)),x81514)) % 165.28/165.05 [8159]~P73(x81592)+~P142(x81592)+E(f332(f332(f9(x81591,x81592),f332(f332(f8(a868,x81592,x81591),f103(x81592)),x81593)),x81594),f332(f103(x81592),f332(f332(f9(x81591,a868),x81593),x81594))) % 165.28/165.05 [8160]~P73(x81602)+~P138(x81602)+E(f332(f332(f9(x81601,x81602),f332(f332(f8(a1,x81602,x81601),f105(x81602)),x81603)),x81604),f332(f105(x81602),f332(f332(f9(x81601,a1),x81603),x81604))) % 165.28/165.05 [8186]E(f332(f332(f22(f875(x81861,a862)),x81862),f332(f332(f22(f875(x81861,a862)),x81863),x81864)),x81864)+~P24(f332(f332(f246(f875(x81861,a862)),x81862),x81863))+~P24(f332(f332(f246(f875(x81861,a862)),x81864),x81862)) % 165.28/165.05 [8279]~P24(f332(f62(x82791),x82794))+E(f332(f332(f22(a868),f332(f332(f6(x82791,a868),x82792),x82793)),f332(f332(f6(x82791,a868),x82792),x82794)),f332(f332(f6(x82791,a868),x82792),f332(f332(f22(f875(x82791,a862)),x82793),x82794)))+~P24(f332(f332(f246(f875(x82791,a862)),x82794),x82793)) % 165.28/165.05 [8428]~P6(x84281,x84284,x84283)+~P24(f332(f332(f334(x84281),x84282),x84284))+P24(f332(f332(f334(x84281),x84282),f332(f286(x84281,x84281,x84283),f332(f332(f310(x84281),x84282),f196(f875(x84281,a862)))))) % 165.28/165.05 [8485]~P24(f332(f332(f246(f875(x84851,a862)),x84852),x84853))+~P24(f332(f332(f246(f875(x84851,a862)),x84852),x84854))+P24(f332(f332(f246(f875(x84851,a862)),x84852),f332(f332(f104(f875(x84851,a862)),x84853),x84854))) % 165.28/165.05 [8582]E(x85821,f196(f875(x85822,a862)))+P24(f332(f62(x85823),x85824))+~P24(f332(f62(f874(x85823,x85822)),f332(f332(f269(x85823,x85822),x85824),f332(f16(f875(x85822,a862),x85823),x85821)))) % 165.28/165.05 [8583]E(x85831,f196(f875(x85832,a862)))+P24(f332(f62(x85833),x85834))+~P24(f332(f62(f874(x85832,x85833)),f332(f332(f269(x85832,x85833),x85831),f332(f16(f875(x85833,a862),x85832),x85834)))) % 165.28/165.05 [8649]P24(f332(f332(f334(x86491),x86492),f321(x86491,x86493)))+~P24(f332(f332(f334(x86491),x86494),f321(x86491,x86493)))+~P24(f332(f332(f334(f874(x86491,x86491)),f332(f332(f267(x86491,x86491),x86492),x86494)),x86493)) % 165.28/165.05 [8701]~P41(x87011,x87014)+P24(f332(f332(f334(f874(x87011,x87011)),f332(f332(f267(x87011,x87011),x87013),x87012)),f308(x87011,x87014)))+P41(x87011,f332(f332(f310(f874(x87011,x87011)),f332(f332(f267(x87011,x87011),x87012),x87013)),x87014)) % 165.28/165.05 [8702]~P56(x87021,x87024)+P24(f332(f332(f334(f874(x87021,x87021)),f332(f332(f267(x87021,x87021),x87023),x87022)),f308(x87021,x87024)))+P56(x87021,f332(f332(f310(f874(x87021,x87021)),f332(f332(f267(x87021,x87021),x87022),x87023)),x87024)) % 165.28/165.05 [8779]~E(x87792,x87793)+~P24(f332(f332(f334(x87791),x87792),f332(f174(x87791),x87794)))+P24(f332(f332(f334(f874(x87791,x87791)),f332(f332(f267(x87791,x87791),x87792),x87793)),f332(f174(f874(x87791,x87791)),f332(f332(f184(x87791,x87791),x87794),x87794)))) % 165.28/165.05 [8860]~E(x88603,x88604)+P24(f332(f332(f271(x88601,x88601,a862),a329),x88602))+~P24(f332(f332(f334(f874(x88601,x88601)),x88602),f332(f174(f874(x88601,x88601)),f332(f332(f184(x88601,x88601),x88603),x88604)))) % 165.28/165.05 [8908]P24(f332(f332(f334(f874(f869(x89081),f869(x89081))),f332(f332(f267(f869(x89081),f869(x89081)),x89082),x89083)),f148(x89081,x89084)))+~E(f332(f332(f177(x89081),f332(f197(f869(x89081)),x89082)),x89083),x89082)+~P24(f332(f332(f247(a868),f332(f197(f869(x89081)),x89082)),f332(f197(f869(x89081)),x89083))) % 165.28/165.05 [9002]~P24(f332(f62(x90021),x90024))+P24(f332(f332(f334(x90021),f465(x90022,x90023,x90024,x90021)),x90024))+P24(f332(f62(x90023),f332(f332(f42(x90021,f875(x90023,a862)),x90024),x90022))) % 165.28/165.05 [9003]~P24(f332(f62(x90031),x90034))+P24(f332(f332(f334(x90031),f481(x90032,x90033,x90034,x90031)),x90034))+P24(f332(f62(x90033),f332(f332(f42(x90031,f875(x90033,a862)),x90034),x90032))) % 165.28/165.05 [9085]P24(f332(f332(f334(f874(x90851,x90851)),x90852),f332(f332(f289(x90851,x90851,x90851),x90853),f308(x90851,x90853))))+~P24(f332(f332(f247(a868),f2(a868)),x90854))+~P24(f332(f332(f334(f874(x90851,x90851)),x90852),f332(f332(f191(f874(x90851,x90851),a862),x90854),x90853))) % 165.28/165.05 [9093]~P41(x90931,x90932)+~P24(f332(f332(f334(f874(x90931,x90931)),f332(f332(f267(x90931,x90931),x90934),x90933)),x90932))+~P24(f332(f332(f334(f874(x90931,x90931)),f332(f332(f267(x90931,x90931),x90933),x90934)),x90932)) % 165.28/165.05 [9211]~P24(f332(f62(x92111),x92114))+E(f332(f332(f6(x92111,a868),f332(f332(f8(f875(x92112,a862),a868,x92111),f38(x92112)),x92113)),x92114),f332(f38(f874(x92111,x92112)),f332(f332(f269(x92111,x92112),x92114),x92113)))+P24(f332(f332(f334(x92111),f577(x92113,x92112,x92114,x92111)),x92114)) % 165.28/165.05 [9215]~P24(f332(f138(x92151),x92152))+P24(f332(f138(x92151),f332(f332(f160(x92151,x92152),x92153),x92154)))+P24(f332(f332(f334(x92151),x92154),f332(f332(f22(f875(x92151,a862)),f332(f174(x92151),x92152)),f332(f332(f310(x92151),f332(f332(f166(x92151),x92152),x92153)),f196(f875(x92151,a862)))))) % 165.28/165.05 [9228]~P24(f332(f62(x92282),x92283))+~P24(f332(f62(x92281),f332(x92284,f465(x92284,x92281,x92283,x92282))))+P24(f332(f62(x92281),f332(f332(f42(x92282,f875(x92281,a862)),x92283),x92284))) % 165.28/165.05 [9229]~P24(f332(f62(x92292),x92293))+~P24(f332(f62(x92291),f332(x92294,f481(x92294,x92291,x92293,x92292))))+P24(f332(f62(x92291),f332(f332(f42(x92292,f875(x92291,a862)),x92293),x92294))) % 165.28/165.05 [9305]~P24(f332(f332(f334(f874(x93051,x93051)),x93052),f332(f332(f289(x93051,x93051,x93051),x93054),f308(x93051,x93054))))+P24(f332(f332(f334(f874(x93051,x93051)),x93052),f332(f332(f289(x93051,x93051,x93051),x93053),f308(x93051,x93053))))+~P24(f332(f332(f246(f875(f874(x93051,x93051),a862)),x93054),x93053)) % 165.28/165.05 [9312]E(f332(f332(f177(x93121),f542(x93124,x93123,x93122,x93121)),x93123),f332(f332(f177(x93121),f542(x93124,x93123,x93122,x93121)),x93122))+~P24(f332(f332(f334(f874(f869(x93121),f869(x93121))),f332(f332(f267(f869(x93121),f869(x93121)),x93122),x93123)),f148(x93121,x93124)))+E(f332(f332(f177(x93121),f332(f197(f869(x93121)),x93122)),x93123),x93122) % 165.28/165.05 [9328]~P24(f332(f62(x93281),x93284))+E(f332(f332(f6(x93281,a868),f332(f332(f8(f875(x93282,a862),a868,x93281),f38(x93282)),x93283)),x93284),f332(f38(f874(x93281,x93282)),f332(f332(f269(x93281,x93282),x93284),x93283)))+~P24(f332(f62(x93282),f332(x93283,f577(x93283,x93282,x93284,x93281)))) % 165.28/165.05 [9331]~E(f332(f197(f869(x93311)),x93313),f332(f197(f869(x93311)),x93312))+P24(f332(f332(f334(f874(f869(x93311),f869(x93311))),f332(f332(f267(f869(x93311),f869(x93311)),x93312),x93313)),f159(x93311,x93314)))+P24(f332(f332(f334(f874(x93311,x93311)),f543(x93314,x93313,x93312,x93311)),f332(f174(f874(x93311,x93311)),f332(f332(f184(x93311,x93311),x93312),x93313)))) % 165.28/165.05 [9407]~P24(f332(f332(f334(f874(f869(x94071),f869(x94071))),f332(f332(f267(f869(x94071),f869(x94071)),x94072),x94073)),f148(x94071,x94074)))+E(f332(f332(f177(x94071),f332(f197(f869(x94071)),x94072)),x94073),x94072)+P24(f332(f332(f247(a868),f542(x94074,x94073,x94072,x94071)),f332(f332(f244(a868),f332(f197(f869(x94071)),x94072)),f332(f197(f869(x94071)),x94073)))) % 165.28/165.05 [9408]E(f332(f180(x94081,x94082),x94083),f332(f180(x94081,x94082),x94084))+~E(f332(f174(x94081),f332(f332(f155(f874(x94081,x94082),x94081),f266(x94081,x94082)),x94083)),f332(f174(x94081),f332(f332(f155(f874(x94081,x94082),x94081),f266(x94081,x94082)),x94084)))+P24(f332(f332(f334(x94081),f687(x94083,x94084,x94082,x94081)),f332(f174(x94081),f332(f332(f155(f874(x94081,x94082),x94081),f266(x94081,x94082)),x94084)))) % 165.28/165.05 [9428]~P24(f332(f332(f334(f874(f869(x94281),f869(x94281))),f332(f332(f267(f869(x94281),f869(x94281)),x94282),x94283)),f148(x94281,x94284)))+P24(f332(f332(f247(a868),f332(f197(f869(x94281)),x94282)),f332(f197(f869(x94281)),x94283)))+P24(f332(f332(f247(a868),f542(x94284,x94283,x94282,x94281)),f332(f332(f244(a868),f332(f197(f869(x94281)),x94282)),f332(f197(f869(x94281)),x94283)))) % 165.28/165.05 [9723]~P24(f332(f332(f332(x97231,f508(x97231,x97234,x97233,x97232)),f509(x97231,x97234,x97233,x97232)),f510(x97231,x97234,x97233,x97232)))+P24(f332(f332(f332(x97231,x97232),x97233),x97234))+~P24(f332(f320(f874(f875(a1,f872(f869(a328))),f874(a1,a1)),a318),f332(f332(f267(f875(a1,f872(f869(a328))),f874(a1,a1)),x97232),f332(f332(f267(a1,a1),x97233),x97234)))) % 165.28/165.05 [9801]P24(f332(f332(f332(x98011,x98012),x98013),x98014))+P24(f332(f320(f874(f875(a1,f872(f869(a328))),f874(a1,a1)),a318),f332(f332(f267(f875(a1,f872(f869(a328))),f874(a1,a1)),f508(x98011,x98014,x98013,x98012)),f332(f332(f267(a1,a1),f509(x98011,x98014,x98013,x98012)),f510(x98011,x98014,x98013,x98012)))))+~P24(f332(f320(f874(f875(a1,f872(f869(a328))),f874(a1,a1)),a318),f332(f332(f267(f875(a1,f872(f869(a328))),f874(a1,a1)),x98012),f332(f332(f267(a1,a1),x98013),x98014)))) % 165.28/165.05 [9841]~P24(f332(f332(f334(f874(f869(x98411),f869(x98411))),f332(f332(f267(f869(x98411),f869(x98411)),x98412),x98413)),f148(x98411,x98414)))+E(f332(f332(f177(x98411),f332(f197(f869(x98411)),x98412)),x98413),x98412)+P24(f332(f332(f334(f874(x98411,x98411)),f332(f332(f267(x98411,x98411),f332(f332(f166(x98411),x98412),f542(x98414,x98413,x98412,x98411))),f332(f332(f166(x98411),x98413),f542(x98414,x98413,x98412,x98411)))),x98414)) % 165.28/165.05 [9842]~P24(f332(f332(f334(f874(f869(x98421),f869(x98421))),f332(f332(f267(f869(x98421),f869(x98421)),x98422),x98423)),f148(x98421,x98424)))+P24(f332(f332(f247(a868),f332(f197(f869(x98421)),x98422)),f332(f197(f869(x98421)),x98423)))+P24(f332(f332(f334(f874(x98421,x98421)),f332(f332(f267(x98421,x98421),f332(f332(f166(x98421),x98422),f542(x98424,x98423,x98422,x98421))),f332(f332(f166(x98421),x98423),f542(x98424,x98423,x98422,x98421)))),x98424)) % 165.28/165.05 [9899]~E(f332(f197(f869(x98991)),x98992),f332(f197(f869(x98991)),x98993))+P24(f332(f332(f334(f874(f869(x98991),f869(x98991))),f332(f332(f267(f869(x98991),f869(x98991)),x98992),x98993)),f159(x98991,x98994)))+~P24(f332(f332(f334(f874(x98991,x98991)),f332(f332(f267(x98991,x98991),f332(f332(f166(x98991),x98992),f541(x98994,x98993,x98992,x98991))),f332(f332(f166(x98991),x98993),f541(x98994,x98993,x98992,x98991)))),x98994)) % 165.28/165.05 [10033]~P74(x100331)+~P24(f332(f62(x100332),x100334))+E(f332(f167(x100331),f332(f332(f155(x100332,x100331),x100333),f91(f869(x100332),f332(f332(f18(f869(x100332),a862,a862),f332(f332(f8(a862,f875(a862,a862),f869(x100332)),a330),f332(f332(f7(f869(x100332),f875(x100332,a862),a862),f332(f332(f8(f875(x100332,a862),f875(f875(x100332,a862),a862),f869(x100332)),a329),f174(x100332))),x100334))),f138(x100332))))),f238(x100332,x100331,x100333,x100334)) % 165.28/165.05 [7376]~P60(x73762)+E(x73761,f2(x73762))+E(f332(f332(f290(x73762),f332(f332(f81(x73762),x73763),f332(f332(f82(x73762),x73764),x73761))),x73761),f332(f332(f81(x73762),x73764),f332(f332(f290(x73762),x73763),x73761))) % 165.28/165.05 [7377]~P28(x73772)+E(x73771,f2(x73772))+E(f332(f332(f39(x73772),f332(f332(f81(x73772),x73773),f332(f332(f82(x73772),x73774),x73771))),x73771),f332(f332(f81(x73772),x73774),f332(f332(f39(x73772),x73773),x73771))) % 165.28/165.05 [7378]~P28(x73782)+E(x73781,f2(x73782))+E(f332(f332(f39(x73782),f332(f332(f81(x73782),x73783),f332(f332(f82(x73782),x73781),x73784))),x73781),f332(f332(f81(x73782),x73784),f332(f332(f39(x73782),x73783),x73781))) % 165.28/165.05 [7612]~P61(x76122)+E(x76121,f2(x76122))+E(f332(f332(f290(x76122),f332(f332(f22(x76122),x76123),f332(f332(f82(x76122),x76121),x76124))),x76121),f332(f332(f22(x76122),f332(f332(f290(x76122),x76123),x76121)),x76124)) % 165.28/165.05 [7613]~P60(x76132)+E(x76131,f2(x76132))+E(f332(f332(f290(x76132),f332(f332(f81(x76132),x76133),f332(f332(f82(x76132),x76134),x76131))),x76131),f332(f332(f81(x76132),f332(f332(f290(x76132),x76133),x76131)),x76134)) % 165.28/165.05 [7614]~P61(x76142)+E(x76141,f2(x76142))+E(f332(f332(f290(x76142),f332(f332(f81(x76142),x76143),f332(f332(f82(x76142),x76141),x76144))),x76141),f332(f332(f81(x76142),f332(f332(f290(x76142),x76143),x76141)),x76144)) % 165.28/165.05 [8307]~P24(f332(f161(x83071,x83073),x83074))+~P24(f332(f161(x83071,x83072),x83074))+P24(f332(f161(x83071,f332(f332(f104(f875(x83071,a862)),x83072),x83073)),x83074)) % 165.28/165.05 [8663]~E(f332(f332(f289(x86631,x86631,x86631),x86632),x86634),f196(f875(f874(x86631,x86631),a862)))+~E(f332(f332(f289(x86631,x86631,x86631),x86632),x86633),f196(f875(f874(x86631,x86631),a862)))+E(f332(f332(f289(x86631,x86631,x86631),x86632),f332(f332(f113(f875(f874(x86631,x86631),a862)),x86633),x86634)),f196(f875(f874(x86631,x86631),a862))) % 165.28/165.05 [8780]~P24(f332(f332(f246(f875(x87801,a862)),x87803),x87804))+~P24(f332(f332(f246(f875(x87801,a862)),x87802),x87804))+P24(f332(f332(f246(f875(x87801,a862)),f332(f332(f113(f875(x87801,a862)),x87802),x87803)),x87804)) % 165.28/165.05 [9146]~P24(f332(f62(x91461),x91464))+~P24(f332(f62(x91461),x91463))+E(f332(f332(f22(a868),f332(f332(f81(a868),f332(f332(f6(x91461,a868),x91462),x91463)),f332(f332(f6(x91461,a868),x91462),x91464))),f332(f332(f6(x91461,a868),x91462),f332(f332(f104(f875(x91461,a862)),x91463),x91464))),f332(f332(f6(x91461,a868),x91462),f332(f332(f113(f875(x91461,a862)),x91463),x91464))) % 165.28/165.05 [9225]~P24(f332(f332(f334(x92251),x92253),x92252))+~P24(f332(f332(f246(f875(x92251,a862)),x92252),f332(f332(f310(x92251),x92253),x92254)))+P24(f332(f332(f246(f875(x92251,a862)),f332(f332(f22(f875(x92251,a862)),x92252),f332(f332(f310(x92251),x92253),f196(f875(x92251,a862))))),x92254)) % 165.28/165.05 [9380]~P24(f332(f332(f334(x93801),x93803),x93802))+P24(f332(f332(f246(f875(x93801,a862)),x93802),f332(f332(f310(x93801),x93803),x93804)))+~P24(f332(f332(f246(f875(x93801,a862)),f332(f332(f22(f875(x93801,a862)),x93802),f332(f332(f310(x93801),x93803),f196(f875(x93801,a862))))),x93804)) % 165.28/165.05 [9465]~P24(f332(f332(f246(a868),x94651),x94653))+~P24(f332(f332(f247(a868),x94652),x94654))+P24(f332(f332(f334(f874(f874(a868,a868),f874(a868,a868))),f332(f332(f267(f874(a868,a868),f874(a868,a868)),f332(f332(f267(a868,a868),x94651),x94652)),f332(f332(f267(a868,a868),x94653),x94654))),a36)) % 165.28/165.05 [9466]~P24(f332(f332(f246(a868),x94662),x94664))+~P24(f332(f332(f246(a868),x94661),x94663))+P24(f332(f332(f334(f874(f874(a868,a868),f874(a868,a868))),f332(f332(f267(f874(a868,a868),f874(a868,a868)),f332(f332(f267(a868,a868),x94661),x94662)),f332(f332(f267(a868,a868),x94663),x94664))),a71)) % 165.28/165.05 [9763]~P24(f332(f332(f334(f869(x97631)),x97634),f162(x97631,x97633)))+~P24(f332(f332(f334(f869(x97631)),x97634),f162(x97631,x97632)))+P24(f332(f161(x97631,f332(f332(f104(f875(x97631,a862)),f332(f332(f7(x97631,f875(x97631,a862),a862),f334(x97631)),x97632)),f332(f332(f7(x97631,f875(x97631,a862),a862),f334(x97631)),x97633))),x97634)) % 165.28/165.05 [9864]~P21(x98641,f875(f875(x98641,a862),a862),f332(f332(f7(x98641,f875(f874(x98641,x98641),a862),f875(f875(x98641,a862),a862)),f332(f332(f8(f875(x98641,a862),f875(f875(f874(x98641,x98641),a862),f875(f875(x98641,a862),a862)),x98641),f61(x98641)),f332(f332(f7(x98641,f875(x98641,a862),f875(x98641,a862)),f310(x98641)),f196(f875(x98641,a862))))),x98643),x98642)+~P24(f332(f332(f334(x98641),x98644),x98642))+E(f332(f332(f22(f875(f875(x98641,a862),a862)),f332(f332(f61(x98641),x98642),x98643)),f332(f332(f61(x98641),f332(f332(f310(x98641),x98644),f196(f875(x98641,a862)))),x98643)),f332(f332(f61(x98641),f332(f332(f22(f875(x98641,a862)),x98642),f332(f332(f310(x98641),x98644),f196(f875(x98641,a862))))),x98643)) % 165.28/165.05 [9998]~P43(x99981,x99982,x99984)+~P24(f332(f332(f334(f874(x99981,x99981)),x99983),x99984))+P24(f332(f332(f271(x99981,x99981,a862),f332(f332(f7(x99981,f875(x99981,a862),f875(x99981,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x99981,a862),f875(x99981,a862)),x99981),f8(a862,a862,x99981)),f332(f332(f8(a862,f875(a862,a862),x99981),a330),f332(f332(f7(x99981,f875(x99981,a862),a862),f334(x99981)),x99982)))),f332(f332(f7(x99981,f875(x99981,a862),a862),f334(x99981)),x99982))),x99983)) % 165.28/165.05 [10010]P24(f332(f62(x100101),x100102))+~P24(f332(f62(x100103),f332(f311(x100101,x100103,x100104),x100102)))+~P24(f332(f62(x100101),f332(f252(x100101),f332(f332(f18(x100101,a862,a862),f332(f332(f8(a862,f875(a862,a862),x100101),a330),f332(f332(f7(x100101,f875(x100101,a862),a862),f334(x100101)),x100102))),f332(f332(f7(x100101,x100103,a862),f332(f332(f8(x100103,f875(x100103,a862),x100101),a329),x100104)),f332(x100104,f466(x100104,x100103,x100102,x100101))))))) % 165.28/165.05 [8063]~P61(x80632)+E(x80631,f2(x80632))+E(f332(f332(f290(x80632),f332(f332(f22(x80632),f332(f332(f82(x80632),x80631),x80633)),x80634)),x80631),f332(f332(f22(x80632),x80633),f332(f332(f290(x80632),x80634),x80631))) % 165.28/165.05 [8064]~P61(x80642)+E(x80641,f2(x80642))+E(f332(f332(f290(x80642),f332(f332(f81(x80642),f332(f332(f82(x80642),x80641),x80643)),x80644)),x80641),f332(f332(f81(x80642),x80643),f332(f332(f290(x80642),x80644),x80641))) % 165.28/165.05 [8936]~E(f332(f332(f289(x89361,x89361,x89361),x89363),x89364),f196(f875(f874(x89361,x89361),a862)))+~E(f332(f332(f289(x89361,x89361,x89361),x89362),x89364),f196(f875(f874(x89361,x89361),a862)))+E(f332(f332(f289(x89361,x89361,x89361),f332(f332(f113(f875(f874(x89361,x89361),a862)),x89362),x89363)),x89364),f196(f875(f874(x89361,x89361),a862))) % 165.28/165.05 [9941]~P143(x99411)+~P143(x99412)+E(f332(f332(f317(x99411),f332(f332(f7(x99411,a102,f872(f869(a328))),f332(f332(f8(f875(x99412,f872(f869(a328))),f875(a102,f872(f869(a328))),x99411),f317(x99412)),f332(f332(f8(f875(x99412,f874(x99411,x99412)),f875(x99412,f872(f869(a328))),x99411),f332(f8(f874(x99411,x99412),f872(f869(a328)),x99412),x99413)),f267(x99411,x99412)))),x99414)),x99414),f332(f332(f317(f874(x99411,x99412)),x99413),x99414)) % 165.28/165.05 [9671]~P24(f332(f161(x96711,x96713),x96714))+~P24(f332(f161(x96711,x96712),x96714))+P24(f332(f161(x96711,f332(f332(f18(x96711,a862,a862),f332(f332(f8(a862,f875(a862,a862),x96711),a330),x96712)),x96713)),x96714)) % 165.28/165.05 [9933]P24(f332(x99331,f433(x99332,x99333,x99331,x99334)))+~P24(f332(f62(x99334),f332(f252(x99334),x99331)))+P24(f332(f62(x99333),f332(f252(x99333),f332(f332(f8(f875(x99334,a862),a862,x99333),f88(x99334)),f332(f332(f8(f875(x99334,a862),f875(x99334,a862),x99333),f332(f18(x99334,a862,a862),f332(f332(f8(a862,f875(a862,a862),x99334),a330),x99331))),x99332))))) % 165.28/165.05 [9954]~P24(f332(f62(x99542),f332(f252(x99542),x99543)))+~P24(f332(f62(x99541),f332(f252(x99541),f332(f332(f7(x99541,x99542,a862),x99544),f433(x99544,x99541,x99543,x99542)))))+P24(f332(f62(x99541),f332(f252(x99541),f332(f332(f8(f875(x99542,a862),a862,x99541),f88(x99542)),f332(f332(f8(f875(x99542,a862),f875(x99542,a862),x99541),f332(f18(x99542,a862,a862),f332(f332(f8(a862,f875(a862,a862),x99542),a330),x99543))),x99544))))) % 165.28/165.05 [5014]~E(x50142,x50144)+E(f171(x50141,x50142,x50143),f171(x50141,x50144,x50145))+~E(x50142,f2(a868)) % 165.28/165.05 [5280]E(x52801,x52802)+~E(f171(x52804,x52803,x52801),f171(x52804,x52805,x52802))+E(x52803,f2(a868)) % 165.28/165.05 [6525]E(x65251,x65252)+~E(f332(x65253,x65251),f332(x65253,x65252))+~P21(x65254,x65255,x65253,f255(f875(x65254,a862))) % 165.28/165.05 [6683]~E(f332(x66833,x66835),f209(x66832))+~E(f332(x66834,x66835),f209(x66832))+E(f332(f187(x66831,x66832,x66833,x66834),x66835),f209(x66832)) % 165.28/165.05 [7412]E(x74121,x74122)+~P21(x74123,x74124,x74125,f255(f875(x74123,a862)))+~E(f332(f311(x74123,x74124,x74125),x74121),f332(f311(x74123,x74124,x74125),x74122)) % 165.28/165.05 [7666]P21(x76662,x76663,f736(x76664,x76663,x76662,x76661),x76661)+~E(f332(f311(x76663,x76662,x76665),x76664),x76661)+E(x76661,f196(f875(x76662,a862))) % 165.28/165.05 [8197]~P24(f332(f332(x81973,x81972),x81975))+~P24(f332(f332(x81973,x81974),x81972))+P24(f332(f332(f334(x81971),x81972),f296(x81971,x81973,x81974,x81975))) % 165.28/165.05 [8198]~P24(f332(f332(x81983,x81982),x81985))+~P24(f332(f332(x81983,x81984),x81982))+P24(f332(f332(f334(x81981),x81982),f299(x81981,x81983,x81984,x81985))) % 165.28/165.05 [8738]~P21(x87381,x87383,x87385,f255(f875(x87381,a862)))+~P21(x87383,x87382,x87384,f255(f875(x87383,a862)))+P21(x87381,x87382,f332(f74(x87383,x87382,x87381,x87384),x87385),f255(f875(x87381,a862))) % 165.28/165.05 [9282]P24(f332(f332(f334(f874(x92821,x92821)),f332(f332(f267(x92821,x92821),x92822),x92823)),f308(x92821,x92824)))+~P24(f332(f332(f334(f874(x92821,x92821)),f332(f332(f267(x92821,x92821),x92822),x92825)),f308(x92821,x92824)))+~P24(f332(f332(f334(f874(x92821,x92821)),f332(f332(f267(x92821,x92821),x92825),x92823)),f308(x92821,x92824))) % 165.28/165.05 [9319]~P106(x93192)+~P24(f332(f138(x93191),x93195))+P24(f332(f138(x93191),f150(x93191,x93192,x93193,x93194,x93195))) % 165.28/165.05 [5351]~E(x53512,f116(x53511))+E(f332(f332(f135(x53511),x53512),x53513),f332(f332(f152(x53511),x53514),x53515))+~E(x53513,f332(f332(f152(x53511),x53514),x53515)) % 165.28/165.05 [5352]~E(x53522,f116(x53521))+E(f332(f332(f135(x53521),x53522),x53523),f332(f332(f152(x53521),x53524),x53525))+~E(f332(f332(f152(x53521),x53524),x53525),x53523) % 165.28/165.05 [6481]~E(f332(f197(f869(x64811)),x64815),f332(f197(f869(x64812)),x64814))+E(f332(f332(f155(f874(x64811,x64812),x64812),f270(x64811,x64812)),x64813),x64814)+~E(f332(f332(f184(x64811,x64812),x64815),x64814),x64813) % 165.28/165.05 [6482]~E(f332(f197(f869(x64821)),x64824),f332(f197(f869(x64822)),x64825))+E(f332(f332(f155(f874(x64821,x64822),x64821),f266(x64821,x64822)),x64823),x64824)+~E(f332(f332(f184(x64821,x64822),x64824),x64825),x64823) % 165.28/165.05 [6954]~P106(x69541)+~P32(x69541,f332(f332(f155(x69542,x69541),x69543),x69545))+P32(x69541,f332(f332(f155(x69542,x69541),x69543),f332(f137(x69542,x69544),x69545))) % 165.28/165.05 [6999]~P24(f332(x69993,x69995))+~P24(f332(f332(x69992,x69994),x69995))+P24(f332(f332(f95(x69991,x69992,x69993),x69994),x69995)) % 165.28/165.05 [7096]~P106(x70961)+P32(x70961,f332(f332(f155(x70962,x70961),x70963),f172(x70962,x70964,x70965)))+~P32(x70961,f332(f332(f155(x70962,x70961),x70963),x70965)) % 165.28/165.05 [7119]~P53(x71193,x71192,x71195)+~P53(x71191,x71193,x71194)+P53(x71191,x71192,f332(f332(f289(x71191,x71193,x71192),x71194),x71195)) % 165.28/165.05 [7211]E(x72111,x72112)+~P21(x72113,x72114,x72115,f255(f875(x72113,a862)))+~E(f332(f332(f155(x72113,x72114),x72115),x72111),f332(f332(f155(x72113,x72114),x72115),x72112)) % 165.28/165.05 [7362]~P24(f332(f332(f246(a868),x73621),f332(x73623,x73625)))+P24(f332(f332(f246(a868),x73621),f156(x73622,x73623,x73624)))+~P24(f332(f332(f334(x73622),x73625),f332(f174(x73622),x73624))) % 165.28/165.05 [7363]~P24(f332(f332(f247(a868),x73631),f332(x73633,x73635)))+P24(f332(f332(f247(a868),x73631),f156(x73632,x73633,x73634)))+~P24(f332(f332(f334(x73632),x73635),f332(f174(x73632),x73634))) % 165.28/165.05 [7765]P24(f332(x77651,x77652))+~P24(f332(x77651,x77653))+~P24(f332(f332(f334(x77654),x77652),f332(f174(x77654),f171(x77654,x77655,x77653)))) % 165.28/165.05 [7766]P24(f332(x77661,x77662))+~P24(f332(x77661,x77663))+~P24(f332(f332(f334(x77664),x77663),f332(f174(x77664),f171(x77664,x77665,x77662)))) % 165.28/165.05 [7770]~P107(x77701)+P24(f332(f332(f246(f875(x77701,a862)),f303(x77701,x77702,x77703)),f303(x77701,x77704,x77705)))+P24(f332(f332(f246(x77701),x77702),x77703)) % 165.28/165.05 [7791]~P30(x77911)+P24(f332(f332(f246(x77911),f332(f332(f43(x77912,x77911),x77913),x77914)),f332(x77914,x77915)))+~P24(f332(f332(f334(x77912),x77915),x77913)) % 165.28/165.05 [7858]~P21(x78581,x78582,x78584,x78583)+E(f332(f78(x78581,x78582,x78583,x78584),f332(x78584,x78585)),x78585)+~P24(f332(f332(f334(x78581),x78585),x78583)) % 165.28/165.05 [8052]~P24(f332(x80521,x80525))+P24(f332(x80521,f860(x80521,x80522,x80523,x80524)))+~P24(f332(f332(f334(x80524),x80525),x80523)) % 165.28/165.05 [8053]~P24(f332(x80531,x80535))+P24(f332(x80531,f860(x80531,x80532,x80533,x80534)))+~P24(f332(f332(f334(x80534),x80535),x80532)) % 165.28/165.05 [8148]P24(f332(f62(x81481),x81482))+~P24(f332(f62(x81483),x81484))+~P24(f332(f332(f246(f875(x81481,a862)),x81482),f332(f311(x81483,x81481,x81485),x81484))) % 165.28/165.05 [8311]E(x83111,x83112)+~P21(x83113,x83114,x83115,f332(f332(f113(f875(x83113,a862)),f332(f174(x83113),x83111)),f332(f174(x83113),x83112)))+~E(f332(f332(f155(x83113,x83114),x83115),x83111),f332(f332(f155(x83113,x83114),x83115),x83112)) % 165.28/165.05 [8365]~P107(x83651)+~P24(f332(f332(f247(f875(x83651,a862)),f303(x83651,x83654,x83655)),f303(x83651,x83652,x83653)))+P24(f332(f332(f246(x83651),x83652),x83653)) % 165.28/165.05 [8427]~P21(x84271,x84274,x84275,f255(f875(x84271,a862)))+~P24(f332(f332(f334(x84274),f332(x84275,x84272)),f332(f311(x84271,x84274,x84275),x84273)))+P24(f332(f332(f334(x84271),x84272),x84273)) % 165.28/165.05 [8498]P24(f332(x84981,x84982))+~P24(f332(x84981,f352(x84981,x84983,x84984,x84985)))+~P24(f332(f332(f334(x84985),x84982),x84984)) % 165.28/165.05 [8499]P24(f332(x84991,x84992))+~P24(f332(x84991,f352(x84991,x84993,x84994,x84995)))+~P24(f332(f332(f334(x84995),x84992),x84993)) % 165.28/165.05 [8777]~P21(x87772,x87773,x87771,x87774)+E(f332(x87771,f332(f78(x87772,x87773,x87774,x87771),x87775)),x87775)+~P24(f332(f332(f334(x87773),x87775),f332(f311(x87772,x87773,x87771),x87774))) % 165.28/165.05 [8881]E(x88811,f116(x88812))+E(f332(f332(f152(x88812),x88813),f583(x88814,x88813,x88815,x88811,x88812)),x88811)+~E(f332(f332(f135(x88812),x88811),x88815),f332(f332(f152(x88812),x88813),x88814)) % 165.28/165.05 [8882]E(x88821,f116(x88822))+E(f332(f332(f152(x88822),x88823),f584(x88824,x88821,x88825,x88823,x88822)),x88821)+~E(f332(f332(f135(x88822),x88821),x88824),f332(f332(f152(x88822),x88823),x88825)) % 165.28/165.05 [8897]E(f332(f332(f152(x88972),x88973),f583(x88974,x88973,x88971,x88975,x88972)),x88975)+~E(f332(f332(f135(x88972),x88975),x88971),f332(f332(f152(x88972),x88973),x88974))+E(x88971,f332(f332(f152(x88972),x88973),x88974)) % 165.28/165.05 [8898]E(f332(f332(f152(x88981),x88982),f584(x88984,x88985,x88983,x88982,x88981)),x88985)+~E(f332(f332(f135(x88981),x88985),x88984),f332(f332(f152(x88981),x88982),x88983))+E(f332(f332(f152(x88981),x88982),x88983),x88984) % 165.28/165.05 [8973]~E(f332(f311(x89733,x89732,x89734),f255(f875(x89733,a862))),f255(f875(x89732,a862)))+~E(f332(f311(x89731,x89733,x89735),f255(f875(x89731,a862))),f255(f875(x89733,a862)))+E(f332(f311(x89731,x89732,f332(f74(x89733,x89732,x89731,x89734),x89735)),f255(f875(x89731,a862))),f255(f875(x89732,a862))) % 165.28/165.05 [9325]E(x93251,f116(x93252))+~E(f332(f332(f135(x93252),x93251),x93253),f332(f332(f152(x93252),x93255),x93254))+E(f332(f332(f135(x93252),f584(x93253,x93251,x93254,x93255,x93252)),x93253),x93254) % 165.28/165.05 [9326]E(x93261,f116(x93262))+~E(f332(f332(f135(x93262),x93261),x93265),f332(f332(f152(x93262),x93264),x93263))+E(f332(f332(f135(x93262),f583(x93263,x93264,x93265,x93261,x93262)),x93265),x93263) % 165.28/165.05 [9332]E(f332(f332(f135(x93322),f583(x93324,x93323,x93321,x93325,x93322)),x93321),x93324)+~E(f332(f332(f135(x93322),x93325),x93321),f332(f332(f152(x93322),x93323),x93324))+E(x93321,f332(f332(f152(x93322),x93323),x93324)) % 165.28/165.05 [9333]~E(f332(f332(f135(x93331),x93335),x93334),f332(f332(f152(x93331),x93332),x93333))+E(f332(f332(f135(x93331),f584(x93334,x93335,x93333,x93332,x93331)),x93334),x93333)+E(f332(f332(f152(x93331),x93332),x93333),x93334) % 165.28/165.05 [9334]E(f332(f332(f135(x93341),x93345),f586(x93343,x93342,x93344,x93345,x93341)),x93342)+E(f332(f332(f135(x93341),x93342),f585(x93343,x93342,x93344,x93345,x93341)),x93345)+~E(f332(f332(f135(x93341),x93345),x93344),f332(f332(f135(x93341),x93342),x93343)) % 165.28/165.05 [9366]~P106(x93661)+P32(x93661,f332(f332(f155(x93662,x93661),x93663),f150(x93662,x93661,x93663,x93664,x93665)))+~P32(x93661,f332(f332(f155(x93662,x93661),x93663),x93665)) % 165.28/165.05 [9377]~P57(x93775,x93771,x93774,x93773)+P24(f332(f332(x93771,x93772),f666(x93773,x93774,x93771,x93775,x93772)))+~P24(f332(f332(f334(x93775),x93772),x93774)) % 165.28/165.05 [9477]~P24(f332(f332(f334(f874(x94771,x94771)),f332(f332(f267(x94771,x94771),x94775),x94773)),f308(x94771,x94774)))+P24(f332(f332(f334(f874(x94771,x94771)),f332(f332(f267(x94771,x94771),x94772),x94773)),f332(f332(f289(x94771,x94771,x94771),x94774),f308(x94771,x94774))))+~P24(f332(f332(f334(f874(x94771,x94771)),f332(f332(f267(x94771,x94771),x94772),x94775)),f332(f332(f289(x94771,x94771,x94771),x94774),f308(x94771,x94774)))) % 165.28/165.05 [9478]~P24(f332(f332(f334(f874(x94781,x94781)),f332(f332(f267(x94781,x94781),x94782),x94785)),f308(x94781,x94784)))+P24(f332(f332(f334(f874(x94781,x94781)),f332(f332(f267(x94781,x94781),x94782),x94783)),f332(f332(f289(x94781,x94781,x94781),x94784),f308(x94781,x94784))))+~P24(f332(f332(f334(f874(x94781,x94781)),f332(f332(f267(x94781,x94781),x94785),x94783)),f332(f332(f289(x94781,x94781,x94781),x94784),f308(x94781,x94784)))) % 165.28/165.05 [9481]P24(f332(f332(f334(f874(f869(x94811),f869(x94811))),f332(f332(f267(f869(x94811),f869(x94811)),x94812),x94813)),f159(x94811,f308(x94811,x94814))))+~P24(f332(f332(f334(f874(f869(x94811),f869(x94811))),f332(f332(f267(f869(x94811),f869(x94811)),x94812),x94815)),f159(x94811,f308(x94811,x94814))))+~P24(f332(f332(f334(f874(f869(x94811),f869(x94811))),f332(f332(f267(f869(x94811),f869(x94811)),x94815),x94813)),f159(x94811,f308(x94811,x94814)))) % 165.28/165.05 [9485]E(f332(f332(f135(x94851),x94852),f585(x94853,x94852,x94854,x94855,x94851)),x94855)+E(f332(f332(f135(x94851),f586(x94853,x94852,x94854,x94855,x94851)),x94853),x94854)+~E(f332(f332(f135(x94851),x94852),x94853),f332(f332(f135(x94851),x94855),x94854)) % 165.28/165.05 [9486]E(f332(f332(f135(x94861),x94862),f586(x94863,x94864,x94865,x94862,x94861)),x94864)+E(f332(f332(f135(x94861),f585(x94863,x94864,x94865,x94862,x94861)),x94865),x94863)+~E(f332(f332(f135(x94861),x94862),x94865),f332(f332(f135(x94861),x94864),x94863)) % 165.28/165.05 [9540]P24(f332(f332(f334(f874(x95401,x95401)),f332(f332(f267(x95401,x95401),x95402),x95403)),f332(f332(f289(x95401,x95401,x95401),x95404),f308(x95401,x95404))))+~P24(f332(f332(f334(f874(x95401,x95401)),f332(f332(f267(x95401,x95401),x95402),x95405)),f332(f332(f289(x95401,x95401,x95401),x95404),f308(x95401,x95404))))+~P24(f332(f332(f334(f874(x95401,x95401)),f332(f332(f267(x95401,x95401),x95405),x95403)),f332(f332(f289(x95401,x95401,x95401),x95404),f308(x95401,x95404)))) % 165.28/165.05 [9567]P38(x95671,x95672,x95673,x95674,x95675)+~E(f332(f197(f869(x95671)),x95674),f332(f197(f869(x95672)),x95675))+~P24(f332(f332(f271(x95671,x95672,a862),x95673),f646(x95675,x95674,x95673,x95672,x95671))) % 165.28/165.05 [9568]P38(x95681,x95682,x95683,x95684,x95685)+~E(f332(f197(f869(x95681)),x95684),f332(f197(f869(x95682)),x95685))+~P24(f332(f332(f271(x95681,x95682,a862),x95683),f657(x95683,x95685,x95684,x95682,x95681))) % 165.28/165.05 [9573]E(f332(f332(f135(x95731),f585(x95732,x95733,x95734,x95735,x95731)),x95734),x95732)+~E(f332(f332(f135(x95731),x95733),x95732),f332(f332(f135(x95731),x95735),x95734))+E(f332(f332(f135(x95731),f586(x95732,x95733,x95734,x95735,x95731)),x95732),x95734) % 165.28/165.05 [9588]~P106(x95882)+E(f332(f332(f149(x95881,x95882,x95883),x95884),x95885),f332(f332(f152(x95881),x95884),x95885))+P24(f332(f332(f334(x95881),f703(x95884,x95883,x95885,x95881,x95882)),f332(f174(x95881),x95885))) % 165.28/165.05 [9593]~P57(x95931,x95934,x95933,x95932)+~P24(f332(f332(f334(x95931),x95935),x95933))+P24(f332(f332(f334(x95931),f666(x95932,x95933,x95934,x95931,x95935)),x95932)) % 165.28/165.05 [9714]~P24(f332(f332(f334(f874(f875(x97141,a862),f875(x97141,a862))),f332(f332(f267(f875(x97141,a862),f875(x97141,a862)),x97144),x97143)),f323(x97141,x97142)))+~P24(f332(f332(f334(x97141),x97145),x97144))+P24(f332(f332(f334(x97141),f722(x97142,x97143,x97144,x97141,x97145)),x97143)) % 165.28/165.05 [9726]~P106(x97262)+E(f332(f332(f149(x97261,x97262,x97263),x97264),x97265),f332(f332(f152(x97261),x97264),x97265))+~P24(f332(f332(f246(x97262),f332(x97263,x97264)),f332(x97263,f703(x97264,x97263,x97265,x97261,x97262)))) % 165.28/165.05 [9916]P38(x99161,x99162,x99163,x99164,x99165)+~E(f332(f197(f869(x99161)),x99164),f332(f197(f869(x99162)),x99165))+~P24(f332(f332(x99163,f332(f332(f166(x99161),x99164),f658(x99165,x99164,x99163,x99162,x99161))),f332(f332(f166(x99162),x99165),f658(x99165,x99164,x99163,x99162,x99161)))) % 165.28/165.05 [9917]P38(x99171,x99172,x99173,x99174,x99175)+~E(f332(f197(f869(x99171)),x99174),f332(f197(f869(x99172)),x99175))+~P24(f332(f332(x99173,f332(f332(f166(x99171),x99174),f696(x99173,x99175,x99172,x99174,x99171))),f332(f332(f166(x99172),x99175),f696(x99173,x99175,x99172,x99174,x99171)))) % 165.28/165.05 [6553]~P13(x65532,x65535,x65531)+~P24(f332(f62(x65532),x65534))+E(f332(x65531,f332(f332(f310(x65532),x65533),x65534)),f332(f332(f65(x65532,x65532,x65535),x65533),x65534)) % 165.28/165.05 [6554]~E(x65543,x65544)+~E(x65542,x65545)+E(f332(f332(f310(x65541),x65542),f332(f332(f310(x65541),x65543),f196(f875(x65541,a862)))),f332(f332(f310(x65541),x65544),f332(f332(f310(x65541),x65545),f196(f875(x65541,a862))))) % 165.28/165.05 [6564]P24(f332(x65642,x65645))+E(f179(x65641,x65642,f332(f332(f135(x65641),x65643),x65644)),f179(x65641,x65642,x65643))+~P24(f332(f332(f334(x65641),x65645),f332(f174(x65641),x65643))) % 165.28/165.05 [6601]E(f332(x66011,x66012),f196(f875(x66013,a862)))+~E(f332(f332(f42(x66014,f875(x66013,a862)),x66015),x66011),f196(f875(x66013,a862)))+~P24(f332(f332(f334(x66014),x66012),x66015)) % 165.28/165.05 [6602]E(f332(x66021,x66022),f255(f875(x66023,a862)))+~E(f332(f332(f43(x66024,f875(x66023,a862)),x66025),x66021),f255(f875(x66023,a862)))+~P24(f332(f332(f334(x66024),x66022),x66025)) % 165.28/165.05 [7106]~E(x71062,x71064)+~P123(x71061)+E(f332(f332(f81(x71061),f332(f332(f82(x71061),x71062),x71063)),f332(f332(f82(x71061),x71064),x71065)),f332(f332(f81(x71061),f332(f332(f82(x71061),x71062),x71065)),f332(f332(f82(x71061),x71064),x71063))) % 165.28/165.05 [7166]~P30(x71661)+~P24(f332(f332(f334(x71664),x71663),x71665))+P24(f332(f332(f246(x71661),f332(x71662,x71663)),f332(f332(f42(x71664,x71661),x71665),x71662))) % 165.28/165.05 [7216]~P105(x72161)+P24(f332(f332(f246(x72161),f332(x72162,x72163)),f332(x72164,x72163)))+~P24(f332(f332(f246(f875(x72165,x72161)),x72162),x72164)) % 165.28/165.05 [7331]E(x73311,x73312)+E(x73313,x73311)+~E(f332(f332(f310(x73314),x73311),f332(f332(f310(x73314),x73315),f196(f875(x73314,a862)))),f332(f332(f310(x73314),x73312),f332(f332(f310(x73314),x73313),f196(f875(x73314,a862))))) % 165.28/165.05 [7332]E(x73321,x73322)+E(x73323,x73321)+~E(f332(f332(f310(x73324),x73323),f332(f332(f310(x73324),x73322),f196(f875(x73324,a862)))),f332(f332(f310(x73324),x73325),f332(f332(f310(x73324),x73321),f196(f875(x73324,a862))))) % 165.28/165.05 [7333]E(x73331,x73332)+E(x73331,x73333)+~E(f332(f332(f310(x73334),x73333),f332(f332(f310(x73334),x73332),f196(f875(x73334,a862)))),f332(f332(f310(x73334),x73335),f332(f332(f310(x73334),x73331),f196(f875(x73334,a862))))) % 165.28/165.05 [7334]E(x73341,x73342)+E(x73341,x73343)+~E(f332(f332(f310(x73344),x73341),f332(f332(f310(x73344),x73345),f196(f875(x73344,a862)))),f332(f332(f310(x73344),x73342),f332(f332(f310(x73344),x73343),f196(f875(x73344,a862))))) % 165.28/165.05 [7868]P21(x78681,x78682,x78683,x78684)+~P21(x78681,x78682,x78683,x78685)+~P24(f332(f332(f246(f875(x78681,a862)),x78684),x78685)) % 165.28/165.05 [8042]E(x80421,x80422)+~E(f332(f311(x80423,x80424,x80425),x80421),f332(f311(x80423,x80424,x80425),x80422))+~P21(x80423,x80424,x80425,f332(f332(f113(f875(x80423,a862)),x80421),x80422)) % 165.28/165.05 [8114]P24(f332(x81142,x81144))+E(f332(f332(f139(x81141),f332(f197(f869(x81141)),f179(x81141,x81142,x81143))),x81143),f332(f332(f152(x81141),x81144),x81145))+~E(f332(f332(f135(x81141),f179(x81141,x81142,x81143)),f332(f332(f152(x81141),x81144),x81145)),x81143) % 165.28/165.05 [8145]~P21(x81451,x81452,x81453,x81455)+~P21(x81451,x81452,x81453,x81454)+P21(x81451,x81452,x81453,f332(f332(f104(f875(x81451,a862)),x81454),x81455)) % 165.28/165.05 [8254]~P74(x82541)+E(f332(f332(f81(x82541),f332(x82542,x82543)),f332(f167(x82541),f332(f332(f155(x82544,x82541),x82542),f172(x82544,x82543,x82545)))),f332(f167(x82541),f332(f332(f155(x82544,x82541),x82542),x82545)))+~P24(f332(f332(f334(x82544),x82543),f332(f174(x82544),x82545))) % 165.28/165.05 [8341]~P106(x83411)+~P32(x83411,f332(f332(f155(x83412,x83411),x83413),x83415))+P32(x83411,f332(f332(f155(x83412,x83411),x83413),f332(f332(f149(x83412,x83411,x83413),x83414),x83415))) % 165.28/165.05 [8423]~P30(x84231)+P24(f332(f332(f246(x84231),f332(f332(f42(x84232,x84231),x84233),x84234)),f332(f332(f42(x84232,x84231),x84235),x84234)))+~P24(f332(f332(f246(f875(x84232,a862)),x84233),x84235)) % 165.28/165.05 [8424]~P30(x84241)+P24(f332(f332(f246(x84241),f332(f332(f43(x84242,x84241),x84243),x84244)),f332(f332(f43(x84242,x84241),x84245),x84244)))+~P24(f332(f332(f246(f875(x84242,a862)),x84245),x84243)) % 165.28/165.05 [8455]~P106(x84553)+P24(f332(f138(x84551),x84552))+~P24(f332(f138(x84551),f332(f332(f149(x84551,x84553,x84554),x84555),x84552))) % 165.28/165.05 [8591]~P106(x85911)+~P24(f332(f332(f334(x85912),x85913),f332(f174(x85912),x85914)))+~P24(f332(f138(x85912),f332(f332(f149(x85912,x85911,x85915),x85913),x85914))) % 165.28/165.05 [8673]~P106(x86731)+P32(x86731,f332(f332(f155(x86732,x86731),x86733),x86734))+~P32(x86731,f332(f332(f155(x86732,x86731),x86733),f332(f332(f149(x86732,x86731,x86733),x86735),x86734))) % 165.28/165.05 [8765]~P106(x87652)+E(f332(f332(f149(x87651,x87652,x87653),x87654),x87655),f150(x87651,x87652,x87653,x87654,x87655))+P24(f332(f332(f334(x87652),f332(x87653,x87654)),f332(f311(x87651,x87652,x87653),f332(f174(x87651),x87655)))) % 165.28/165.05 [8839]~P106(x88392)+E(f150(x88391,x88392,x88393,x88394,x88395),x88395)+~P24(f332(f332(f334(x88392),f332(x88393,x88394)),f332(f311(x88391,x88392,x88393),f332(f174(x88391),x88395)))) % 165.28/165.05 [8853]~P21(x88532,x88531,x88533,x88535)+P24(f332(f332(f247(f875(x88531,a862)),f332(f311(x88532,x88531,x88533),x88534)),f332(f311(x88532,x88531,x88533),x88535)))+~P24(f332(f332(f247(f875(x88532,a862)),x88534),x88535)) % 165.28/165.05 [9014]~P21(x90141,x90142,x90143,f255(f875(x90141,a862)))+~P24(f332(f332(f246(f875(x90142,a862)),x90144),f332(f311(x90141,x90142,x90143),x90145)))+P24(f332(f332(f246(f875(x90141,a862)),f332(f312(x90141,x90142,x90143),x90144)),x90145)) % 165.28/165.05 [9034]~E(f332(f311(x90343,x90341,x90344),f255(f875(x90343,a862))),f255(f875(x90341,a862)))+P24(f332(f332(f246(f875(x90341,a862)),x90342),f332(f311(x90343,x90341,x90344),x90345)))+~P24(f332(f332(f246(f875(x90343,a862)),f332(f312(x90343,x90341,x90344),x90342)),x90345)) % 165.28/165.05 [9059]~E(f332(f208(x90592),x90594),f332(f332(f180(x90591,x90592),x90595),x90593))+~P24(f332(f138(x90591),f332(f332(f155(f874(x90591,x90592),x90591),f266(x90591,x90592)),x90595)))+P24(f332(f332(f334(f874(x90591,x90592)),f332(f332(f267(x90591,x90592),x90593),x90594)),f332(f174(f874(x90591,x90592)),x90595))) % 165.28/165.05 [9138]~P21(x91381,x91384,x91385,f255(f875(x91381,a862)))+~P24(f332(f332(f246(f875(x91384,a862)),f332(f311(x91381,x91384,x91385),x91382)),f332(f311(x91381,x91384,x91385),x91383)))+P24(f332(f332(f246(f875(x91381,a862)),x91382),x91383)) % 165.28/165.05 [9198]E(f332(f208(x91981),x91982),f332(f332(f180(x91983,x91981),x91984),x91985))+~P24(f332(f138(x91983),f332(f332(f155(f874(x91983,x91981),x91983),f266(x91983,x91981)),x91984)))+~P24(f332(f332(f334(f874(x91983,x91981)),f332(f332(f267(x91983,x91981),x91985),x91982)),f332(f174(f874(x91983,x91981)),x91984))) % 165.28/165.05 [9200]E(f332(f332(f180(x92001,x92002),x92003),x92004),f332(f208(x92002),x92005))+~P24(f332(f138(x92001),f332(f332(f155(f874(x92001,x92002),x92001),f266(x92001,x92002)),x92003)))+~P24(f332(f332(f334(f874(x92001,x92002)),f332(f332(f267(x92001,x92002),x92004),x92005)),f332(f174(f874(x92001,x92002)),x92003))) % 165.28/165.05 [9250]~P80(x92501)+~E(f332(x92503,f624(x92503,x92504,x92505,x92502,x92501)),f2(x92501))+E(f332(f167(x92501),f332(f332(f155(x92502,x92501),x92503),f332(f137(x92502,x92504),x92505))),f332(f167(x92501),f332(f332(f155(x92502,x92501),x92503),x92505))) % 165.28/165.05 [9423]~P12(x94231,x94232,x94233)+~P24(f332(f62(x94231),x94235))+P24(f332(f67(x94231,x94232,x94233,x94234,x94235),f332(f332(f65(x94231,x94232,x94233),x94234),x94235))) % 165.28/165.05 [9498]P24(f332(x94981,f775(x94982,x94981,x94983,x94984,x94985)))+~P24(f332(f332(f246(f875(x94985,a862)),x94984),x94983))+P24(f332(f332(f246(f875(x94985,a862)),f332(f332(f104(f875(x94985,a862)),x94984),f332(f252(x94985),x94981))),f332(f332(f104(f875(x94985,a862)),x94983),f332(f252(x94985),x94982)))) % 165.28/165.05 [9512]~P80(x95121)+~P24(f332(x95124,f624(x95123,x95124,x95125,x95122,x95121)))+E(f332(f167(x95121),f332(f332(f155(x95122,x95121),x95123),f332(f137(x95122,x95124),x95125))),f332(f167(x95121),f332(f332(f155(x95122,x95121),x95123),x95125))) % 165.28/165.05 [9591]~P30(x95915)+P24(f332(f332(f334(x95911),f599(x95912,x95913,x95911,x95914,x95915)),x95913))+P24(f332(f332(f246(x95915),x95914),f332(f332(f43(x95911,x95915),x95913),x95912))) % 165.28/165.05 [9594]~P80(x95941)+E(f332(f167(x95941),f332(f332(f155(x95942,x95941),x95943),f332(f137(x95942,x95944),x95945))),f332(f167(x95941),f332(f332(f155(x95942,x95941),x95943),x95945)))+P24(f332(f332(f334(x95942),f624(x95943,x95944,x95945,x95942,x95941)),f332(f174(x95942),x95945))) % 165.28/165.05 [9604]~P24(f332(x96045,f775(x96045,x96043,x96044,x96042,x96041)))+~P24(f332(f332(f246(f875(x96041,a862)),x96042),x96044))+P24(f332(f332(f246(f875(x96041,a862)),f332(f332(f104(f875(x96041,a862)),x96042),f332(f252(x96041),x96043))),f332(f332(f104(f875(x96041,a862)),x96044),f332(f252(x96041),x96045)))) % 165.28/165.05 [9639]P38(x96391,x96392,x96393,x96394,x96395)+~E(f332(f197(f869(x96392)),x96395),f332(f197(f869(x96391)),x96394))+P24(f332(f332(f247(a868),f658(x96395,x96394,x96393,x96392,x96391)),f332(f197(f869(x96391)),x96394))) % 165.28/165.05 [9640]P38(x96401,x96402,x96403,x96404,x96405)+~E(f332(f197(f869(x96402)),x96405),f332(f197(f869(x96401)),x96404))+P24(f332(f332(f247(a868),f696(x96403,x96405,x96402,x96404,x96401)),f332(f197(f869(x96401)),x96404))) % 165.28/165.05 [9673]P24(f332(f332(f334(x96731),f775(x96732,x96733,x96734,x96735,x96731)),x96735))+~P24(f332(f332(f246(f875(x96731,a862)),x96735),x96734))+P24(f332(f332(f246(f875(x96731,a862)),f332(f332(f104(f875(x96731,a862)),x96735),f332(f252(x96731),x96733))),f332(f332(f104(f875(x96731,a862)),x96734),f332(f252(x96731),x96732)))) % 165.28/165.05 [9727]~P30(x97271)+~P24(f332(f332(f246(x97271),x97272),f332(x97275,f599(x97275,x97274,x97273,x97272,x97271))))+P24(f332(f332(f246(x97271),x97272),f332(f332(f43(x97273,x97271),x97274),x97275))) % 165.28/165.05 [9761]~P73(x97611)+~P24(f332(f62(x97612),x97615))+E(f332(f332(f332(f66(x97611,x97612,f82(x97611)),f332(f332(f18(x97612,x97611,x97611),f332(f332(f8(x97611,f875(x97611,x97611),x97612),f82(x97611)),x97613)),x97614)),f79(x97611)),x97615),f332(f332(f82(x97611),f332(f332(f332(f66(x97611,x97612,f82(x97611)),x97613),f79(x97611)),x97615)),f332(f332(f332(f66(x97611,x97612,f82(x97611)),x97614),f79(x97611)),x97615))) % 165.28/165.05 [9823]~P24(f332(f332(f334(f874(f875(x98231,a862),f875(x98231,a862))),f332(f332(f267(f875(x98231,a862),f875(x98231,a862)),x98235),x98234)),f323(x98231,x98233)))+~P24(f332(f332(f334(x98231),x98232),x98235))+P24(f332(f332(f334(f874(x98231,x98231)),f332(f332(f267(x98231,x98231),x98232),f722(x98233,x98234,x98235,x98231,x98232))),x98233)) % 165.28/165.05 [9951]~P24(f332(f332(f334(f874(f869(x99511),f869(x99511))),f332(f332(f267(f869(x99511),f869(x99511)),f332(f332(f135(x99511),x99515),x99512)),f332(f332(f135(x99511),x99515),x99513))),f148(x99511,x99514)))+P24(f332(f332(f334(f874(f869(x99511),f869(x99511))),f332(f332(f267(f869(x99511),f869(x99511)),x99512),x99513)),f148(x99511,x99514)))+P24(f332(f332(f334(f874(x99511,x99511)),f332(f332(f267(x99511,x99511),f591(x99514,x99513,x99512,x99515,x99511)),f591(x99514,x99513,x99512,x99515,x99511))),x99514)) % 165.28/165.05 [7146]~E(f332(f197(f869(x71461)),x71463),f332(f197(f869(x71462)),x71464))+E(f332(f332(f180(x71461,x71462),f332(f332(f184(x71461,x71462),x71463),x71464)),x71465),f209(x71462))+P24(f332(f332(f334(x71461),x71465),f332(f174(x71461),x71463))) % 165.28/165.05 [7219]~E(x72193,x72195)+E(f332(f332(f166(x72191),f332(f332(f160(x72191,x72192),x72193),x72194)),x72195),x72194)+~P24(f332(f332(f247(a868),x72193),f332(f197(f869(x72191)),x72192))) % 165.28/165.05 [7328]~E(f332(f332(f135(x73281),x73282),x73284),f332(f332(f135(x73281),x73283),x73285))+E(f332(f332(f177(x73281),f332(f197(f869(x73281)),x73282)),x73283),x73282)+P24(f332(f332(f246(a868),f332(f197(f869(x73281)),x73283)),f332(f197(f869(x73281)),x73282))) % 165.28/165.05 [7829]~E(f332(f332(f135(x78291),x78292),x78294),f332(f332(f135(x78291),x78293),x78295))+E(f332(f332(f177(x78291),f332(f197(f869(x78291)),x78292)),x78293),x78292)+~P24(f332(f332(f246(a868),f332(f197(f869(x78291)),x78292)),f332(f197(f869(x78291)),x78293))) % 165.28/165.05 [7853]~P24(f332(f62(x78531),f332(x78534,x78535)))+~P24(f332(f332(f334(x78532),x78535),x78533))+P24(f332(f62(x78531),f332(f332(f43(x78532,f875(x78531,a862)),x78533),x78534))) % 165.28/165.05 [7905]~E(f332(f197(f869(x79051)),x79052),f332(f197(f869(x79053)),x79054))+~E(f332(f332(f180(x79051,x79053),f332(f332(f184(x79051,x79053),x79052),x79054)),x79055),f209(x79053))+~P24(f332(f332(f334(x79051),x79055),f332(f174(x79051),x79052))) % 165.28/165.05 [8027]~P43(x80271,x80273,x80275)+~P43(x80271,x80272,x80274)+P43(x80271,f332(f332(f113(f875(x80271,a862)),x80272),x80273),f332(f332(f113(f875(f874(x80271,x80271),a862)),x80274),x80275)) % 165.28/165.05 [8028]~P43(x80281,x80283,x80285)+~P43(x80281,x80282,x80284)+P43(x80281,f332(f332(f104(f875(x80281,a862)),x80282),x80283),f332(f332(f104(f875(f874(x80281,x80281),a862)),x80284),x80285)) % 165.28/165.05 [8377]E(f332(f332(f267(x83771,x83772),f332(f332(f166(x83771),x83773),x83774)),f332(f332(f166(x83772),x83775),x83774)),f332(f332(f166(f874(x83771,x83772)),f332(f332(f184(x83771,x83772),x83773),x83775)),x83774))+~P24(f332(f332(f247(a868),x83774),f332(f197(f869(x83771)),x83773)))+~P24(f332(f332(f247(a868),x83774),f332(f197(f869(x83772)),x83775))) % 165.28/165.05 [8526]~P43(x85261,x85263,x85264)+P24(f332(f332(f334(x85261),x85262),x85263))+~P24(f332(f332(f334(f874(x85261,x85261)),f332(f332(f267(x85261,x85261),x85265),x85262)),x85264)) % 165.28/165.05 [8527]~P43(x85271,x85273,x85274)+P24(f332(f332(f334(x85271),x85272),x85273))+~P24(f332(f332(f334(f874(x85271,x85271)),f332(f332(f267(x85271,x85271),x85272),x85275)),x85274)) % 165.28/165.05 [8528]~P6(x85281,x85283,x85284)+P24(f332(f332(f334(x85281),x85282),x85283))+~P24(f332(f332(f334(f874(x85281,x85281)),f332(f332(f267(x85281,x85281),x85285),x85282)),x85284)) % 165.28/165.05 [8529]~P6(x85291,x85293,x85294)+P24(f332(f332(f334(x85291),x85292),x85293))+~P24(f332(f332(f334(f874(x85291,x85291)),f332(f332(f267(x85291,x85291),x85292),x85295)),x85294)) % 165.28/165.05 [8787]~P6(x87871,x87875,x87872)+E(f332(f286(x87871,x87871,x87872),f332(f332(f310(x87871),x87873),f196(f875(x87871,a862)))),f332(f286(x87871,x87871,x87872),f332(f332(f310(x87871),x87874),f196(f875(x87871,a862)))))+~P24(f332(f332(f334(f874(x87871,x87871)),f332(f332(f267(x87871,x87871),x87873),x87874)),x87872)) % 165.28/165.05 [8970]P24(f332(x89701,x89702))+~P24(f332(f332(f334(x89703),x89702),x89705))+P24(f332(f332(f334(x89703),f352(x89701,x89704,x89705,x89703)),f332(f332(f113(f875(x89703,a862)),x89705),x89704))) % 165.28/165.05 [8971]P24(f332(x89711,x89712))+~P24(f332(f332(f334(x89713),x89712),x89714))+P24(f332(f332(f334(x89713),f352(x89711,x89714,x89715,x89713)),f332(f332(f113(f875(x89713,a862)),x89715),x89714))) % 165.28/165.05 [8979]~P24(f332(x89792,x89795))+~P24(f332(f332(f334(x89791),x89795),x89794))+P24(f332(f332(f334(x89791),f860(x89792,x89793,x89794,x89791)),f332(f332(f113(f875(x89791,a862)),x89794),x89793))) % 165.28/165.05 [8980]~P24(f332(x89802,x89805))+~P24(f332(f332(f334(x89801),x89805),x89803))+P24(f332(f332(f334(x89801),f860(x89802,x89803,x89804,x89801)),f332(f332(f113(f875(x89801,a862)),x89804),x89803))) % 165.28/165.05 [8995]~P24(f332(f332(f246(f875(x89951,a862)),x89953),x89955))+~P24(f332(f332(f246(f875(x89951,a862)),x89952),x89954))+P24(f332(f332(f246(f875(x89951,a862)),f332(f332(f113(f875(x89951,a862)),x89952),x89953)),f332(f332(f113(f875(x89951,a862)),x89954),x89955))) % 165.28/165.05 [8996]~P24(f332(f332(f246(f875(x89961,a862)),x89965),x89963))+~P24(f332(f332(f246(f875(x89961,a862)),x89962),x89964))+P24(f332(f332(f246(f875(x89961,a862)),f332(f332(f22(f875(x89961,a862)),x89962),x89963)),f332(f332(f22(f875(x89961,a862)),x89964),x89965))) % 165.28/165.05 [8997]~P24(f332(f332(f246(f875(x89971,a862)),x89973),x89975))+~P24(f332(f332(f246(f875(x89971,a862)),x89972),x89974))+P24(f332(f332(f246(f875(x89971,a862)),f332(f332(f104(f875(x89971,a862)),x89972),x89973)),f332(f332(f104(f875(x89971,a862)),x89974),x89975))) % 165.28/165.05 [9084]~E(f332(f197(f869(x90841)),x90843),f332(f197(f869(x90842)),x90844))+E(f332(f332(f180(x90841,x90842),f332(f332(f184(x90841,x90842),x90843),x90844)),x90845),f332(f208(x90842),f523(x90845,x90844,x90842,x90843,x90841)))+~P24(f332(f332(f334(x90841),x90845),f332(f174(x90841),x90843))) % 165.28/165.05 [9088]P24(f332(f332(f334(f874(x90881,x90881)),f332(f332(f267(x90881,x90881),x90882),x90883)),f326(x90881,x90884,x90885)))+~P24(f332(f332(f246(a868),f332(x90884,x90882)),f332(x90884,x90883)))+~P24(f332(f332(f334(f874(x90881,x90881)),f332(f332(f267(x90881,x90881),x90882),x90883)),x90885)) % 165.28/165.05 [9260]P24(f332(f332(f334(f874(x92601,x92601)),f332(f332(f267(x92601,x92601),x92602),x92603)),f308(x92601,x92604)))+~P24(f332(f332(f334(f874(x92601,x92601)),f332(f332(f267(x92601,x92601),x92602),x92605)),f308(x92601,x92604)))+~P24(f332(f332(f334(f874(x92601,x92601)),f332(f332(f267(x92601,x92601),x92605),x92603)),x92604)) % 165.28/165.05 [9261]P24(f332(f332(f334(f874(x92611,x92611)),f332(f332(f267(x92611,x92611),x92612),x92613)),f308(x92611,x92614)))+~P24(f332(f332(f334(f874(x92611,x92611)),f332(f332(f267(x92611,x92611),x92615),x92613)),f308(x92611,x92614)))+~P24(f332(f332(f334(f874(x92611,x92611)),f332(f332(f267(x92611,x92611),x92612),x92615)),x92614)) % 165.28/165.05 [9355]E(x93551,x93552)+E(f332(a115,f744(x93553,x93554,x93551,x93552,x93555)),x93554)+~P24(f332(f332(f334(f874(x93555,x93555)),f332(f332(f267(x93555,x93555),x93552),x93551)),f332(f332(f191(f874(x93555,x93555),a862),x93554),x93553))) % 165.28/165.05 [9356]E(x93561,x93562)+E(f332(a115,f746(x93563,x93564,x93561,x93562,x93565)),x93564)+~P24(f332(f332(f334(f874(x93565,x93565)),f332(f332(f267(x93565,x93565),x93562),x93561)),f332(f332(f191(f874(x93565,x93565),a862),x93564),x93563))) % 165.28/165.05 [9357]E(x93571,f2(a868))+E(f332(a115,f744(x93572,x93571,x93573,x93574,x93575)),x93571)+~P24(f332(f332(f334(f874(x93575,x93575)),f332(f332(f267(x93575,x93575),x93574),x93573)),f332(f332(f191(f874(x93575,x93575),a862),x93571),x93572))) % 165.28/165.05 [9358]E(x93581,f2(a868))+E(f332(a115,f746(x93582,x93581,x93583,x93584,x93585)),x93581)+~P24(f332(f332(f334(f874(x93585,x93585)),f332(f332(f267(x93585,x93585),x93584),x93583)),f332(f332(f191(f874(x93585,x93585),a862),x93581),x93582))) % 165.28/165.05 [9374]P24(f332(f332(f334(f874(x93741,x93741)),f332(f332(f267(x93741,x93741),x93742),x93743)),f332(f332(f289(x93741,x93741,x93741),x93744),f308(x93741,x93744))))+~P24(f332(f332(f334(f874(x93741,x93741)),f332(f332(f267(x93741,x93741),x93742),x93745)),x93744))+~P24(f332(f332(f334(f874(x93741,x93741)),f332(f332(f267(x93741,x93741),x93745),x93743)),x93744)) % 165.28/165.05 [9381]~P24(f332(f332(f334(f874(x93811,x93811)),f332(f332(f267(x93811,x93811),x93812),x93815)),f308(x93811,x93814)))+P24(f332(f332(f334(f874(x93811,x93811)),f332(f332(f267(x93811,x93811),x93812),x93813)),f332(f332(f289(x93811,x93811,x93811),x93814),f308(x93811,x93814))))+~P24(f332(f332(f334(f874(x93811,x93811)),f332(f332(f267(x93811,x93811),x93815),x93813)),x93814)) % 165.28/165.05 [9419]~P6(x94191,x94195,x94192)+~P24(f332(f332(f334(f874(x94191,x94191)),f332(f332(f267(x94191,x94191),x94193),x94194)),x94192))+P24(f332(f332(f246(f875(x94191,a862)),f332(f286(x94191,x94191,x94192),f332(f332(f310(x94191),x94193),f196(f875(x94191,a862))))),f332(f286(x94191,x94191,x94192),f332(f332(f310(x94191),x94194),f196(f875(x94191,a862)))))) % 165.28/165.05 [9470]P24(f332(f332(f334(f874(x94701,x94701)),f332(f332(f267(x94701,x94701),x94702),x94703)),f332(f332(f289(x94701,x94701,x94701),x94704),f308(x94701,x94704))))+~P24(f332(f332(f334(f874(x94701,x94701)),f332(f332(f267(x94701,x94701),x94702),x94705)),f332(f332(f289(x94701,x94701,x94701),x94704),f308(x94701,x94704))))+~P24(f332(f332(f334(f874(x94701,x94701)),f332(f332(f267(x94701,x94701),x94705),x94703)),x94704)) % 165.28/165.05 [9471]P24(f332(f332(f334(f874(x94711,x94711)),f332(f332(f267(x94711,x94711),x94712),x94713)),f332(f332(f289(x94711,x94711,x94711),x94714),f308(x94711,x94714))))+~P24(f332(f332(f334(f874(x94711,x94711)),f332(f332(f267(x94711,x94711),x94715),x94713)),f332(f332(f289(x94711,x94711,x94711),x94714),f308(x94711,x94714))))+~P24(f332(f332(f334(f874(x94711,x94711)),f332(f332(f267(x94711,x94711),x94712),x94715)),x94714)) % 165.28/165.05 [9521]~P24(f332(f67(x95211,x95211,x95214,x95212,x95213),x95215))+P24(f332(f332(f334(x95211),x95212),x95213))+P24(f332(f63(x95211,x95214,f332(f332(f310(x95211),x95212),x95213)),x95215)) % 165.28/165.05 [9560]~E(f332(f311(x95603,x95602,x95605),x95604),x95601)+E(x95601,f196(f875(x95602,a862)))+P24(f332(f332(f246(f875(x95603,a862)),f332(f311(x95602,x95603,f736(x95604,x95603,x95602,x95601)),x95601)),x95604)) % 165.28/165.05 [9607]~P30(x96075)+P24(f332(f332(f334(x96071),f472(x96072,x96073,x96074,x96071,x96075)),x96074))+P24(f332(f332(f246(x96075),f332(f332(f42(x96071,x96075),x96074),x96073)),x96072)) % 165.28/165.05 [9659]P38(x96591,x96592,x96593,x96594,x96595)+~E(f332(f197(f869(x96591)),x96594),f332(f197(f869(x96592)),x96595))+P24(f332(f332(f334(f874(x96591,x96592)),f646(x96595,x96594,x96593,x96592,x96591)),f332(f174(f874(x96591,x96592)),f332(f332(f184(x96591,x96592),x96594),x96595)))) % 165.28/165.05 [9660]P38(x96601,x96602,x96603,x96604,x96605)+~E(f332(f197(f869(x96601)),x96604),f332(f197(f869(x96602)),x96605))+P24(f332(f332(f334(f874(x96601,x96602)),f657(x96603,x96605,x96604,x96602,x96601)),f332(f174(f874(x96601,x96602)),f332(f332(f184(x96601,x96602),x96604),x96605)))) % 165.28/165.05 [9799]E(x97991,x97992)+P24(f332(f332(f334(f874(x97993,x97993)),f332(f332(f267(x97993,x97993),x97991),f745(x97994,x97995,x97992,x97991,x97993))),x97994))+~P24(f332(f332(f334(f874(x97993,x97993)),f332(f332(f267(x97993,x97993),x97991),x97992)),f332(f332(f191(f874(x97993,x97993),a862),x97995),x97994))) % 165.28/165.05 [9800]E(x98001,f2(a868))+P24(f332(f332(f334(f874(x98002,x98002)),f332(f332(f267(x98002,x98002),x98003),f745(x98004,x98001,x98005,x98003,x98002))),x98004))+~P24(f332(f332(f334(f874(x98002,x98002)),f332(f332(f267(x98002,x98002),x98003),x98005)),f332(f332(f191(f874(x98002,x98002),a862),x98001),x98004))) % 165.28/165.05 [9844]~P30(x98441)+~P24(f332(f332(f246(x98441),f332(x98444,f472(x98445,x98444,x98443,x98442,x98441))),x98445))+P24(f332(f332(f246(x98441),f332(f332(f42(x98442,x98441),x98443),x98444)),x98445)) % 165.28/165.05 [9886]E(x98861,x98862)+P24(f332(f332(f334(f874(x98863,x98863)),f332(f332(f267(x98863,x98863),f747(x98864,x98865,x98861,x98862,x98863)),x98861)),x98864))+~P24(f332(f332(f334(f874(x98863,x98863)),f332(f332(f267(x98863,x98863),x98862),x98861)),f332(f332(f191(f874(x98863,x98863),a862),x98865),x98864))) % 165.28/165.05 [9887]E(x98871,f2(a868))+P24(f332(f332(f334(f874(x98872,x98872)),f332(f332(f267(x98872,x98872),f747(x98873,x98871,x98874,x98875,x98872)),x98874)),x98873))+~P24(f332(f332(f334(f874(x98872,x98872)),f332(f332(f267(x98872,x98872),x98875),x98874)),f332(f332(f191(f874(x98872,x98872),a862),x98871),x98873))) % 165.28/165.05 [9891]E(x98911,x98912)+P24(f332(f332(f334(f874(x98913,x98913)),f332(f332(f267(x98913,x98913),x98911),f747(x98914,x98915,x98912,x98911,x98913))),f332(f332(f191(f874(x98913,x98913),a862),f746(x98914,x98915,x98912,x98911,x98913)),x98914)))+~P24(f332(f332(f334(f874(x98913,x98913)),f332(f332(f267(x98913,x98913),x98911),x98912)),f332(f332(f191(f874(x98913,x98913),a862),x98915),x98914))) % 165.28/165.05 [9892]E(x98921,f2(a868))+P24(f332(f332(f334(f874(x98922,x98922)),f332(f332(f267(x98922,x98922),x98923),f747(x98924,x98921,x98925,x98923,x98922))),f332(f332(f191(f874(x98922,x98922),a862),f746(x98924,x98921,x98925,x98923,x98922)),x98924)))+~P24(f332(f332(f334(f874(x98922,x98922)),f332(f332(f267(x98922,x98922),x98923),x98925)),f332(f332(f191(f874(x98922,x98922),a862),x98921),x98924))) % 165.28/165.05 [9942]E(x99421,x99422)+P24(f332(f332(f334(f874(x99423,x99423)),f332(f332(f267(x99423,x99423),f745(x99424,x99425,x99421,x99422,x99423)),x99421)),f332(f332(f191(f874(x99423,x99423),a862),f744(x99424,x99425,x99421,x99422,x99423)),x99424)))+~P24(f332(f332(f334(f874(x99423,x99423)),f332(f332(f267(x99423,x99423),x99422),x99421)),f332(f332(f191(f874(x99423,x99423),a862),x99425),x99424))) % 165.28/165.05 [9943]E(x99431,f2(a868))+P24(f332(f332(f334(f874(x99432,x99432)),f332(f332(f267(x99432,x99432),f745(x99433,x99431,x99434,x99435,x99432)),x99434)),f332(f332(f191(f874(x99432,x99432),a862),f744(x99433,x99431,x99434,x99435,x99432)),x99433)))+~P24(f332(f332(f334(f874(x99432,x99432)),f332(f332(f267(x99432,x99432),x99435),x99434)),f332(f332(f191(f874(x99432,x99432),a862),x99431),x99433))) % 165.28/165.05 [9977]~P74(x99772)+~P24(f332(f62(x99771),x99775))+E(f332(f332(f6(x99771,x99772),f332(f332(f7(x99771,x99772,x99772),f332(f332(f18(x99771,x99772,f875(x99772,x99772)),f332(f332(f8(a862,f875(x99772,f875(x99772,x99772)),x99771),f99(x99772)),f332(f332(f7(x99771,f875(x99771,a862),a862),f334(x99771)),x99773))),x99774)),f2(x99772))),x99775),f332(f332(f6(x99771,x99772),x99774),f332(f332(f104(f875(x99771,a862)),x99775),x99773))) % 165.28/165.05 [8588]~P74(x85881)+~P24(f332(f62(x85884),x85885))+E(f332(f332(f81(x85881),f332(x85882,x85883)),f332(f332(f6(x85884,x85881),x85882),f332(f332(f22(f875(x85884,a862)),x85885),f332(f332(f310(x85884),x85883),f196(f875(x85884,a862)))))),f332(f332(f6(x85884,x85881),x85882),f332(f332(f310(x85884),x85883),x85885))) % 165.28/165.05 [8589]~P73(x85891)+~P24(f332(f62(x85894),x85895))+E(f332(f332(f82(x85891),f332(x85892,x85893)),f332(f332(f9(x85894,x85891),x85892),f332(f332(f22(f875(x85894,a862)),x85895),f332(f332(f310(x85894),x85893),f196(f875(x85894,a862)))))),f332(f332(f9(x85894,x85891),x85892),f332(f332(f310(x85894),x85893),x85895))) % 165.28/165.05 [8903]~P106(x89032)+~P32(x89032,f332(f170(x89032),f332(f332(f155(x89031,x89032),x89034),x89035)))+E(f332(f137(x89031,f332(f332(f8(x89032,a862,x89031),f332(f247(x89032),x89033)),x89034)),x89035),f179(x89031,f332(f332(f8(x89032,a862,x89031),f332(f247(x89032),x89033)),x89034),x89035)) % 165.28/165.05 [8925]~P74(x89251)+E(f332(f332(f81(x89251),f332(f332(f6(a868,x89251),x89252),f303(a868,x89253,x89254))),f332(f332(f6(a868,x89251),x89252),f303(a868,f332(f332(f81(a868),x89254),f79(a868)),f332(f332(f81(a868),x89254),x89255)))),f332(f332(f6(a868,x89251),x89252),f303(a868,x89253,f332(f332(f81(a868),x89254),x89255))))+~P24(f332(f332(f246(a868),x89253),f332(f332(f81(a868),x89254),f79(a868)))) % 165.28/165.05 [8926]~P24(f332(f332(f334(x89261),x89264),x89265))+~P24(f332(f332(f246(f875(x89261,a862)),f332(f174(x89261),x89262)),x89265))+P24(f332(f332(f246(f875(x89261,a862)),f332(f174(x89261),f332(f332(f160(x89261,x89262),x89263),x89264))),x89265)) % 165.28/165.05 [9148]~P30(x91482)+~P24(f332(f62(x91481),x91485))+E(f332(f332(f65(x91481,x91482,f332(f332(f8(x91482,f875(x91482,x91482),x91481),f113(x91482)),x91483)),x91484),x91485),f332(f332(f113(x91482),x91484),f332(f332(f42(x91481,x91482),x91485),x91483))) % 165.28/165.05 [9149]~P30(x91492)+~P24(f332(f62(x91491),x91495))+E(f332(f332(f65(x91491,x91492,f332(f332(f8(x91492,f875(x91492,x91492),x91491),f104(x91492)),x91493)),x91494),x91495),f332(f332(f104(x91492),x91494),f332(f332(f43(x91491,x91492),x91495),x91493))) % 165.28/165.05 [9190]E(f332(x91901,x91902),f332(x91901,x91903))+P24(f332(f332(f247(a868),f332(x91901,x91902)),f332(x91901,x91903)))+~P24(f332(f332(f334(f874(x91904,x91904)),f332(f332(f267(x91904,x91904),x91902),x91903)),f154(x91904,f332(f332(f152(f875(x91904,a868)),x91901),x91905)))) % 165.28/165.05 [9222]~E(f332(x92224,x92222),f332(x92224,x92223))+~P24(f332(f332(f334(f874(x92221,x92221)),f332(f332(f267(x92221,x92221),x92222),x92223)),f154(x92221,x92225)))+P24(f332(f332(f334(f874(x92221,x92221)),f332(f332(f267(x92221,x92221),x92222),x92223)),f154(x92221,f332(f332(f152(f875(x92221,a868)),x92224),x92225)))) % 165.28/165.05 [9240]~P21(x92401,x92402,x92403,x92405)+P21(x92401,x92402,x92403,f332(f332(f310(x92401),x92404),x92405))+P24(f332(f332(f334(x92402),f332(x92403,x92404)),f332(f311(x92401,x92402,x92403),f332(f332(f22(f875(x92401,a862)),x92405),f332(f332(f310(x92401),x92404),f196(f875(x92401,a862))))))) % 165.28/165.05 [9243]P24(f332(x92432,x92435))+~P24(f332(f332(f334(x92431),x92435),f332(f174(x92431),x92433)))+E(f332(f332(f139(x92431),f332(f197(f869(x92431)),f179(x92431,x92432,f332(f332(f135(x92431),x92433),x92434)))),f332(f332(f135(x92431),x92433),x92434)),f332(f332(f135(x92431),f332(f332(f139(x92431),f332(f197(f869(x92431)),f179(x92431,x92432,x92433))),x92433)),x92434)) % 165.28/165.05 [9246]~P24(f332(f332(f334(f874(x92461,x92461)),f332(f332(f267(x92461,x92461),x92462),x92463)),f154(x92461,x92465)))+~P24(f332(f332(f246(a868),f332(x92464,x92462)),f332(x92464,x92463)))+P24(f332(f332(f334(f874(x92461,x92461)),f332(f332(f267(x92461,x92461),x92462),x92463)),f154(x92461,f332(f332(f152(f875(x92461,a868)),x92464),x92465)))) % 165.28/165.05 [9310]P24(f332(f332(f334(f874(x93104,x93104)),f332(f332(f267(x93104,x93104),x93102),x93103)),f154(x93104,x93105)))+P24(f332(f332(f247(a868),f332(x93101,x93102)),f332(x93101,x93103)))+~P24(f332(f332(f334(f874(x93104,x93104)),f332(f332(f267(x93104,x93104),x93102),x93103)),f154(x93104,f332(f332(f152(f875(x93104,a868)),x93101),x93105)))) % 165.28/165.05 [9444]~P24(f332(f332(f334(f874(f869(x94441),f869(x94441))),f332(f332(f267(f869(x94441),f869(x94441)),x94442),x94444)),f159(x94441,x94445)))+~P24(f332(f332(f247(a868),x94443),f332(f197(f869(x94441)),x94442)))+P24(f332(f332(f334(f874(x94441,x94441)),f332(f332(f267(x94441,x94441),f332(f332(f166(x94441),x94442),x94443)),f332(f332(f166(x94441),x94444),x94443))),x94445)) % 165.28/165.05 [9687]E(x96871,f2(a1))+~P24(f332(f49(x96873,x96871),f332(f332(f267(a1,a1),x96874),x96875)))+P24(f332(f49(f332(f332(f82(a1),x96872),x96873),x96871),f332(f332(f267(a1,a1),f332(f332(f81(a1),f332(f332(f82(a1),x96872),x96874)),f332(f332(f39(a1),f332(f332(f82(a1),x96872),x96875)),x96871))),f45(a1,f332(f332(f82(a1),x96872),x96875),x96871)))) % 165.28/165.05 [9689]~P24(f332(f332(f247(a868),f2(a868)),x96893))+~P24(f332(f48(x96892,x96893),f332(f332(f267(a868,a868),x96894),x96895)))+P24(f332(f48(f332(f332(f82(a868),x96891),x96892),x96893),f332(f332(f267(a868,a868),f332(f332(f81(a868),f332(f332(f82(a868),x96891),x96894)),f332(f332(f39(a868),f332(f332(f82(a868),x96891),x96895)),x96893))),f45(a868,f332(f332(f82(a868),x96891),x96895),x96893)))) % 165.28/165.05 [9999]~P74(x99992)+~P24(f332(f62(x99991),x99994))+E(f332(f332(f6(x99991,x99992),x99993),f332(f252(x99991),f332(f332(f18(x99991,a862,a862),f332(f332(f8(a862,f875(a862,a862),x99991),a330),f332(f332(f7(x99991,f875(x99991,a862),a862),f334(x99991)),x99994))),f332(f332(f7(x99991,f875(x99991,a862),a862),f334(x99991)),x99995)))),f332(f332(f6(x99991,x99992),f332(f332(f7(x99991,x99992,x99992),f332(f332(f18(x99991,x99992,f875(x99992,x99992)),f332(f332(f8(a862,f875(x99992,f875(x99992,x99992)),x99991),f99(x99992)),f332(f332(f7(x99991,f875(x99991,a862),a862),f334(x99991)),x99995))),x99993)),f2(x99992))),x99994)) % 165.28/165.05 [8236]~E(f332(f332(f135(x82361),x82362),x82365),f332(f332(f135(x82361),x82363),x82364))+E(f332(f332(f135(x82361),f332(f332(f139(x82361),f332(f197(f869(x82361)),x82362)),x82363)),x82364),x82365)+P24(f332(f332(f246(a868),f332(f197(f869(x82361)),x82363)),f332(f197(f869(x82361)),x82362))) % 165.28/165.05 [8426]~E(f332(f332(f135(x84262),x84263),x84261),f332(f332(f135(x84262),x84264),x84265))+E(x84261,f332(f332(f135(x84262),f332(f332(f139(x84262),f332(f197(f869(x84262)),x84263)),x84264)),x84265))+~P24(f332(f332(f246(a868),f332(f197(f869(x84262)),x84263)),f332(f197(f869(x84262)),x84264))) % 165.28/165.05 [8509]~E(f332(f332(f81(a868),f332(f332(f82(a868),x85093),x85094)),x85091),f332(f332(f81(a868),f332(f332(f82(a868),x85092),x85094)),x85095))+~P24(f332(f332(f246(a868),x85093),x85092))+E(x85091,f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x85092),x85093)),x85094)),x85095)) % 165.28/165.05 [8510]~E(f332(f332(f81(a868),f332(f332(f82(a868),x85101),x85103)),x85104),f332(f332(f81(a868),f332(f332(f82(a868),x85102),x85103)),x85105))+~P24(f332(f332(f246(a868),x85102),x85101))+E(f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x85101),x85102)),x85103)),x85104),x85105) % 165.28/165.05 [8666]E(f332(f332(f81(a868),f332(f332(f82(a868),x86661),x86662)),x86663),f332(f332(f81(a868),f332(f332(f82(a868),x86664),x86662)),x86665))+~P24(f332(f332(f246(a868),x86664),x86661))+~E(x86665,f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x86661),x86664)),x86662)),x86663)) % 165.28/165.05 [8667]E(f332(f332(f81(a868),f332(f332(f82(a868),x86671),x86672)),x86673),f332(f332(f81(a868),f332(f332(f82(a868),x86674),x86672)),x86675))+~P24(f332(f332(f246(a868),x86674),x86671))+~E(f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x86671),x86674)),x86672)),x86673),x86675) % 165.28/165.05 [9497]~P60(x94972)+~P24(f332(f62(x94971),x94975))+E(f332(f332(f9(x94971,x94972),f332(f332(f18(x94971,x94972,x94972),f332(f332(f8(x94972,f875(x94972,x94972),x94971),f290(x94972)),x94973)),x94974)),x94975),f332(f332(f290(x94972),f332(f332(f9(x94971,x94972),x94973),x94975)),f332(f332(f9(x94971,x94972),x94974),x94975))) % 165.28/165.05 [9623]~E(f749(x96235,x96234,x96233,x96232,x96231),f750(x96235,x96234,x96233,x96232,x96231))+P24(f332(f332(f334(f874(x96231,x96231)),f332(f332(f267(x96231,x96231),x96232),x96233)),f308(x96231,x96234)))+~P24(f332(f332(f334(f874(x96231,x96231)),f332(f332(f267(x96231,x96231),x96232),x96233)),f308(x96231,f332(f332(f113(f875(f874(x96231,x96231),a862)),x96234),x96235)))) % 165.28/165.05 [9624]~E(f751(x96245,x96244,x96243,x96242,x96241),f752(x96245,x96244,x96243,x96242,x96241))+P24(f332(f332(f334(f874(x96241,x96241)),f332(f332(f267(x96241,x96241),x96242),x96243)),f308(x96241,x96244)))+~P24(f332(f332(f334(f874(x96241,x96241)),f332(f332(f267(x96241,x96241),x96242),x96243)),f308(x96241,f332(f332(f113(f875(f874(x96241,x96241),a862)),x96244),x96245)))) % 165.28/165.05 [9834]P24(f332(f332(f334(f874(x98341,x98341)),f332(f332(f267(x98341,x98341),x98342),f752(x98345,x98344,x98343,x98342,x98341))),f308(x98341,x98344)))+P24(f332(f332(f334(f874(x98341,x98341)),f332(f332(f267(x98341,x98341),x98342),x98343)),f308(x98341,x98344)))+~P24(f332(f332(f334(f874(x98341,x98341)),f332(f332(f267(x98341,x98341),x98342),x98343)),f308(x98341,f332(f332(f113(f875(f874(x98341,x98341),a862)),x98344),x98345)))) % 165.28/165.05 [9913]P24(f332(f332(f334(f874(x99131,x99131)),f332(f332(f267(x99131,x99131),f750(x99135,x99134,x99133,x99132,x99131)),x99133)),f308(x99131,x99134)))+P24(f332(f332(f334(f874(x99131,x99131)),f332(f332(f267(x99131,x99131),x99132),x99133)),f308(x99131,x99134)))+~P24(f332(f332(f334(f874(x99131,x99131)),f332(f332(f267(x99131,x99131),x99132),x99133)),f308(x99131,f332(f332(f113(f875(f874(x99131,x99131),a862)),x99134),x99135)))) % 165.28/165.05 [9949]P24(f332(f332(f334(f874(x99491,x99491)),f332(f332(f267(x99491,x99491),x99492),x99493)),f308(x99491,x99494)))+P24(f332(f332(f334(f874(x99491,x99491)),f332(f332(f267(x99491,x99491),f749(x99495,x99494,x99493,x99492,x99491)),f750(x99495,x99494,x99493,x99492,x99491))),x99495))+~P24(f332(f332(f334(f874(x99491,x99491)),f332(f332(f267(x99491,x99491),x99492),x99493)),f308(x99491,f332(f332(f113(f875(f874(x99491,x99491),a862)),x99494),x99495)))) % 165.28/165.05 [9950]P24(f332(f332(f334(f874(x99501,x99501)),f332(f332(f267(x99501,x99501),x99502),x99503)),f308(x99501,x99504)))+P24(f332(f332(f334(f874(x99501,x99501)),f332(f332(f267(x99501,x99501),f752(x99505,x99504,x99503,x99502,x99501)),f751(x99505,x99504,x99503,x99502,x99501))),x99505))+~P24(f332(f332(f334(f874(x99501,x99501)),f332(f332(f267(x99501,x99501),x99502),x99503)),f308(x99501,f332(f332(f113(f875(f874(x99501,x99501),a862)),x99504),x99505)))) % 165.28/165.05 [10069]~P24(f332(f332(f334(f874(f869(x100691),f869(x100691))),f332(f332(f267(f869(x100691),f869(x100691)),x100694),x100695)),f159(x100691,x100692)))+~P24(f332(f332(f334(f874(x100691,x100691)),x100693),f332(f174(f874(x100691,x100691)),f332(f332(f184(x100691,x100691),x100694),x100695))))+P24(f332(f332(f271(x100691,x100691,a862),f332(f332(f7(x100691,f875(f874(x100691,x100691),a862),f875(x100691,a862)),f332(f332(f8(f875(x100691,f875(f875(f874(x100691,x100691),a862),a862)),f875(f875(f874(x100691,x100691),a862),f875(x100691,a862)),x100691),f7(x100691,f875(f874(x100691,x100691),a862),a862)),f332(f332(f8(f875(x100691,f874(x100691,x100691)),f875(x100691,f875(f875(f874(x100691,x100691),a862),a862)),x100691),f332(f8(f874(x100691,x100691),f875(f875(f874(x100691,x100691),a862),a862),x100691),f334(f874(x100691,x100691)))),f267(x100691,x100691)))),x100692)),x100693)) % 165.28/165.05 [9525]~P24(f332(f332(f246(a868),x95253),x95252))+~P24(f332(f332(f246(a868),f332(f332(f81(a868),f332(f332(f82(a868),x95253),x95254)),x95251)),f332(f332(f81(a868),f332(f332(f82(a868),x95252),x95254)),x95255)))+P24(f332(f332(f246(a868),x95251),f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x95252),x95253)),x95254)),x95255))) % 165.28/165.05 [9526]~P24(f332(f332(f246(a868),x95263),x95262))+~P24(f332(f332(f247(a868),f332(f332(f81(a868),f332(f332(f82(a868),x95263),x95264)),x95261)),f332(f332(f81(a868),f332(f332(f82(a868),x95262),x95264)),x95265)))+P24(f332(f332(f247(a868),x95261),f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x95262),x95263)),x95264)),x95265))) % 165.28/165.05 [9544]~P24(f332(f332(f246(a868),x95441),x95444))+P24(f332(f332(f246(a868),f332(f332(f81(a868),f332(f332(f82(a868),x95441),x95442)),x95443)),f332(f332(f81(a868),f332(f332(f82(a868),x95444),x95442)),x95445)))+~P24(f332(f332(f246(a868),x95443),f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x95444),x95441)),x95442)),x95445))) % 165.28/165.05 [9545]~P24(f332(f332(f246(a868),x95451),x95454))+P24(f332(f332(f247(a868),f332(f332(f81(a868),f332(f332(f82(a868),x95451),x95452)),x95453)),f332(f332(f81(a868),f332(f332(f82(a868),x95454),x95452)),x95455)))+~P24(f332(f332(f247(a868),x95453),f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x95454),x95451)),x95452)),x95455))) % 165.28/165.05 [9657]~P24(f332(f332(f246(a868),x96572),x96571))+~P24(f332(f332(f246(a868),f332(f332(f81(a868),f332(f332(f82(a868),x96571),x96573)),x96574)),f332(f332(f81(a868),f332(f332(f82(a868),x96572),x96573)),x96575)))+P24(f332(f332(f246(a868),f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x96571),x96572)),x96573)),x96574)),x96575)) % 165.28/165.05 [9658]~P24(f332(f332(f246(a868),x96582),x96581))+~P24(f332(f332(f247(a868),f332(f332(f81(a868),f332(f332(f82(a868),x96581),x96583)),x96584)),f332(f332(f81(a868),f332(f332(f82(a868),x96582),x96583)),x96585)))+P24(f332(f332(f247(a868),f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x96581),x96582)),x96583)),x96584)),x96585)) % 165.28/165.05 [9711]~P24(f332(f332(f246(a868),x97114),x97111))+P24(f332(f332(f246(a868),f332(f332(f81(a868),f332(f332(f82(a868),x97111),x97112)),x97113)),f332(f332(f81(a868),f332(f332(f82(a868),x97114),x97112)),x97115)))+~P24(f332(f332(f246(a868),f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x97111),x97114)),x97112)),x97113)),x97115)) % 165.28/165.05 [9712]~P24(f332(f332(f246(a868),x97124),x97121))+P24(f332(f332(f247(a868),f332(f332(f81(a868),f332(f332(f82(a868),x97121),x97122)),x97123)),f332(f332(f81(a868),f332(f332(f82(a868),x97124),x97122)),x97125)))+~P24(f332(f332(f247(a868),f332(f332(f81(a868),f332(f332(f82(a868),f332(f332(f22(a868),x97121),x97124)),x97122)),x97123)),x97125)) % 165.28/165.05 [9934]~P9(x99341,x99342,x99345,x99343)+~P24(f332(f332(f334(f874(x99341,x99341)),x99344),x99345))+P24(f332(f332(f271(x99341,x99341,a862),f332(f332(f7(x99341,f875(x99341,x99342),f875(x99341,a862)),f332(f332(f8(f875(x99342,a862),f875(f875(x99341,x99342),f875(x99341,a862)),x99341),f8(x99342,a862,x99341)),f332(f332(f8(x99342,f875(x99342,a862),x99341),a329),x99343))),x99343)),x99344)) % 165.28/165.05 [6793]~E(f332(x67934,x67935),f209(x67932))+E(f332(f187(x67931,x67932,x67933,x67934),x67935),f332(f208(x67932),x67936))+~E(f332(x67933,x67935),f332(f208(x67932),x67936)) % 165.28/165.05 [6894]~E(f332(x68943,x68946),f209(x68941))+E(f332(f241(f872(x68941),x68942,f209(x68941),x68943),f332(x68944,x68945)),f209(x68941))+~E(f332(x68944,x68945),f332(f208(x68942),x68946)) % 165.28/165.05 [7472]E(f332(x74721,x74722),f209(x74723))+~E(f332(f187(x74725,x74723,x74726,x74721),x74722),f332(f208(x74723),x74724))+E(f332(x74721,x74722),f332(f208(x74723),x74724)) % 165.28/165.05 [7508]~E(f332(f187(x75086,x75083,x75085,x75081),x75082),f332(f208(x75083),x75084))+E(f332(x75081,x75082),f332(f208(x75083),x75084))+E(f332(x75085,x75082),f332(f208(x75083),x75084)) % 165.28/165.05 [8389]~P15(x83896,x83891,x83892,x83894)+E(f332(f74(x83891,x83891,x83891,f332(x83892,x83893)),f332(x83894,x83895)),f332(f74(x83891,x83891,x83891,f332(x83894,x83895)),f332(x83892,x83893)))+~P24(f332(f62(x83896),x83895)) % 165.28/165.05 [8799]~P21(x87991,x87993,x87995,x87996)+~P21(x87993,x87992,x87994,f332(f311(x87991,x87993,x87995),x87996))+P21(x87991,x87992,f332(f74(x87993,x87992,x87991,x87994),x87995),x87996) % 165.28/165.05 [9340]~P24(f332(f332(x93403,x93402),x93406))+~P24(f332(f332(x93404,x93405),x93402))+P24(f332(f332(f334(x93401),x93402),f300(x93401,x93403,x93404,x93405,x93406))) % 165.28/165.05 [9341]~P24(f332(f332(x93414,x93412),x93416))+~P24(f332(f332(x93413,x93415),x93412))+P24(f332(f332(f334(x93411),x93412),f297(x93411,x93413,x93414,x93415,x93416))) % 165.28/165.05 [9445]E(x94451,x94452)+E(x94453,x94454)+~P24(f332(f332(f334(f874(f869(x94455),f869(x94455))),f332(f332(f267(f869(x94455),f869(x94455)),f332(f332(f152(x94455),x94453),x94451)),f332(f332(f152(x94455),x94454),x94452))),f158(x94455,x94456))) % 165.28/165.05 [9454]~E(x94542,x94544)+P24(f332(f332(f334(f874(f869(x94541),f869(x94541))),f332(f332(f267(f869(x94541),f869(x94541)),f332(f332(f152(x94541),x94542),x94543)),f332(f332(f152(x94541),x94544),x94545))),f148(x94541,x94546)))+~P24(f332(f332(f334(f874(f869(x94541),f869(x94541))),f332(f332(f267(f869(x94541),f869(x94541)),x94543),x94545)),f148(x94541,x94546))) % 165.28/165.05 [9455]~E(x94552,x94554)+P24(f332(f332(f334(f874(f869(x94551),f869(x94551))),f332(f332(f267(f869(x94551),f869(x94551)),f332(f332(f152(x94551),x94552),x94553)),f332(f332(f152(x94551),x94554),x94555))),f146(x94551,x94556)))+~P24(f332(f332(f334(f874(f869(x94551),f869(x94551))),f332(f332(f267(f869(x94551),f869(x94551)),x94553),x94555)),f146(x94551,x94556))) % 165.28/165.05 [9456]~E(x94562,x94564)+P24(f332(f332(f334(f874(f869(x94561),f869(x94561))),f332(f332(f267(f869(x94561),f869(x94561)),f332(f332(f152(x94561),x94562),x94563)),f332(f332(f152(x94561),x94564),x94565))),f158(x94561,x94566)))+~P24(f332(f332(f334(f874(f869(x94561),f869(x94561))),f332(f332(f267(f869(x94561),f869(x94561)),x94563),x94565)),f158(x94561,x94566))) % 165.28/165.05 [9457]~E(x94572,x94574)+P24(f332(f332(f334(f874(f869(x94571),f869(x94571))),f332(f332(f267(f869(x94571),f869(x94571)),f332(f332(f135(x94571),x94572),x94573)),f332(f332(f135(x94571),x94574),x94575))),f158(x94571,x94576)))+~P24(f332(f332(f334(f874(f869(x94571),f869(x94571))),f332(f332(f267(f869(x94571),f869(x94571)),x94573),x94575)),f158(x94571,x94576))) % 165.28/165.05 [9458]~E(x94583,x94585)+P24(f332(f332(f334(f874(f869(x94581),f869(x94581))),f332(f332(f267(f869(x94581),f869(x94581)),f332(f332(f135(x94581),x94582),x94583)),f332(f332(f135(x94581),x94584),x94585))),f158(x94581,x94586)))+~P24(f332(f332(f334(f874(f869(x94581),f869(x94581))),f332(f332(f267(f869(x94581),f869(x94581)),x94582),x94584)),f158(x94581,x94586))) % 165.28/165.05 [9513]E(x95131,x95132)+P24(f332(f332(f334(f874(f869(x95133),f869(x95133))),f332(f332(f267(f869(x95133),f869(x95133)),x95131),x95132)),f158(x95133,x95134)))+~P24(f332(f332(f334(f874(f869(x95133),f869(x95133))),f332(f332(f267(f869(x95133),f869(x95133)),f332(f332(f152(x95133),x95135),x95131)),f332(f332(f152(x95133),x95136),x95132))),f158(x95133,x95134))) % 165.28/165.05 [9661]~E(x96613,x96615)+P24(f332(f332(f334(f874(f869(x96611),f869(x96611))),f332(f332(f267(f869(x96611),f869(x96611)),f332(f332(f135(x96611),x96612),f332(f332(f152(x96611),x96613),f116(x96611)))),f332(f332(f135(x96611),x96614),f332(f332(f152(x96611),x96615),f116(x96611))))),f158(x96611,x96616)))+~P24(f332(f332(f334(f874(f869(x96611),f869(x96611))),f332(f332(f267(f869(x96611),f869(x96611)),x96612),x96614)),f158(x96611,x96616))) % 165.28/165.05 [9677]E(f332(x96771,x96772),f209(x96773))+~E(f332(f241(f872(x96776),x96773,f209(x96776),x96774),f332(x96771,x96772)),f209(x96776))+E(f332(x96774,f647(x96772,x96771,x96774,x96775,x96776,x96773)),f209(x96776)) % 165.28/165.05 [9678]E(f332(x96781,x96782),f209(x96783))+~E(f332(f241(f872(x96786),x96783,f209(x96786),x96784),f332(x96781,x96782)),f209(x96786))+E(f332(f208(x96783),f647(x96782,x96781,x96784,x96785,x96786,x96783)),f332(x96781,x96782)) % 165.28/165.05 [9715]E(x97151,x97152)+E(x97153,x97154)+~P24(f332(f332(f334(f874(f869(x97155),f869(x97155))),f332(f332(f267(f869(x97155),f869(x97155)),f332(f332(f135(x97155),x97153),f332(f332(f152(x97155),x97151),f116(x97155)))),f332(f332(f135(x97155),x97154),f332(f332(f152(x97155),x97152),f116(x97155))))),f158(x97155,x97156))) % 165.28/165.05 [9741]E(x97411,x97412)+~P24(f332(f332(f334(f874(f869(x97413),f869(x97413))),f332(f332(f267(f869(x97413),f869(x97413)),f332(f332(f135(x97413),x97411),f332(f332(f152(x97413),x97415),f116(x97413)))),f332(f332(f135(x97413),x97412),f332(f332(f152(x97413),x97416),f116(x97413))))),f158(x97413,x97414)))+P24(f332(f332(f334(f874(f869(x97413),f869(x97413))),f332(f332(f267(f869(x97413),f869(x97413)),x97411),x97412)),f158(x97413,x97414))) % 165.28/165.05 [9778]~P24(f332(f332(f334(f874(f875(x97781,a862),f875(x97781,a862))),f332(f332(f267(f875(x97781,a862),f875(x97781,a862)),x97782),x97784)),f323(x97781,x97786)))+~P24(f332(f332(f334(f874(f875(x97781,a862),f875(x97781,a862))),f332(f332(f267(f875(x97781,a862),f875(x97781,a862)),x97783),x97785)),f323(x97781,x97786)))+P24(f332(f332(f334(f874(f875(x97781,a862),f875(x97781,a862))),f332(f332(f267(f875(x97781,a862),f875(x97781,a862)),f332(f332(f113(f875(x97781,a862)),x97782),x97783)),f332(f332(f113(f875(x97781,a862)),x97784),x97785))),f323(x97781,x97786))) % 165.28/165.05 [5233]~E(f332(x52333,x52336),x52335)+~E(x52334,f332(f208(x52331),x52336))+E(f332(f332(f210(x52331,x52332),x52333),x52334),f332(f208(x52332),x52335)) % 165.28/165.05 [5651]~E(f332(f332(f135(x56511),x56516),x56513),x56515)+E(f332(f332(f135(x56511),x56512),x56513),f332(f332(f152(x56511),x56514),x56515))+~E(x56512,f332(f332(f152(x56511),x56514),x56516)) % 165.28/165.05 [5652]~E(f332(f332(f135(x56521),x56526),x56523),x56525)+E(f332(f332(f135(x56521),x56522),x56523),f332(f332(f135(x56521),x56524),x56525))+~E(x56522,f332(f332(f135(x56521),x56524),x56526)) % 165.28/165.05 [5654]E(f332(f332(f135(x56541),x56542),x56543),f332(f332(f152(x56541),x56544),x56545))+~E(f332(f332(f152(x56541),x56544),x56546),x56542)+~E(x56545,f332(f332(f135(x56541),x56546),x56543)) % 165.28/165.05 [5656]~E(f332(f332(f135(x56561),x56562),x56566),x56564)+E(f332(f332(f135(x56561),x56562),x56563),f332(f332(f135(x56561),x56564),x56565))+~E(x56563,f332(f332(f135(x56561),x56566),x56565)) % 165.28/165.05 [6787]E(f332(x67871,x67872),f332(x67873,x67872))+~E(f332(f332(f155(x67874,x67875),x67871),x67876),f332(f332(f155(x67874,x67875),x67873),x67876))+~P24(f332(f332(f334(x67874),x67872),f332(f174(x67874),x67876))) % 165.28/165.05 [7169]~P15(x71694,x71695,x71696,x71691)+E(f332(f332(x71691,x71692),x71693),f332(f332(f65(x71694,x71695,x71696),x71693),x71692))+~P24(f332(f62(x71694),x71692)) % 165.28/165.05 [7235]~E(x72352,f332(x72354,x72356))+~P24(f332(f332(f334(x72353),x72356),x72355))+P24(f332(f332(f334(x72351),x72352),f332(f311(x72353,x72351,x72354),x72355))) % 165.28/165.05 [7236]~E(f332(x72364,x72362),x72366)+~P24(f332(f332(f334(x72363),x72366),x72365))+P24(f332(f332(f334(x72361),x72362),f332(f312(x72361,x72363,x72364),x72365))) % 165.28/165.05 [7688]~P36(x76881,x76882,x76884,x76886)+P36(x76881,x76882,f332(f332(f152(x76881),x76883),x76884),f332(f332(f152(x76881),x76885),x76886))+~P24(f332(f332(x76882,x76883),x76885)) % 165.28/165.05 [8674]~P55(x86744,x86745,x86741,x86742,x86746)+E(f332(x86741,f332(x86742,x86743)),x86743)+~P24(f332(f332(f334(x86745),x86743),x86746)) % 165.28/165.05 [9447]E(x94471,x94472)+E(f332(f197(f869(x94473)),x94474),f332(f197(f869(x94473)),x94475))+~P24(f332(f332(f334(f874(f869(x94473),f869(x94473))),f332(f332(f267(f869(x94473),f869(x94473)),f332(f332(f152(x94473),x94471),x94474)),f332(f332(f152(x94473),x94472),x94475))),f146(x94473,x94476))) % 165.28/165.05 [9509]~P12(x95091,x95092,x95093)+E(f332(f332(f65(x95091,x95092,x95093),x95094),x95095),x95096)+~P24(f332(f67(x95091,x95092,x95093,x95094,x95095),x95096)) % 165.28/165.05 [9516]E(f332(f197(f869(x95161)),x95162),f332(f197(f869(x95161)),x95163))+P24(f332(f332(f334(f874(f869(x95161),f869(x95161))),f332(f332(f267(f869(x95161),f869(x95161)),x95162),x95163)),f146(x95161,x95164)))+~P24(f332(f332(f334(f874(f869(x95161),f869(x95161))),f332(f332(f267(f869(x95161),f869(x95161)),f332(f332(f152(x95161),x95165),x95162)),f332(f332(f152(x95161),x95166),x95163))),f146(x95161,x95164))) % 165.28/165.05 [9538]~P24(f332(f332(f334(f874(x95381,x95381)),f332(f332(f267(x95381,x95381),x95382),x95384)),f308(x95381,x95386)))+P24(f332(f332(f334(f874(f869(x95381),f869(x95381))),f332(f332(f267(f869(x95381),f869(x95381)),f332(f332(f152(x95381),x95382),x95383)),f332(f332(f152(x95381),x95384),x95385))),f308(f869(x95381),f158(x95381,x95386))))+~P24(f332(f332(f334(f874(f869(x95381),f869(x95381))),f332(f332(f267(f869(x95381),f869(x95381)),x95383),x95385)),f308(f869(x95381),f158(x95381,x95386)))) % 165.28/165.05 [9721]~P24(f332(x97212,x97216))+~E(f332(f137(x97211,x97212),x97213),f332(f332(f152(x97211),x97214),x97215))+~P24(f332(f332(f334(x97211),x97216),f332(f174(x97211),f715(x97215,x97214,x97213,x97212,x97211)))) % 165.28/165.05 [9722]~P24(f332(x97224,x97226))+~E(f332(f332(f152(x97221),x97222),x97223),f332(f137(x97221,x97224),x97225))+~P24(f332(f332(f334(x97221),x97226),f332(f174(x97221),f714(x97225,x97224,x97223,x97222,x97221)))) % 165.28/165.05 [10026]~P74(x100262)+E(f332(f332(f6(x100261,x100262),f332(f332(f8(f875(x100263,a862),x100262,x100261),f332(f6(x100263,x100262),x100264)),f332(f332(f8(f875(x100263,a862),f875(x100263,a862),x100261),f252(x100263)),f332(f332(f8(f875(x100263,a862),f875(x100263,a862),x100261),f332(f18(x100263,a862,a862),f332(f332(f8(a862,f875(a862,a862),x100263),a330),f332(f332(f7(x100263,f875(x100263,a862),a862),f334(x100263)),x100265)))),f332(f7(x100263,x100261,a862),f332(f332(f8(x100261,f875(x100261,a862),x100263),a329),x100266)))))),f332(f311(x100263,x100261,x100266),x100265)),f332(f332(f6(x100263,x100262),x100264),x100265))+~P24(f332(f62(x100263),x100265)) % 165.28/165.05 [6845]~P106(x68453)+P24(f332(x68452,x68455))+E(f332(f137(x68451,x68452),f332(f332(f149(x68451,x68453,x68454),x68455),x68456)),f332(f137(x68451,x68452),x68456)) % 165.28/165.05 [6847]P24(f332(x68471,x68472))+~E(f168(x68473,x68471,x68474),f332(f332(f267(f869(x68473),f869(x68473)),x68475),x68476))+~P24(f332(f332(f334(x68473),x68472),f332(f174(x68473),x68475))) % 165.28/165.05 [6891]~P24(f332(x68912,x68916))+~E(f168(x68911,x68912,x68913),f332(f332(f267(f869(x68911),f869(x68911)),x68914),x68915))+~P24(f332(f332(f334(x68911),x68916),f332(f174(x68911),x68915))) % 165.28/165.05 [7553]~P11(x75531,x75532,x75533)+~P24(f332(f62(x75531),x75536))+E(f332(f332(f65(x75531,x75532,x75533),x75534),f332(f332(f310(x75531),x75535),x75536)),f332(f332(f65(x75531,x75532,x75533),f332(f332(x75533,x75535),x75534)),x75536)) % 165.28/165.05 [7603]~P106(x76032)+~P24(f332(f332(f246(x76032),f332(x76033,x76034)),f332(x76033,x76035)))+E(f332(f332(f149(x76031,x76032,x76033),x76034),f332(f332(f152(x76031),x76035),x76036)),f332(f332(f152(x76031),x76034),f332(f332(f152(x76031),x76035),x76036))) % 165.28/165.05 [7718]E(x77181,x77182)+~E(f332(f332(f269(x77183,x77184),x77181),f332(f16(f875(x77184,a862),x77183),x77185)),f332(f332(f269(x77183,x77184),x77182),f332(f16(f875(x77184,a862),x77183),x77185)))+~P24(f332(f332(f334(x77184),x77186),x77185)) % 165.28/165.05 [7783]~P11(x77831,x77832,x77833)+~P24(f332(f62(x77831),x77836))+E(f332(f332(f65(x77831,x77832,x77833),x77834),f332(f332(f310(x77831),x77835),x77836)),f332(f332(x77833,x77835),f332(f332(f65(x77831,x77832,x77833),x77834),x77836))) % 165.28/165.05 [7897]~P12(x78971,x78972,x78973)+~P24(f332(f62(x78971),x78976))+E(f332(f332(f65(x78971,x78972,x78973),f332(f332(x78973,x78974),x78975)),x78976),f332(f332(x78973,x78974),f332(f332(f65(x78971,x78972,x78973),x78975),x78976))) % 165.28/165.05 [7967]~P16(x79672,x79675,x79676,x79671)+~P24(f332(f62(x79672),x79674))+E(f332(x79671,f332(f332(f310(x79672),x79673),x79674)),f332(f74(x79675,x79675,x79675,f332(x79671,x79674)),f332(x79676,x79673))) % 165.28/165.05 [7999]~P106(x79992)+P24(f332(f332(f246(x79992),f332(x79993,x79994)),f332(x79993,x79995)))+E(f332(f332(f149(x79991,x79992,x79993),x79994),f332(f332(f152(x79991),x79995),x79996)),f332(f332(f152(x79991),x79995),f332(f332(f149(x79991,x79992,x79993),x79994),x79996))) % 165.28/165.05 [8137]~E(f332(f197(f869(x81371)),x81375),f332(f197(f869(x81372)),x81376))+~E(f332(f197(f869(x81371)),x81373),f332(f197(f869(x81372)),x81374))+E(f332(f332(f135(f874(x81371,x81372)),f332(f332(f184(x81371,x81372),x81373),x81374)),f332(f332(f184(x81371,x81372),x81375),x81376)),f332(f332(f184(x81371,x81372),f332(f332(f135(x81371),x81373),x81375)),f332(f332(f135(x81372),x81374),x81376))) % 165.28/165.05 [8251]~E(x82512,f332(f311(x82513,x82511,x82514),x82516))+P24(f332(f332(f246(f875(x82511,a862)),x82512),f332(f311(x82513,x82511,x82514),x82515)))+~P24(f332(f332(f246(f875(x82513,a862)),x82516),x82515)) % 165.28/165.05 [8350]~P106(x83505)+E(f332(x83501,x83502),f332(x83501,x83503))+E(f332(f332(f149(x83504,x83505,x83501),x83502),f332(f332(f149(x83504,x83505,x83501),x83503),x83506)),f332(f332(f149(x83504,x83505,x83501),x83503),f332(f332(f149(x83504,x83505,x83501),x83502),x83506))) % 165.28/165.05 [8383]~P21(x83833,x83831,x83834,x83835)+P21(x83833,x83831,f332(f332(f332(f73(x83833,x83831),x83834),x83836),x83832),x83835)+P24(f332(f332(f334(x83831),x83832),f332(f311(x83833,x83831,x83834),x83835))) % 165.28/165.05 [8518]~P24(f332(f332(f334(x85182),x85184),f332(x85186,x85183)))+~P24(f332(f332(f334(x85181),x85183),x85185))+P24(f332(f332(f334(f874(x85181,x85182)),f332(f332(f267(x85181,x85182),x85183),x85184)),f332(f332(f269(x85181,x85182),x85185),x85186))) % 165.28/165.05 [8968]~P74(x89682)+~P21(x89684,x89681,x89685,x89686)+E(f332(f332(f6(x89681,x89682),x89683),f332(f311(x89684,x89681,x89685),x89686)),f332(f332(f6(x89684,x89682),f332(f74(x89681,x89682,x89684,x89683),x89685)),x89686)) % 165.28/165.05 [8969]~P73(x89692)+~P21(x89694,x89691,x89695,x89696)+E(f332(f332(f9(x89691,x89692),x89693),f332(f311(x89694,x89691,x89695),x89696)),f332(f332(f9(x89694,x89692),f332(f74(x89691,x89692,x89694,x89693),x89695)),x89696)) % 165.28/165.05 [9016]~P38(x90162,x90165,x90161,x90163,x90166)+P24(f332(f332(x90161,f332(f332(f166(x90162),x90163),x90164)),f332(f332(f166(x90165),x90166),x90164)))+~P24(f332(f332(f247(a868),x90164),f332(f197(f869(x90165)),x90166))) % 165.28/165.05 [9017]~P38(x90172,x90175,x90171,x90173,x90176)+P24(f332(f332(x90171,f332(f332(f166(x90172),x90173),x90174)),f332(f332(f166(x90175),x90176),x90174)))+~P24(f332(f332(f247(a868),x90174),f332(f197(f869(x90172)),x90173))) % 165.28/165.05 [9218]~P15(x92183,x92181,x92186,x92182)+~P24(f332(f62(x92183),x92184))+E(f332(f74(x92181,x92181,x92181,f332(x92182,f332(f332(f22(f875(x92183,a862)),x92184),f332(f332(f310(x92183),x92185),f196(f875(x92183,a862)))))),f332(x92186,x92185)),f332(x92182,f332(f332(f310(x92183),x92185),x92184))) % 165.28/165.05 [9814]~E(f332(f311(x98142,x98144,x98146),f255(f875(x98142,a862))),f255(f875(x98144,a862)))+~E(f332(f311(x98141,x98143,x98145),f255(f875(x98141,a862))),f255(f875(x98143,a862)))+E(f332(f311(f874(x98141,x98142),f874(x98143,x98144),f272(x98141,x98143,x98142,x98144,x98145,x98146)),f255(f875(f874(x98141,x98142),a862))),f255(f875(f874(x98143,x98144),a862))) % 165.28/165.05 [9862]~P21(x98623,x98624,x98625,f332(x98626,f688(x98626,x98625,x98624,x98623,x98622,x98621)))+P21(x98623,x98624,x98625,f332(f332(f43(x98622,f875(x98623,a862)),x98621),x98626))+E(x98621,f196(f875(x98622,a862))) % 165.28/165.05 [9920]P21(x99206,x99205,x99204,f332(f332(f43(x99202,f875(x99206,a862)),x99201),x99203))+E(x99201,f196(f875(x99202,a862)))+P24(f332(f332(f334(x99202),f688(x99203,x99204,x99205,x99206,x99202,x99201)),x99201)) % 165.28/165.05 [9925]P24(f332(f332(f334(x99251),f717(x99252,x99253,x99254,x99255,x99256,x99251)),x99256))+P24(f332(f332(f246(f875(f874(x99251,x99254),a862)),f332(f332(f269(x99251,x99254),x99256),x99253)),f332(f332(f269(x99251,x99254),x99255),x99252)))+~P24(f332(f332(f246(f875(x99251,a862)),x99256),x99255)) % 165.28/165.05 [9963]P20(x99636,x99635,f332(f332(f310(f867(x99636)),f332(f332(f332(f93(x99636),x99634),x99633),x99632)),f196(f875(f867(x99636),a862))))+~P20(x99636,x99635,f332(f332(f310(f867(x99636)),f332(f332(f332(f93(x99636),x99634),x99633),x99631)),f196(f875(f867(x99636),a862))))+P24(f332(f332(x99631,f515(x99632,x99631,x99633,x99634,x99635,x99636)),f528(x99632,x99631,x99633,x99634,x99635,x99636))) % 165.28/165.05 [9964]P20(x99646,x99645,f332(f332(f310(f867(x99646)),f332(f332(f332(f93(x99646),x99641),x99643),x99642)),f196(f875(f867(x99646),a862))))+~P20(x99646,x99645,f332(f332(f310(f867(x99646)),f332(f332(f332(f93(x99646),x99644),x99643),x99642)),f196(f875(f867(x99646),a862))))+P24(f332(f332(x99641,f540(x99641,x99642,x99643,x99644,x99645,x99646)),f550(x99641,x99642,x99643,x99644,x99645,x99646))) % 165.28/165.05 [10002]~P20(x100021,x100022,f332(f332(f310(f867(x100021)),f332(f332(f332(f93(x100021),x100023),x100024),x100026)),f196(f875(f867(x100021),a862))))+P20(x100021,x100022,f332(f332(f310(f867(x100021)),f332(f332(f332(f93(x100021),x100023),x100024),x100025)),f196(f875(f867(x100021),a862))))+~P24(f332(f332(x100025,f515(x100025,x100026,x100024,x100023,x100022,x100021)),f528(x100025,x100026,x100024,x100023,x100022,x100021))) % 165.28/165.05 [10003]~P20(x100031,x100032,f332(f332(f310(f867(x100031)),f332(f332(f332(f93(x100031),x100036),x100034),x100035)),f196(f875(f867(x100031),a862))))+P20(x100031,x100032,f332(f332(f310(f867(x100031)),f332(f332(f332(f93(x100031),x100033),x100034),x100035)),f196(f875(f867(x100031),a862))))+~P24(f332(f332(x100036,f540(x100033,x100035,x100034,x100036,x100032,x100031)),f550(x100033,x100035,x100034,x100036,x100032,x100031))) % 165.28/165.05 [10037]~P24(f332(f332(f246(f875(x100372,a862)),f332(x100374,f717(x100376,x100374,x100372,x100375,x100373,x100371))),f332(x100376,f717(x100376,x100374,x100372,x100375,x100373,x100371))))+~P24(f332(f332(f246(f875(x100371,a862)),x100373),x100375))+P24(f332(f332(f246(f875(f874(x100371,x100372),a862)),f332(f332(f269(x100371,x100372),x100373),x100374)),f332(f332(f269(x100371,x100372),x100375),x100376))) % 165.28/165.05 [7738]~P24(f332(x77381,x77385))+~P24(f332(x77386,x77384))+P24(f332(x77381,f332(f270(x77382,x77383),f332(f332(f267(x77382,x77383),x77384),x77385)))) % 165.28/165.05 [7739]~P24(f332(x77391,x77394))+~P24(f332(x77396,x77395))+P24(f332(x77391,f332(f266(x77392,x77393),f332(f332(f267(x77392,x77393),x77394),x77395)))) % 165.28/165.05 [7760]~E(f332(f197(f869(x77601)),x77603),f332(f197(f869(x77604)),x77605))+~E(f332(f332(f180(x77601,x77604),f332(f332(f184(x77601,x77604),x77603),x77605)),x77602),f332(f208(x77604),x77606))+P24(f332(f332(f334(x77601),x77602),f332(f174(x77601),x77603))) % 165.28/165.05 [7788]~P24(f332(f332(x77884,x77886),x77885))+~P24(f332(f332(f334(x77881),x77886),x77883))+P24(f332(f332(f332(f42(x77881,f875(x77882,a862)),x77883),x77884),x77885)) % 165.28/165.05 [8087]~P24(f332(f332(f334(x80871),x80872),f332(x80875,x80876)))+~P24(f332(f332(f334(x80873),x80876),x80874))+P24(f332(f332(f334(x80871),x80872),f332(f332(f42(x80873,f875(x80871,a862)),x80874),x80875))) % 165.28/165.05 [8130]P24(f332(f332(x81301,x81302),x81303))+~P24(f332(f332(x81304,x81302),x81303))+~P24(f332(f332(f246(f875(x81305,f875(x81306,a862))),x81304),x81301)) % 165.28/165.05 [8273]P24(f332(f332(x82731,x82732),x82733))+~P24(f332(f332(f334(x82734),x82732),x82735))+~P24(f332(f332(f332(f43(x82734,f875(x82736,a862)),x82735),x82731),x82733)) % 165.28/165.05 [8405]P24(f332(f332(f334(x84051),x84052),f332(x84053,x84054)))+~P24(f332(f332(f334(x84055),x84054),x84056))+~P24(f332(f332(f334(x84051),x84052),f332(f332(f43(x84055,f875(x84051,a862)),x84056),x84053))) % 165.28/165.05 [8656]~P9(x86564,x86565,x86566,x86561)+E(f332(x86561,x86562),f332(x86561,x86563))+~P24(f332(f332(f334(f874(x86564,x86564)),f332(f332(f267(x86564,x86564),x86562),x86563)),x86566)) % 165.28/165.05 [8687]P24(f332(f332(f246(f875(x86871,a862)),x86872),f332(x86873,x86874)))+~P24(f332(f332(f334(x86875),x86874),x86876))+~P24(f332(f332(f246(f875(x86871,a862)),x86872),f332(f332(f43(x86875,f875(x86871,a862)),x86876),x86873))) % 165.28/165.05 [8715]~P53(x87153,x87154,f332(f287(x87154,x87153),x87155))+E(x87151,f196(f875(x87152,a862)))+E(f332(f332(f43(x87152,f875(x87153,a862)),x87151),f332(f332(f8(f875(x87154,a862),f875(x87153,a862),x87152),f286(x87154,x87153,x87155)),x87156)),f332(f286(x87154,x87153,x87155),f332(f332(f43(x87152,f875(x87154,a862)),x87151),x87156))) % 165.28/165.05 [8790]P24(f332(f332(f334(x87901),x87902),f332(f286(x87903,x87901,x87904),x87905)))+~P24(f332(f332(f334(x87903),x87906),x87905))+~P24(f332(f332(f334(f874(x87903,x87901)),f332(f332(f267(x87903,x87901),x87906),x87902)),x87904)) % 165.28/165.05 [9090]P24(f332(f332(f246(f875(x90901,a862)),f332(f286(x90902,x90901,x90903),x90904)),f332(f286(x90902,x90901,x90905),x90906)))+~P24(f332(f332(f246(f875(x90902,a862)),x90904),x90906))+~P24(f332(f332(f246(f875(f874(x90902,x90901),a862)),x90903),x90905)) % 165.28/165.05 [9262]~P24(f332(f332(f334(x92622),x92626),x92624))+~P24(f332(f332(f246(f875(x92621,a862)),x92623),x92625))+P24(f332(f332(f246(f875(f874(x92621,x92622),a862)),f332(f332(f269(x92621,x92622),x92623),f332(f16(f875(x92622,a862),x92621),x92624))),f332(f332(f269(x92621,x92622),x92625),f332(f16(f875(x92622,a862),x92621),x92624)))) % 165.28/165.05 [9275]~P38(x92751,x92752,x92753,x92755,x92756)+P24(f332(f332(f271(x92751,x92752,a862),x92753),x92754))+~P24(f332(f332(f334(f874(x92751,x92752)),x92754),f332(f174(f874(x92751,x92752)),f332(f332(f184(x92751,x92752),x92755),x92756)))) % 165.28/165.05 [9405]~E(x94053,x94055)+P24(f332(f332(f334(f874(f869(x94051),f869(x94051))),f332(f332(f267(f869(x94051),f869(x94051)),f332(f332(f152(x94051),x94052),x94053)),f332(f332(f152(x94051),x94054),x94055))),f158(x94051,x94056)))+~P24(f332(f332(f334(f874(x94051,x94051)),f332(f332(f267(x94051,x94051),x94052),x94054)),x94056)) % 165.28/165.05 [9411]~E(f332(f197(f869(x94111)),x94115),f332(f197(f869(x94112)),x94116))+E(f189(x94111,x94112,f190(x94111,x94112,x94113,f332(f332(f22(f875(x94111,a862)),x94114),f332(f174(x94111),x94115))),x94115,x94116),f190(x94111,x94112,f189(x94111,x94112,x94113,x94115,x94116),x94114))+~P24(f332(f332(f246(f875(x94111,a862)),f332(f174(x94111),x94115)),x94114)) % 165.28/165.05 [9412]~E(f332(f197(f869(x94121)),x94123),f332(f197(f869(x94121)),x94125))+P24(f332(f332(f334(f874(f869(x94121),f869(x94121))),f332(f332(f267(f869(x94121),f869(x94121)),f332(f332(f152(x94121),x94122),x94123)),f332(f332(f152(x94121),x94124),x94125))),f146(x94121,x94126)))+~P24(f332(f332(f334(f874(x94121,x94121)),f332(f332(f267(x94121,x94121),x94122),x94124)),x94126)) % 165.28/165.05 [9439]P24(f332(f332(f334(f874(x94391,x94391)),f332(f332(f267(x94391,x94391),x94392),x94393)),f332(f332(f191(f874(x94391,x94391),a862),f332(a115,x94394)),x94395)))+~P24(f332(f332(f334(f874(x94391,x94391)),f332(f332(f267(x94391,x94391),x94396),x94393)),x94395))+~P24(f332(f332(f334(f874(x94391,x94391)),f332(f332(f267(x94391,x94391),x94392),x94396)),f332(f332(f191(f874(x94391,x94391),a862),x94394),x94395))) % 165.28/165.05 [9440]P24(f332(f332(f334(f874(x94401,x94401)),f332(f332(f267(x94401,x94401),x94402),x94403)),f332(f332(f191(f874(x94401,x94401),a862),f332(a115,x94404)),x94405)))+~P24(f332(f332(f334(f874(x94401,x94401)),f332(f332(f267(x94401,x94401),x94402),x94406)),x94405))+~P24(f332(f332(f334(f874(x94401,x94401)),f332(f332(f267(x94401,x94401),x94406),x94403)),f332(f332(f191(f874(x94401,x94401),a862),x94404),x94405))) % 165.28/165.05 [9443]~P24(f332(f332(f334(x94434),x94435),x94436))+P24(f332(f332(f246(f875(x94431,a862)),x94432),x94433))+~P24(f332(f332(f246(f875(f874(x94431,x94434),a862)),f332(f332(f269(x94431,x94434),x94432),f332(f16(f875(x94434,a862),x94431),x94436))),f332(f332(f269(x94431,x94434),x94433),f332(f16(f875(x94434,a862),x94431),x94436)))) % 165.28/165.05 [9487]E(x94871,x94872)+~P24(f332(f332(f334(f874(f869(x94873),f869(x94873))),f332(f332(f267(f869(x94873),f869(x94873)),f332(f332(f152(x94873),x94871),x94875)),f332(f332(f152(x94873),x94872),x94876))),f148(x94873,x94874)))+P24(f332(f332(f334(f874(x94873,x94873)),f332(f332(f267(x94873,x94873),x94871),x94872)),x94874)) % 165.28/165.05 [9488]E(x94881,x94882)+~P24(f332(f332(f334(f874(f869(x94883),f869(x94883))),f332(f332(f267(f869(x94883),f869(x94883)),f332(f332(f152(x94883),x94881),x94885)),f332(f332(f152(x94883),x94882),x94886))),f146(x94883,x94884)))+P24(f332(f332(f334(f874(x94883,x94883)),f332(f332(f267(x94883,x94883),x94881),x94882)),x94884)) % 165.28/165.05 [9489]E(x94891,x94892)+~P24(f332(f332(f334(f874(f869(x94893),f869(x94893))),f332(f332(f267(f869(x94893),f869(x94893)),f332(f332(f152(x94893),x94891),x94895)),f332(f332(f152(x94893),x94892),x94896))),f158(x94893,x94894)))+P24(f332(f332(f334(f874(x94893,x94893)),f332(f332(f267(x94893,x94893),x94891),x94892)),x94894)) % 165.28/165.05 [9524]P24(f332(f332(f334(f874(f869(x95241),f869(x95241))),f332(f332(f267(f869(x95241),f869(x95241)),f332(f332(f152(x95241),x95242),x95243)),f332(f332(f152(x95241),x95244),x95245))),f159(x95241,x95246)))+~P24(f332(f332(f334(f874(f869(x95241),f869(x95241))),f332(f332(f267(f869(x95241),f869(x95241)),x95243),x95245)),f159(x95241,x95246)))+~P24(f332(f332(f334(f874(x95241,x95241)),f332(f332(f267(x95241,x95241),x95242),x95244)),x95246)) % 165.28/165.05 [9542]P24(f332(x95421,x95422))+~P24(f332(x95421,f469(x95421,x95423,x95424,x95425,x95426)))+~P24(f332(f332(f334(x95426),x95422),f332(f332(f42(x95425,f875(x95426,a862)),x95424),x95423))) % 165.28/165.05 [9547]~P24(f332(f332(f334(f874(f869(x95471),f869(x95471))),f332(f332(f267(f869(x95471),f869(x95471)),f332(f332(f152(x95471),x95472),x95475)),f332(f332(f152(x95471),x95473),x95476))),f148(x95471,x95474)))+P24(f332(f332(f334(f874(f869(x95471),f869(x95471))),f332(f332(f267(f869(x95471),f869(x95471)),x95475),x95476)),f148(x95471,x95474)))+P24(f332(f332(f334(f874(x95471,x95471)),f332(f332(f267(x95471,x95471),x95472),x95473)),x95474)) % 165.28/165.05 [9548]~P24(f332(f332(f334(f874(f869(x95481),f869(x95481))),f332(f332(f267(f869(x95481),f869(x95481)),f332(f332(f152(x95481),x95482),x95485)),f332(f332(f152(x95481),x95483),x95486))),f146(x95481,x95484)))+P24(f332(f332(f334(f874(f869(x95481),f869(x95481))),f332(f332(f267(f869(x95481),f869(x95481)),x95485),x95486)),f146(x95481,x95484)))+P24(f332(f332(f334(f874(x95481,x95481)),f332(f332(f267(x95481,x95481),x95482),x95483)),x95484)) % 165.28/165.05 [9549]~P24(f332(f332(f334(f874(f869(x95491),f869(x95491))),f332(f332(f267(f869(x95491),f869(x95491)),f332(f332(f152(x95491),x95492),x95495)),f332(f332(f152(x95491),x95493),x95496))),f158(x95491,x95494)))+P24(f332(f332(f334(f874(f869(x95491),f869(x95491))),f332(f332(f267(f869(x95491),f869(x95491)),x95495),x95496)),f158(x95491,x95494)))+P24(f332(f332(f334(f874(x95491,x95491)),f332(f332(f267(x95491,x95491),x95492),x95493)),x95494)) % 165.28/165.05 [9633]P24(f332(x96331,x96332))+P24(f332(f332(f334(x96333),f470(x96331,x96334,x96335,x96333,x96336)),x96335))+~P24(f332(f332(f334(x96336),x96332),f332(f332(f42(x96333,f875(x96336,a862)),x96335),x96334))) % 165.28/165.05 [9644]~E(x96442,x96444)+P24(f332(f332(f334(f874(f869(x96441),f869(x96441))),f332(f332(f267(f869(x96441),f869(x96441)),f332(f332(f135(x96441),x96442),f332(f332(f152(x96441),x96443),f116(x96441)))),f332(f332(f135(x96441),x96444),f332(f332(f152(x96441),x96445),f116(x96441))))),f158(x96441,x96446)))+~P24(f332(f332(f334(f874(x96441,x96441)),f332(f332(f267(x96441,x96441),x96443),x96445)),x96446)) % 165.28/165.05 [9731]E(x97311,x97312)+~P24(f332(f332(f334(f874(f869(x97313),f869(x97313))),f332(f332(f267(f869(x97313),f869(x97313)),f332(f332(f135(x97313),x97315),f332(f332(f152(x97313),x97311),f116(x97313)))),f332(f332(f135(x97313),x97316),f332(f332(f152(x97313),x97312),f116(x97313))))),f158(x97313,x97314)))+P24(f332(f332(f334(f874(x97313,x97313)),f332(f332(f267(x97313,x97313),x97311),x97312)),x97314)) % 165.28/165.05 [9760]~P24(f332(f332(f334(f874(f869(x97601),f869(x97601))),f332(f332(f267(f869(x97601),f869(x97601)),f332(f332(f135(x97601),x97605),f332(f332(f152(x97601),x97602),f116(x97601)))),f332(f332(f135(x97601),x97606),f332(f332(f152(x97601),x97603),f116(x97601))))),f158(x97601,x97604)))+P24(f332(f332(f334(f874(f869(x97601),f869(x97601))),f332(f332(f267(f869(x97601),f869(x97601)),x97605),x97606)),f158(x97601,x97604)))+P24(f332(f332(f334(f874(x97601,x97601)),f332(f332(f267(x97601,x97601),x97602),x97603)),x97604)) % 165.28/165.05 [9779]P24(f332(x97791,x97792))+P24(f332(f332(f334(x97793),f469(x97791,x97794,x97795,x97796,x97793)),f332(x97794,f470(x97791,x97794,x97795,x97796,x97793))))+~P24(f332(f332(f334(x97793),x97792),f332(f332(f42(x97796,f875(x97793,a862)),x97795),x97794))) % 165.28/165.05 [8805]~P12(x88053,x88054,x88051)+~P24(f332(f62(x88053),x88056))+E(f332(f332(x88051,x88052),f332(f332(f65(x88053,x88054,x88051),x88055),f332(f332(f22(f875(x88053,a862)),x88056),f332(f332(f310(x88053),x88052),f196(f875(x88053,a862)))))),f332(f332(f65(x88053,x88054,x88051),x88055),f332(f332(f310(x88053),x88052),x88056))) % 165.28/165.05 [8888]~E(f332(f332(f180(x88881,x88882),x88884),x88885),f332(f208(x88882),x88886))+~P24(f332(f332(x88883,x88885),x88886))+E(f332(f332(f180(x88881,x88882),f332(f137(f874(x88881,x88882),f332(f271(x88881,x88882,a862),x88883)),x88884)),x88885),f332(f208(x88882),x88886)) % 165.28/165.05 [9097]~P24(f332(f332(f334(x90975),x90973),x90976))+P24(f332(f332(f246(f875(x90971,a862)),f332(x90972,x90973)),x90974))+~P24(f332(f332(f246(f875(x90971,a862)),f332(f332(f42(x90975,f875(x90971,a862)),x90976),x90972)),x90974)) % 165.28/165.05 [9704]~P6(x97041,x97045,x97044)+P24(f332(f332(f334(f874(x97041,x97041)),f332(f332(f267(x97041,x97041),x97042),x97043)),x97044))+~P24(f332(f332(f334(x97041),x97046),f332(f332(f104(f875(x97041,a862)),f332(f286(x97041,x97041,x97044),f332(f332(f310(x97041),x97042),f196(f875(x97041,a862))))),f332(f286(x97041,x97041,x97044),f332(f332(f310(x97041),x97043),f196(f875(x97041,a862))))))) % 165.28/165.05 [8554]~P125(x85542)+~E(f332(f332(f81(x85542),f332(f332(f82(x85542),x85544),x85545)),x85541),f332(f332(f81(x85542),f332(f332(f82(x85542),x85543),x85545)),x85546))+E(x85541,f332(f332(f81(x85542),f332(f332(f82(x85542),f332(f332(f22(x85542),x85543),x85544)),x85545)),x85546)) % 165.28/165.05 [8555]~P125(x85551)+~E(f332(f332(f81(x85551),f332(f332(f82(x85551),x85552),x85554)),x85555),f332(f332(f81(x85551),f332(f332(f82(x85551),x85553),x85554)),x85556))+E(f332(f332(f81(x85551),f332(f332(f82(x85551),f332(f332(f22(x85551),x85552),x85553)),x85554)),x85555),x85556) % 165.28/165.05 [8718]~P125(x87181)+E(f332(f332(f81(x87181),f332(f332(f82(x87181),x87182),x87183)),x87184),f332(f332(f81(x87181),f332(f332(f82(x87181),x87185),x87183)),x87186))+~E(x87186,f332(f332(f81(x87181),f332(f332(f82(x87181),f332(f332(f22(x87181),x87182),x87185)),x87183)),x87184)) % 165.28/165.05 [8719]~P125(x87191)+E(f332(f332(f81(x87191),f332(f332(f82(x87191),x87192),x87193)),x87194),f332(f332(f81(x87191),f332(f332(f82(x87191),x87195),x87193)),x87196))+~E(f332(f332(f81(x87191),f332(f332(f82(x87191),f332(f332(f22(x87191),x87192),x87195)),x87193)),x87194),x87196) % 165.28/165.05 [9036]~P24(f332(f332(x90364,x90365),x90366))+~P24(f332(f332(x90363,x90365),x90366))+P24(f332(f332(f332(f332(f104(f875(x90361,f875(x90362,a862))),x90363),x90364),x90365),x90366)) % 165.28/165.05 [9283]P24(f332(f332(x92831,x92832),x92833))+P24(f332(f332(x92834,x92832),x92833))+~P24(f332(f332(f332(f332(f113(f875(x92835,f875(x92836,a862))),x92834),x92831),x92832),x92833)) % 165.28/165.05 [9562]~P126(x95621)+~P24(f332(f332(f246(x95621),f332(f332(f81(x95621),f332(f332(f82(x95621),x95624),x95625)),x95622)),f332(f332(f81(x95621),f332(f332(f82(x95621),x95623),x95625)),x95626)))+P24(f332(f332(f246(x95621),x95622),f332(f332(f81(x95621),f332(f332(f82(x95621),f332(f332(f22(x95621),x95623),x95624)),x95625)),x95626))) % 165.28/165.05 [9563]~P126(x95631)+~P24(f332(f332(f247(x95631),f332(f332(f81(x95631),f332(f332(f82(x95631),x95634),x95635)),x95632)),f332(f332(f81(x95631),f332(f332(f82(x95631),x95633),x95635)),x95636)))+P24(f332(f332(f247(x95631),x95632),f332(f332(f81(x95631),f332(f332(f82(x95631),f332(f332(f22(x95631),x95633),x95634)),x95635)),x95636))) % 165.28/165.05 [9586]~P126(x95861)+P24(f332(f332(f246(x95861),f332(f332(f81(x95861),f332(f332(f82(x95861),x95862),x95863)),x95864)),f332(f332(f81(x95861),f332(f332(f82(x95861),x95865),x95863)),x95866)))+~P24(f332(f332(f246(x95861),x95864),f332(f332(f81(x95861),f332(f332(f82(x95861),f332(f332(f22(x95861),x95865),x95862)),x95863)),x95866))) % 165.28/165.05 [9587]~P126(x95871)+P24(f332(f332(f247(x95871),f332(f332(f81(x95871),f332(f332(f82(x95871),x95872),x95873)),x95874)),f332(f332(f81(x95871),f332(f332(f82(x95871),x95875),x95873)),x95876)))+~P24(f332(f332(f247(x95871),x95874),f332(f332(f81(x95871),f332(f332(f82(x95871),f332(f332(f22(x95871),x95875),x95872)),x95873)),x95876))) % 165.28/165.05 [9692]~P126(x96921)+~P24(f332(f332(f246(x96921),f332(f332(f81(x96921),f332(f332(f82(x96921),x96922),x96924)),x96925)),f332(f332(f81(x96921),f332(f332(f82(x96921),x96923),x96924)),x96926)))+P24(f332(f332(f246(x96921),f332(f332(f81(x96921),f332(f332(f82(x96921),f332(f332(f22(x96921),x96922),x96923)),x96924)),x96925)),x96926)) % 165.28/165.05 [9693]~P126(x96931)+~P24(f332(f332(f247(x96931),f332(f332(f81(x96931),f332(f332(f82(x96931),x96932),x96934)),x96935)),f332(f332(f81(x96931),f332(f332(f82(x96931),x96933),x96934)),x96936)))+P24(f332(f332(f247(x96931),f332(f332(f81(x96931),f332(f332(f82(x96931),f332(f332(f22(x96931),x96932),x96933)),x96934)),x96935)),x96936)) % 165.28/165.05 [9743]~P126(x97431)+P24(f332(f332(f246(x97431),f332(f332(f81(x97431),f332(f332(f82(x97431),x97432),x97433)),x97434)),f332(f332(f81(x97431),f332(f332(f82(x97431),x97435),x97433)),x97436)))+~P24(f332(f332(f246(x97431),f332(f332(f81(x97431),f332(f332(f82(x97431),f332(f332(f22(x97431),x97432),x97435)),x97433)),x97434)),x97436)) % 165.28/165.05 [9744]~P126(x97441)+P24(f332(f332(f247(x97441),f332(f332(f81(x97441),f332(f332(f82(x97441),x97442),x97443)),x97444)),f332(f332(f81(x97441),f332(f332(f82(x97441),x97445),x97443)),x97446)))+~P24(f332(f332(f247(x97441),f332(f332(f81(x97441),f332(f332(f82(x97441),f332(f332(f22(x97441),x97442),x97445)),x97443)),x97444)),x97446)) % 165.28/165.05 [9914]~P74(x99142)+~P24(f332(f62(x99141),x99146))+E(f332(f332(f6(x99141,x99142),f332(f332(f18(x99141,x99142,x99142),f332(f332(f18(x99141,x99142,f875(x99142,x99142)),f332(f332(f8(a862,f875(x99142,f875(x99142,x99142)),x99141),f99(x99142)),x99143)),x99144)),x99145)),x99146),f332(f332(f81(x99142),f332(f332(f6(x99141,x99142),x99144),f332(f332(f104(f875(x99141,a862)),x99146),f332(f252(x99141),x99143)))),f332(f332(f6(x99141,x99142),x99145),f332(f332(f104(f875(x99141,a862)),x99146),f332(f80(f875(x99141,a862)),f332(f252(x99141),x99143)))))) % 165.28/165.05 [9973]P24(f332(f332(f334(x99732),x99734),x99736))+P24(f332(f332(f334(x99732),x99735),x99736))+E(f332(f312(x99731,x99732,f332(f332(f7(x99731,x99732,x99732),f332(f332(f7(x99731,x99732,f875(x99732,x99732)),f332(f332(f8(a862,f875(x99732,f875(x99732,x99732)),x99731),f99(x99732)),f332(f332(f7(x99731,f875(x99731,a862),a862),f334(x99731)),x99733))),x99734)),x99735)),x99736),f196(f875(x99731,a862))) % 165.28/165.05 [9974]P24(f332(f332(f334(x99742),x99745),x99746))+~P24(f332(f332(f334(x99742),x99744),x99746))+E(f332(f312(x99741,x99742,f332(f332(f7(x99741,x99742,x99742),f332(f332(f7(x99741,x99742,f875(x99742,x99742)),f332(f332(f8(a862,f875(x99742,f875(x99742,x99742)),x99741),f99(x99742)),f332(f332(f7(x99741,f875(x99741,a862),a862),f334(x99741)),x99743))),x99744)),x99745)),x99746),x99743) % 165.28/165.05 [9975]P24(f332(f332(f334(x99752),x99754),x99756))+~P24(f332(f332(f334(x99752),x99755),x99756))+E(f332(f312(x99751,x99752,f332(f332(f7(x99751,x99752,x99752),f332(f332(f7(x99751,x99752,f875(x99752,x99752)),f332(f332(f8(a862,f875(x99752,f875(x99752,x99752)),x99751),f99(x99752)),f332(f332(f7(x99751,f875(x99751,a862),a862),f334(x99751)),x99753))),x99754)),x99755)),x99756),f332(f80(f875(x99751,a862)),x99753)) % 165.28/165.05 [9976]~P24(f332(f332(f334(x99762),x99764),x99766))+~P24(f332(f332(f334(x99762),x99765),x99766))+E(f332(f312(x99761,x99762,f332(f332(f7(x99761,x99762,x99762),f332(f332(f7(x99761,x99762,f875(x99762,x99762)),f332(f332(f8(a862,f875(x99762,f875(x99762,x99762)),x99761),f99(x99762)),f332(f332(f7(x99761,f875(x99761,a862),a862),f334(x99761)),x99763))),x99764)),x99765)),x99766),f255(f875(x99761,a862))) % 165.28/165.05 [10103]P20(x101031,x101032,f332(f332(f310(f867(x101031)),f332(f332(f332(f93(x101031),f332(x101033,x101034)),f332(a28,x101034)),f332(x101035,x101034))),f196(f875(f867(x101031),a862))))+~P24(f332(f332(f334(a865),x101034),x101036))+~P20(x101031,f332(f332(f113(f875(f867(x101031),a862)),x101032),f332(f311(a865,f867(x101031),f332(f332(f18(a865,f875(x101031,f875(a864,a862)),f867(x101031)),f332(f332(f18(a865,a863,f875(f875(x101031,f875(a864,a862)),f867(x101031))),f332(f332(f8(f875(x101031,f875(a864,a862)),f875(a863,f875(f875(x101031,f875(a864,a862)),f867(x101031))),a865),f93(x101031)),x101033)),a28)),x101035)),x101036)),f332(f311(a865,f867(x101031),f332(f332(f18(a865,f875(x101031,f875(a864,a862)),f867(x101031)),f332(f332(f18(a865,a863,f875(f875(x101031,f875(a864,a862)),f867(x101031))),f332(f332(f8(f875(x101031,f875(a864,a862)),f875(a863,f875(f875(x101031,f875(a864,a862)),f867(x101031))),a865),f93(x101031)),x101033)),f332(f332(f8(f872(a863),a863,a865),f243(a863)),a26))),x101035)),x101036)) % 165.28/165.05 [8584]E(x85841,x85842)+~P55(x85844,x85845,x85843,x85846,x85847)+~E(f332(x85843,x85841),f332(x85843,x85842)) % 165.28/165.05 [6997]E(f332(f241(f872(x69971),x69972,f209(x69971),x69973),f332(x69974,x69975)),f332(f208(x69971),x69976))+~E(f332(x69974,x69975),f332(f208(x69972),x69977))+~E(f332(x69973,x69977),f332(f208(x69971),x69976)) % 165.28/165.05 [8611]~P3(x86116,x86115,x86117,x86114,x86111)+E(f332(f332(x86111,x86112),x86113),x86114)+P24(f332(f62(x86115),x86113)) % 165.28/165.05 [9431]P46(x94311,x94312,x94313,x94314,x94315,f332(f332(x94313,x94316),x94317))+~E(f332(f332(x94313,x94316),x94317),x94314)+~E(x94315,f196(f875(x94311,a862))) % 165.28/165.05 [9608]~P24(f332(x96086,x96083))+~P24(f332(f332(f334(f874(x96082,x96082)),f332(f332(f267(x96082,x96082),x96084),x96085)),f332(x96087,x96083)))+P24(f332(f332(f334(f874(f874(x96081,x96082),f874(x96081,x96082))),f332(f332(f267(f874(x96081,x96082),f874(x96081,x96082)),f332(f332(f267(x96081,x96082),x96083),x96084)),f332(f332(f267(x96081,x96082),x96083),x96085))),f284(x96081,x96082,x96086,x96087))) % 165.28/165.05 [10028]~P46(x100282,x100287,x100283,x100286,x100281,f332(f332(x100283,x100285),x100284))+E(f332(f332(x100283,f771(x100284,x100285,x100281,x100286,x100283,x100287,x100282)),f779(x100284,x100285,x100281,x100286,x100283,x100287,x100282)),f332(f332(x100283,x100285),x100284))+E(x100281,f196(f875(x100282,a862))) % 165.28/165.05 [10029]~P46(x100297,x100296,x100291,x100294,x100295,f332(f332(x100291,x100292),x100293))+E(f332(f332(x100291,f771(x100293,x100292,x100295,x100294,x100291,x100296,x100297)),f779(x100293,x100292,x100295,x100294,x100291,x100296,x100297)),f332(f332(x100291,x100292),x100293))+E(f332(f332(x100291,x100292),x100293),x100294) % 165.28/165.05 [9132]~P38(x91321,x91322,x91323,x91325,x91327)+P38(x91321,x91322,x91323,f332(f332(f152(x91321),x91324),x91325),f332(f332(f152(x91322),x91326),x91327))+~P24(f332(f332(x91323,x91324),x91326)) % 165.28/165.05 [9150]P38(x91501,x91502,x91503,x91504,x91505)+~P38(x91501,x91502,x91503,f332(f332(f135(x91501),x91506),x91504),f332(f332(f135(x91502),x91507),x91505))+~E(f332(f197(f869(x91501)),x91506),f332(f197(f869(x91502)),x91507)) % 165.28/165.05 [9151]P38(x91511,x91512,x91513,x91514,x91515)+~P38(x91511,x91512,x91513,f332(f332(f135(x91511),x91514),x91516),f332(f332(f135(x91512),x91515),x91517))+~E(f332(f197(f869(x91511)),x91514),f332(f197(f869(x91512)),x91515)) % 165.28/165.05 [9343]~P38(x93431,x93432,x93433,x93435,x93437)+~P38(x93431,x93432,x93433,x93434,x93436)+P38(x93431,x93432,x93433,f332(f332(f135(x93431),x93434),x93435),f332(f332(f135(x93432),x93436),x93437)) % 165.28/165.05 [9681]~P24(f332(f67(x96811,x96814,x96815,x96816,x96813),x96817))+P24(f332(f67(x96811,x96814,x96815,x96816,f332(f332(f310(x96811),x96812),x96813)),f332(f332(x96815,x96812),x96817)))+P24(f332(f332(f334(x96811),x96812),x96813)) % 165.28/165.05 [9812]~P21(x98123,x98121,x98124,f255(f875(x98123,a862)))+E(f332(f332(f180(x98121,x98122),f332(f332(f155(f874(x98123,x98122),f874(x98121,x98122)),f332(f271(x98123,x98122,f874(x98121,x98122)),f332(f332(f8(x98121,f875(x98122,f874(x98121,x98122)),x98123),f267(x98121,x98122)),x98124))),x98125)),f332(x98124,x98126)),f332(f208(x98122),x98127))+~E(f332(f332(f180(x98123,x98122),x98125),x98126),f332(f208(x98122),x98127)) % 165.28/165.05 [10049]~P46(x100492,x100497,x100496,x100495,x100491,f332(f332(x100496,x100494),x100493))+E(x100491,f196(f875(x100492,a862)))+P24(f332(f332(f334(x100492),f771(x100493,x100494,x100491,x100495,x100496,x100497,x100492)),x100491)) % 165.28/165.05 [10050]~P46(x100505,x100507,x100501,x100504,x100506,f332(f332(x100501,x100502),x100503))+E(f332(f332(x100501,x100502),x100503),x100504)+P24(f332(f332(f334(x100505),f771(x100503,x100502,x100506,x100504,x100501,x100507,x100505)),x100506)) % 165.28/165.05 [6786]~E(x67865,x67867)+~E(x67866,x67864)+E(f332(f332(f332(f332(f73(x67861,f872(x67862)),x67863),x67864),f332(f208(x67862),x67865)),x67866),f332(f208(x67862),x67867)) % 165.28/165.05 [6913]E(x69131,x69132)+~E(f332(x69135,x69131),f332(f208(x69134),x69137))+E(f332(f332(f332(f332(f73(x69133,f872(x69134)),x69135),x69132),f332(f208(x69134),x69136)),x69131),f332(f208(x69134),x69137)) % 165.28/165.05 [7628]E(x76281,x76282)+~E(x76283,x76284)+~E(f332(f332(f332(f332(f73(x76285,f872(x76286)),x76287),x76284),f332(f208(x76286),x76281)),x76283),f332(f208(x76286),x76282)) % 165.28/165.05 [7694]E(x76941,x76942)+E(f332(x76943,x76944),f332(f208(x76945),x76941))+~E(f332(f332(f332(f332(f73(x76946,f872(x76945)),x76943),x76947),f332(f208(x76945),x76942)),x76944),f332(f208(x76945),x76941)) % 165.28/165.05 [7695]E(x76951,x76952)+E(f332(x76953,x76951),f332(f208(x76954),x76955))+~E(f332(f332(f332(f332(f73(x76956,f872(x76954)),x76953),x76952),f332(f208(x76954),x76957)),x76951),f332(f208(x76954),x76955)) % 165.28/165.05 [8830]~P17(x88304,x88305,x88306,x88307,x88301)+~P24(f332(f62(x88305),x88303))+E(f332(f332(x88301,x88302),x88303),f332(f332(f332(f66(x88304,x88305,x88306),x88302),x88307),x88303)) % 165.28/165.05 [8831]~P3(x88314,x88315,x88316,x88317,x88311)+~P24(f332(f62(x88315),x88313))+E(f332(f332(x88311,x88312),x88313),f332(f332(f332(f66(x88314,x88315,x88316),x88312),x88317),x88313)) % 165.28/165.05 [9398]~P20(x93981,x93982,f332(f332(f310(f867(x93981)),f332(f332(f332(f93(x93981),x93983),x93984),x93987)),f196(f875(f867(x93981),a862))))+P20(x93981,x93982,f332(f332(f310(f867(x93981)),f332(f332(f332(f93(x93981),x93983),f34(x93984,x93985)),x93986)),f196(f875(f867(x93981),a862))))+~P20(x93981,x93982,f332(f332(f310(f867(x93981)),f332(f332(f332(f93(x93981),x93987),x93985),x93986)),f196(f875(f867(x93981),a862)))) % 165.28/165.05 [9581]~P19(x95813,x95814,x95815,x95817,x95816,x95811)+~P24(f332(f62(x95814),x95812))+E(f332(x95811,x95812),f332(f332(f332(f66(x95813,x95814,x95815),x95816),x95817),x95812)) % 165.28/165.05 [9738]P46(x97381,x97382,x97383,x97384,x97385,f332(f332(x97383,x97386),x97387))+~P46(x97381,x97382,x97383,x97384,f332(f332(f22(f875(x97381,a862)),x97385),f332(f332(f310(x97381),x97386),f196(f875(x97381,a862)))),x97387)+~P24(f332(f332(f334(x97381),x97386),x97385)) % 165.28/165.05 [10004]~P20(x100041,x100042,f332(f332(f310(f867(x100041)),f332(f332(f332(f93(x100041),f95(x100041,x100043,x100044)),x100045),x100047)),f196(f875(f867(x100041),a862))))+P20(x100041,x100042,f332(f332(f310(f867(x100041)),f332(f332(f332(f93(x100041),x100043),f31(x100044,x100045,x100046)),x100047)),f196(f875(f867(x100041),a862))))+~P20(x100041,x100042,f332(f332(f310(f867(x100041)),f332(f332(f332(f93(x100041),f95(x100041,x100043,f332(f74(a862,a862,a864,a327),x100044))),x100046),x100047)),f196(f875(f867(x100041),a862)))) % 165.28/165.05 [10074]~P46(x100742,x100743,x100744,x100745,x100741,f332(f332(x100744,x100747),x100746))+P46(x100742,x100743,x100744,x100745,f332(f332(f22(f875(x100742,a862)),x100741),f332(f332(f310(x100742),f771(x100746,x100747,x100741,x100745,x100744,x100743,x100742)),f196(f875(x100742,a862)))),f779(x100746,x100747,x100741,x100745,x100744,x100743,x100742))+E(x100741,f196(f875(x100742,a862))) % 165.28/165.05 [10075]~P46(x100755,x100756,x100751,x100754,x100757,f332(f332(x100751,x100752),x100753))+P46(x100755,x100756,x100751,x100754,f332(f332(f22(f875(x100755,a862)),x100757),f332(f332(f310(x100755),f771(x100753,x100752,x100757,x100754,x100751,x100756,x100755)),f196(f875(x100755,a862)))),f779(x100753,x100752,x100757,x100754,x100751,x100756,x100755))+E(f332(f332(x100751,x100752),x100753),x100754) % 165.28/165.05 [9139]E(f189(x91391,x91392,x91393,x91394,f332(f332(f160(x91392,x91395),x91396),x91397)),f189(x91391,x91392,x91393,x91394,x91395))+~P24(f332(f332(f247(a868),x91396),f332(f197(f869(x91392)),x91395)))+~P24(f332(f332(f246(a868),f332(f197(f869(x91391)),x91394)),x91396)) % 165.28/165.05 [9420]P24(f332(f332(f246(f875(f874(x94201,x94202),a862)),f332(f332(f289(x94201,x94203,x94202),x94204),x94205)),f332(f332(f289(x94201,x94203,x94202),x94206),x94207)))+~P24(f332(f332(f246(f875(f874(x94203,x94202),a862)),x94205),x94207))+~P24(f332(f332(f246(f875(f874(x94201,x94203),a862)),x94204),x94206)) % 165.28/165.05 [9749]~P24(f332(f332(f334(x97491),x97496),x97495))+P24(f332(f67(x97491,x97492,x97493,x97494,x97495),f332(f332(x97493,x97496),x97497)))+~P24(f332(f67(x97491,x97492,x97493,x97494,f332(f332(f22(f875(x97491,a862)),x97495),f332(f332(f310(x97491),x97496),f196(f875(x97491,a862))))),x97497)) % 165.28/165.05 [10131]~P140(x101311)+~P21(f874(x101312,x101313),x101311,f332(f271(x101312,x101313,x101311),f332(f332(f7(x101312,f875(x101313,x101311),f875(x101313,x101311)),f332(f332(f8(f875(x101311,x101311),f875(f875(x101313,x101311),f875(x101313,x101311)),x101312),f8(x101311,x101311,x101313)),f332(f332(f8(x101311,f875(x101311,x101311),x101312),f82(x101311)),x101314))),x101315)),f332(f332(f269(x101312,x101313),x101316),f332(f16(f875(x101313,a862),x101312),x101317)))+E(f332(f332(f6(x101311,x101311),f35(x101311)),f332(f252(x101311),f332(f332(f8(f875(x101312,a862),a862,x101311),f88(x101312)),f332(f332(f8(f875(x101312,f875(x101313,a862)),f875(x101312,a862),x101311),f332(f8(f875(x101313,a862),a862,x101312),f88(x101313))),f332(f332(f7(x101311,f875(x101312,f875(x101313,a862)),f875(x101312,f875(x101313,a862))),f332(f332(f8(f875(x101312,f875(f875(x101313,a862),f875(x101313,a862))),f875(f875(x101312,f875(x101313,a862)),f875(x101312,f875(x101313,a862))),x101311),f18(x101312,f875(x101313,a862),f875(x101313,a862))),f332(f332(f8(f875(x101312,f875(x101313,f875(a862,a862))),f875(x101312,f875(f875(x101313,a862),f875(x101313,a862))),x101311),f332(f8(f875(x101313,f875(a862,a862)),f875(f875(x101313,a862),f875(x101313,a862)),x101312),f18(x101313,a862,a862))),f332(f332(f8(f875(x101312,f875(x101313,a862)),f875(x101312,f875(x101313,f875(a862,a862))),x101311),f332(f8(f875(x101313,a862),f875(x101313,f875(a862,a862)),x101312),f332(f8(a862,f875(a862,a862),x101313),a330))),f332(f332(f7(x101311,f875(x101312,f875(x101313,x101311)),f875(x101312,f875(x101313,a862))),f332(f332(f8(f875(f875(x101313,x101311),f875(x101313,a862)),f875(f875(x101312,f875(x101313,x101311)),f875(x101312,f875(x101313,a862))),x101311),f8(f875(x101313,x101311),f875(x101313,a862),x101312)),f332(f332(f8(f875(x101311,a862),f875(f875(x101313,x101311),f875(x101313,a862)),x101311),f8(x101311,a862,x101313)),a329))),f332(f332(f7(x101312,f875(x101313,x101311),f875(x101313,x101311)),f332(f332(f8(f875(x101311,x101311),f875(f875(x101313,x101311),f875(x101313,x101311)),x101312),f8(x101311,x101311,x101313)),f332(f332(f8(x101311,f875(x101311,x101311),x101312),f82(x101311)),x101314))),x101315)))))),f332(f332(f7(x101312,f875(x101313,a862),f875(x101313,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x101313,a862),f875(x101313,a862)),x101312),f8(a862,a862,x101313)),f332(f332(f8(a862,f875(a862,a862),x101312),a330),f332(f332(f7(x101312,f875(x101312,a862),a862),f334(x101312)),x101316)))),f332(f332(f7(x101313,f875(x101313,a862),a862),f334(x101313)),x101317))))))),f332(f332(f82(x101311),f332(f332(f6(x101312,x101311),x101314),x101316)),f332(f332(f6(x101313,x101311),x101315),x101317))) % 165.28/165.05 [9579]~P24(f332(f332(x95794,x95796),x95798))+~P24(f332(f332(x95795,x95798),x95797))+P24(f332(f332(f268(x95791,x95792,x95793,x95794,x95795),x95796),x95797)) % 165.28/165.05 [9195]~P15(x91958,x91951,x91953,x91955)+~P24(f332(f62(x91958),x91956))+E(f332(f74(x91951,x91951,x91952,f332(x91953,x91954)),f332(f74(x91951,x91951,x91952,f332(x91955,x91956)),x91957)),f332(f74(x91951,x91951,x91952,f332(x91955,x91956)),f332(f74(x91951,x91951,x91952,f332(x91953,x91954)),x91957))) % 165.28/165.05 [9569]~P18(x95697,x95692,x95695,x95698,x95696,x95691)+~P24(f332(f62(x95692),x95694))+E(f332(x95691,f332(f332(f310(x95692),x95693),x95694)),f332(f332(x95695,f332(x95696,x95693)),f332(x95691,x95694))) % 165.28/165.05 [9690]~P21(x96902,x96904,x96906,x96908)+~P21(x96901,x96903,x96905,x96907)+P21(f874(x96901,x96902),f874(x96903,x96904),f272(x96901,x96903,x96902,x96904,x96905,x96906),f332(f332(f269(x96901,x96902),x96907),f332(f16(f875(x96902,a862),x96901),x96908))) % 165.28/165.05 [9367]P24(f332(f332(f334(f874(x93671,x93672)),f332(f332(f267(x93671,x93672),x93673),x93674)),f332(f332(f289(x93671,x93675,x93672),x93676),x93677)))+~P24(f332(f332(f334(f874(x93671,x93675)),f332(f332(f267(x93671,x93675),x93673),x93678)),x93676))+~P24(f332(f332(f334(f874(x93675,x93672)),f332(f332(f267(x93675,x93672),x93678),x93674)),x93677)) % 165.28/165.05 [9550]~P24(f332(f332(f246(f875(f874(x95503,x95502),a862)),x95505),f332(f332(f269(x95503,x95502),x95508),f332(f16(f875(x95502,a862),x95503),x95507))))+~P24(f332(f332(f246(f875(f874(x95501,x95503),a862)),x95504),f332(f332(f269(x95501,x95503),x95506),f332(f16(f875(x95503,a862),x95501),x95508))))+P24(f332(f332(f246(f875(f874(x95501,x95502),a862)),f332(f332(f289(x95501,x95503,x95502),x95504),x95505)),f332(f332(f269(x95501,x95502),x95506),f332(f16(f875(x95502,a862),x95501),x95507)))) % 165.28/165.05 [9603]~E(x96033,x96035)+P24(f332(f332(f334(f874(f874(x96031,x96032),f874(x96031,x96032))),f332(f332(f267(f874(x96031,x96032),f874(x96031,x96032)),f332(f332(f267(x96031,x96032),x96033),x96034)),f332(f332(f267(x96031,x96032),x96035),x96036))),f324(x96031,x96032,x96037,x96038)))+~P24(f332(f332(f334(f874(x96032,x96032)),f332(f332(f267(x96032,x96032),x96034),x96036)),x96038)) % 165.28/165.05 [9713]E(x97131,x97132)+~P24(f332(f332(f334(f874(f874(x97133,x97135),f874(x97133,x97135))),f332(f332(f267(f874(x97133,x97135),f874(x97133,x97135)),f332(f332(f267(x97133,x97135),x97131),x97136)),f332(f332(f267(x97133,x97135),x97132),x97137))),f324(x97133,x97135,x97134,x97138)))+P24(f332(f332(f334(f874(x97133,x97133)),f332(f332(f267(x97133,x97133),x97131),x97132)),x97134)) % 165.28/165.05 [9730]~P24(f332(f332(f334(f874(f874(x97301,x97305),f874(x97301,x97305))),f332(f332(f267(f874(x97301,x97305),f874(x97301,x97305)),f332(f332(f267(x97301,x97305),x97302),x97306)),f332(f332(f267(x97301,x97305),x97303),x97307))),f324(x97301,x97305,x97304,x97308)))+P24(f332(f332(f334(f874(x97301,x97301)),f332(f332(f267(x97301,x97301),x97302),x97303)),x97304))+P24(f332(f332(f334(f874(x97305,x97305)),f332(f332(f267(x97305,x97305),x97306),x97307)),x97308)) % 165.28/165.05 [9634]~P19(x96347,x96345,x96341,x96348,x96342,x96344)+~P24(f332(f62(x96345),x96346))+E(f332(f332(x96341,f332(x96342,x96343)),f332(x96344,f332(f332(f22(f875(x96345,a862)),x96346),f332(f332(f310(x96345),x96343),f196(f875(x96345,a862)))))),f332(x96344,f332(f332(f310(x96345),x96343),x96346))) % 165.28/165.05 [9158]~P24(f332(f332(f332(x91585,x91588),x91586),x91587))+~P24(f332(f332(f334(x91581),x91588),x91584))+P24(f332(f332(f332(f332(f42(x91581,f875(x91582,f875(x91583,a862))),x91584),x91585),x91586),x91587)) % 165.28/165.05 [9354]P24(f332(f332(f332(x93541,x93542),x93543),x93544))+~P24(f332(f332(f334(x93545),x93542),x93546))+~P24(f332(f332(f332(f332(f43(x93545,f875(x93547,f875(x93548,a862))),x93546),x93541),x93543),x93544)) % 165.28/165.05 [9543]~P17(x95433,x95432,x95434,x95438,x95431)+~P24(f332(f62(x95432),x95437))+E(f332(f332(x95431,f332(f332(f18(x95432,x95433,x95433),f332(f332(f8(x95433,f875(x95433,x95433),x95432),x95434),x95435)),x95436)),x95437),f332(f332(x95434,f332(f332(x95431,x95435),x95437)),f332(f332(x95431,x95436),x95437))) % 165.28/165.05 [9820]~E(f332(f311(x98202,x98204,x98206),x98208),x982010)+~E(f332(f311(x98201,x98203,x98205),x98207),x98209)+E(f332(f311(f874(x98201,x98202),f874(x98203,x98204),f272(x98201,x98203,x98202,x98204,x98205,x98206)),f332(f332(f269(x98201,x98202),x98207),f332(f16(f875(x98202,a862),x98201),x98208))),f332(f332(f269(x98203,x98204),x98209),f332(f16(f875(x98204,a862),x98203),x982010))) % 165.28/165.05 [9806]~P1(a5000)+~P4(a5000)+P20(a864,f332(f311(a865,f867(a864),f332(f332(f8(a863,f867(a864),a865),a94),a28)),f186(a865,a863,a26)),x98061)+~P24(f332(f332(f246(f875(f867(a864),a862)),x98061),f332(f311(a865,f867(a864),f332(f332(f8(a863,f867(a864),a865),a94),f332(f332(f8(f872(a863),a863,a865),f243(a863)),a26))),f186(a865,a863,a26)))) % 165.28/165.05 [6498]~P1(a5000)+~P4(a5000)+~P24(f332(a25,x64981))+P20(a864,f196(f875(f867(a864),a862)),f332(f332(f310(f867(a864)),f332(a94,x64981)),f196(f875(f867(a864),a862)))) % 165.28/165.05 [4823]~P106(x48232)+~P32(x48232,x48231)+P32(x48232,f117(x48232,x48231))+E(x48231,f116(x48232)) % 165.28/165.05 [4824]~P106(x48242)+~P32(x48242,x48241)+P32(x48242,f607(x48241,x48242))+E(x48241,f116(x48242)) % 165.28/165.05 [5059]~P30(x50592)+E(f10(x50592,x50591),f40(x50592,x50591))+E(x50591,f196(f875(x50592,a862)))+~P24(f332(f62(x50592),x50591)) % 165.28/165.05 [5060]~P30(x50602)+E(f11(x50602,x50601),f41(x50602,x50601))+E(x50601,f196(f875(x50602,a862)))+~P24(f332(f62(x50602),x50601)) % 165.28/165.05 [5221]~P106(x52212)+~P32(x52212,x52211)+E(x52211,f116(x52212))+E(f332(f332(f152(x52212),f648(x52211,x52212)),f607(x52211,x52212)),x52211) % 165.28/165.05 [6021]~P26(x60212)+E(x60211,f196(f875(x60212,a862)))+P24(f332(f332(f246(x60212),f11(x60212,x60211)),f10(x60212,x60211)))+~P24(f332(f62(x60212),x60211)) % 165.28/165.05 [6033]~P42(x60332)+~P42(x60331)+E(x60331,x60332)+~E(f332(f311(a1,a868,a107),x60331),f332(f311(a1,a868,a107),x60332)) % 165.28/165.05 [9018]~P118(x90181)+~P24(f332(f332(f334(x90181),x90182),f112(x90181)))+P24(f332(f332(f247(x90181),f332(f332(f81(x90181),f332(f332(f81(x90181),f79(x90181)),x90182)),x90182)),f2(x90181)))+~P24(f332(f332(f247(x90181),x90182),f2(x90181))) % 165.28/165.05 [9245]~P118(x92451)+~P24(f332(f332(f334(x92451),x92452),f112(x92451)))+~P24(f332(f332(f247(x92451),f332(f332(f81(x92451),f332(f332(f81(x92451),f79(x92451)),x92452)),x92452)),f2(x92451)))+P24(f332(f332(f247(x92451),x92452),f2(x92451))) % 165.28/165.05 [4879]~P140(x48792)+~P110(x48792)+E(x48791,f2(a868))+E(f332(f332(f257(x48792),f2(x48792)),x48791),f2(x48792)) % 165.28/165.05 [4883]~P140(x48831)+~P110(x48831)+~E(x48832,f2(a868))+E(f332(f332(f257(x48831),f2(x48831)),x48832),f79(x48831)) % 165.28/165.05 [5046]~P137(x50462)+E(x50461,f79(x50462))+E(x50461,f332(f80(x50462),f79(x50462)))+~E(f332(f332(f82(x50462),x50461),x50461),f79(x50462)) % 165.28/165.05 [5307]~P88(x53072)+E(x53071,f2(x53072))+E(f83(x53072,x53071),f332(f80(x53072),f79(x53072)))+P24(f332(f332(f247(x53072),f2(x53072)),x53071)) % 165.28/165.05 [5542]~P88(x55422)+E(f83(x55422,x55421),f79(x55422))+E(x55421,f2(x55422))+~P24(f332(f332(f247(x55422),f2(x55422)),x55421)) % 165.28/165.05 [5551]E(x55511,x55512)+~E(f332(f106(a868),x55511),f332(f106(a868),x55512))+P24(f332(a201,f332(f106(a1),x55512)))+P24(f332(a201,f332(f106(a1),x55511))) % 165.28/165.05 [5601]~P91(x56011)+~E(x56012,f2(x56011))+E(f332(f332(f81(x56011),x56012),x56012),f2(x56011))+~P24(f332(f332(f334(x56011),x56012),f112(x56011))) % 165.28/165.05 [5639]E(x56391,f2(a1))+~E(f332(f332(f39(a1),x56392),x56391),f2(a1))+P24(f332(f332(f247(a1),x56391),x56392))+P24(f332(f332(f247(a1),x56392),x56391)) % 165.28/165.05 [5670]E(x56701,f2(a1))+~E(f332(f332(f39(a1),x56702),x56701),f2(a1))+P24(f332(f332(f246(a1),x56702),f2(a1)))+P24(f332(f332(f247(a1),x56702),x56701)) % 165.28/165.05 [5704]E(x57041,f2(a1))+~E(f332(f332(f39(a1),x57042),x57041),f2(a1))+P24(f332(f332(f246(a1),f2(a1)),x57042))+P24(f332(f332(f247(a1),x57041),x57042)) % 165.28/165.05 [5740]~P91(x57402)+E(x57401,f2(x57402))+~E(f332(f332(f81(x57402),x57401),x57401),f2(x57402))+~P24(f332(f332(f334(x57402),x57401),f112(x57402))) % 165.28/165.05 [5800]E(f332(f106(a868),x58001),f332(f106(a868),x58002))+~E(f332(f106(a1),x58002),f2(a1))+P24(f332(a201,f332(f106(a1),x58002)))+~P24(f332(a201,f332(f106(a1),x58001))) % 165.28/165.05 [5827]~E(f332(f106(a868),x58272),f332(f106(a868),x58271))+E(f332(f106(a1),x58271),f2(a1))+P24(f332(a201,f332(f106(a1),x58271)))+~P24(f332(a201,f332(f106(a1),x58272))) % 165.28/165.05 [5836]~P106(x58362)+E(x58361,f196(f875(x58362,a862)))+~P24(f332(f62(x58362),x58361))+P24(f332(f332(f334(x58362),f14(x58362,x58361)),x58361)) % 165.28/165.05 [5837]~P106(x58372)+E(x58371,f196(f875(x58372,a862)))+~P24(f332(f62(x58372),x58371))+P24(f332(f332(f334(x58372),f15(x58372,x58371)),x58371)) % 165.28/165.05 [6001]~P118(x60011)+~P92(x60011)+P24(f332(f332(f246(x60011),f2(x60011)),f332(f106(x60011),x60012)))+~P24(f332(f332(f246(a1),a84),x60012)) % 165.28/165.05 [6002]~P118(x60021)+~P92(x60021)+P24(f332(f332(f247(x60021),f2(x60021)),f332(f106(x60021),x60022)))+~P24(f332(f332(f247(a1),a84),x60022)) % 165.28/165.05 [6020]~P118(x60201)+~P92(x60201)+E(f332(f76(x60201),f332(f106(x60201),x60202)),f332(f106(x60201),x60202))+P24(f332(f332(f247(x60201),f332(f106(x60201),x60202)),f2(x60201))) % 165.28/165.05 [6060]E(x60601,x60602)+~E(f332(a107,x60601),f332(a107,x60602))+~P24(f332(f332(f246(a1),f2(a1)),x60602))+~P24(f332(f332(f246(a1),f2(a1)),x60601)) % 165.28/165.05 [6258]~P92(x62582)+~P118(x62582)+~P24(f332(f332(f246(x62582),f2(x62582)),f332(f106(x62582),x62581)))+P24(f332(f332(f246(a1),a84),x62581)) % 165.28/165.05 [6259]~P92(x62592)+~P118(x62592)+~P24(f332(f332(f247(x62592),f2(x62592)),f332(f106(x62592),x62591)))+P24(f332(f332(f247(a1),a84),x62591)) % 165.28/165.05 [6264]~P118(x62641)+~P92(x62641)+P24(f332(f332(f246(x62641),f332(f106(x62641),x62642)),f2(x62641)))+~P24(f332(f332(f246(a1),x62642),a84)) % 165.28/165.05 [6265]~P118(x62651)+~P92(x62651)+P24(f332(f332(f247(x62651),f332(f106(x62651),x62652)),f2(x62651)))+~P24(f332(f332(f247(a1),x62652),a84)) % 165.28/165.05 [6575]~P92(x65752)+~P118(x65752)+~P24(f332(f332(f246(x65752),f332(f106(x65752),x65751)),f2(x65752)))+P24(f332(f332(f246(a1),x65751),a84)) % 165.28/165.05 [6576]~P92(x65762)+~P118(x65762)+~P24(f332(f332(f247(x65762),f332(f106(x65762),x65761)),f2(x65762)))+P24(f332(f332(f247(a1),x65761),a84)) % 165.28/165.05 [6666]~P118(x66661)+~P92(x66661)+E(f332(f76(x66661),f332(f106(x66661),x66662)),f332(f80(x66661),f332(f106(x66661),x66662)))+~P24(f332(f332(f247(x66661),f332(f106(x66661),x66662)),f2(x66661))) % 165.28/165.05 [6684]E(f332(f106(a868),x66841),f332(f106(a868),x66842))+~E(f332(f106(a1),x66842),f2(a1))+~P24(f332(f332(f246(a1),f332(f106(a1),x66841)),f2(a1)))+~P24(f332(a201,f332(f106(a1),x66841))) % 165.28/165.05 [7559]~P106(x75592)+E(x75591,f196(f875(x75592,a862)))+~P24(f332(f62(x75592),x75591))+P24(f332(f332(f246(x75592),f12(x75592,f244(x75592),x75591)),f13(x75592,f245(x75592),x75591))) % 165.28/165.05 [7874]~P42(x78742)+~P31(x78741)+P24(f332(f332(f334(a1),x78741),x78742))+~P24(f332(f332(f334(a868),f332(a107,x78741)),f332(f311(a1,a868,a107),x78742))) % 165.28/165.05 [8140]~P59(x81402)+P24(f332(x81401,f209(x81402)))+~P24(f332(f58(f872(x81402)),x81401))+P24(f332(f58(x81402),f332(f332(f8(f872(x81402),a862,x81402),x81401),f208(x81402)))) % 165.28/165.05 [8590]~P59(x85901)+~P24(f332(x85902,f209(x85901)))+P24(f332(f59(f872(x85901)),x85902))+~P24(f332(f59(x85901),f332(f332(f8(f872(x85901),a862,x85901),x85902),f208(x85901)))) % 165.28/165.05 [5833]~P138(x58332)+E(x58331,f2(a1))+E(f332(f80(x58332),f332(f105(x58332),f332(f80(a1),x58331))),f332(f105(x58332),x58331))+~P24(f332(f332(f247(a1),x58331),f2(a1))) % 165.28/165.05 [5906]~P91(x59061)+~P92(x59061)+~P34(x59061,f332(f106(x59061),x59062))+P34(x59061,f332(f106(x59061),f332(f332(f81(a1),x59062),x59062))) % 165.28/165.05 [6247]~P75(x62472)+E(x62471,f196(f875(x62472,a862)))+E(f15(x62472,f332(f311(x62472,x62472,f80(x62472)),x62471)),f332(f80(x62472),f14(x62472,x62471)))+~P24(f332(f62(x62472),x62471)) % 165.28/165.05 [6248]~P75(x62482)+E(x62481,f196(f875(x62482,a862)))+E(f14(x62482,f332(f311(x62482,x62482,f80(x62482)),x62481)),f332(f80(x62482),f15(x62482,x62481)))+~P24(f332(f62(x62482),x62481)) % 165.28/165.05 [6279]~P91(x62791)+~P92(x62791)+P34(x62791,f332(f106(x62791),x62792))+~P34(x62791,f332(f106(x62791),f332(f332(f81(a1),x62792),x62792))) % 165.28/165.05 [6370]E(x63701,f2(a1))+E(f332(a51,f50(f332(f80(a1),x63701),f332(f80(a1),x63702))),f46(x63701,x63702))+P24(f332(f332(f246(a1),f2(a1)),x63702))+~P24(f332(f332(f246(a1),f2(a1)),x63701)) % 165.28/165.05 [7382]~P4(a5000)+~P24(f332(a25,x73821))+P20(a864,x73822,f332(f332(f310(f867(a864)),f332(a94,x73821)),f196(f875(f867(a864),a862))))+P24(f332(f332(f334(a865),f668(x73821,x73822)),f186(a865,a863,a26))) % 165.28/165.05 [8622]~P4(a5000)+~P24(f332(a25,x86222))+P20(a864,x86221,f332(f332(f310(f867(a864)),f332(a94,x86222)),f196(f875(f867(a864),a862))))+~P20(a864,x86221,f332(f332(f310(f867(a864)),f332(a94,f332(a28,f668(x86222,x86221)))),f196(f875(f867(a864),a862)))) % 165.28/165.05 [8636]~P42(x86362)+~P42(x86361)+P24(f332(f332(f247(f875(a868,a862)),f332(f311(a1,a868,a107),x86361)),f332(f311(a1,a868,a107),x86362)))+~P24(f332(f332(f247(f875(a1,a862)),x86361),x86362)) % 165.28/165.05 [8848]~E(f662(x88482,x88481),f663(x88482,x88481))+~P24(f332(f138(x88481),f664(x88482,x88481)))+~P24(f332(f138(f869(x88481)),x88482))+P24(f332(f138(x88481),f332(f143(f869(x88481),f869(x88481),f135(x88481),f116(x88481)),x88482))) % 165.28/165.05 [8937]~P42(x89372)+~P42(x89371)+~P24(f332(f332(f246(f875(a868,a862)),f332(f311(a1,a868,a107),x89371)),f332(f311(a1,a868,a107),x89372)))+P24(f332(f332(f246(f875(a1,a862)),x89371),x89372)) % 165.28/165.05 [8938]~P42(x89382)+~P42(x89381)+~P24(f332(f332(f247(f875(a868,a862)),f332(f311(a1,a868,a107),x89381)),f332(f311(a1,a868,a107),x89382)))+P24(f332(f332(f247(f875(a1,a862)),x89381),x89382)) % 165.28/165.05 [8944]~E(f662(x89442,x89441),f663(x89442,x89441))+~P24(f332(f138(f869(x89441)),x89442))+P24(f332(f138(x89441),f332(f143(f869(x89441),f869(x89441),f135(x89441),f116(x89441)),x89442)))+P24(f332(f332(f334(f869(x89441)),f664(x89442,x89441)),f332(f174(f869(x89441)),x89442))) % 165.28/165.05 [8986]~P24(f332(f138(x89861),f664(x89862,x89861)))+~P24(f332(f138(f869(x89861)),x89862))+P24(f332(f138(x89861),f332(f143(f869(x89861),f869(x89861),f135(x89861),f116(x89861)),x89862)))+P24(f332(f332(f334(f869(x89861)),f663(x89862,x89861)),f332(f174(f869(x89861)),x89862))) % 165.28/165.05 [8987]~P24(f332(f138(x89871),f664(x89872,x89871)))+~P24(f332(f138(f869(x89871)),x89872))+P24(f332(f138(x89871),f332(f143(f869(x89871),f869(x89871),f135(x89871),f116(x89871)),x89872)))+P24(f332(f332(f334(f869(x89871)),f662(x89872,x89871)),f332(f174(f869(x89871)),x89872))) % 165.28/165.05 [9062]~P24(f332(f138(f869(x90621)),x90622))+P24(f332(f138(x90621),f332(f143(f869(x90621),f869(x90621),f135(x90621),f116(x90621)),x90622)))+P24(f332(f332(f334(f869(x90621)),f663(x90622,x90621)),f332(f174(f869(x90621)),x90622)))+P24(f332(f332(f334(f869(x90621)),f664(x90622,x90621)),f332(f174(f869(x90621)),x90622))) % 165.28/165.05 [9063]~P24(f332(f138(f869(x90631)),x90632))+P24(f332(f138(x90631),f332(f143(f869(x90631),f869(x90631),f135(x90631),f116(x90631)),x90632)))+P24(f332(f332(f334(f869(x90631)),f662(x90632,x90631)),f332(f174(f869(x90631)),x90632)))+P24(f332(f332(f334(f869(x90631)),f664(x90632,x90631)),f332(f174(f869(x90631)),x90632))) % 165.28/165.05 [9076]~E(f332(f332(f104(f875(x90761,a862)),f332(f174(x90761),f663(x90762,x90761))),f332(f174(x90761),f662(x90762,x90761))),f196(f875(x90761,a862)))+~P24(f332(f138(x90761),f664(x90762,x90761)))+~P24(f332(f138(f869(x90761)),x90762))+P24(f332(f138(x90761),f332(f143(f869(x90761),f869(x90761),f135(x90761),f116(x90761)),x90762))) % 165.28/165.05 [9135]~E(f332(f332(f104(f875(x91351,a862)),f332(f174(x91351),f663(x91352,x91351))),f332(f174(x91351),f662(x91352,x91351))),f196(f875(x91351,a862)))+~P24(f332(f138(f869(x91351)),x91352))+P24(f332(f138(x91351),f332(f143(f869(x91351),f869(x91351),f135(x91351),f116(x91351)),x91352)))+P24(f332(f332(f334(f869(x91351)),f664(x91352,x91351)),f332(f174(f869(x91351)),x91352))) % 165.28/165.05 [9390]E(x93901,f2(a1))+E(x93902,f2(a1))+E(f332(f332(f87(a1,f874(a1,a1)),f332(f332(a229,x93902),x93901)),f332(f332(f18(a1,a1,f874(a1,a1)),f332(f332(f8(a1,f875(a1,f874(a1,a1)),a1),f267(a1,a1)),f332(f39(a1),x93902))),f332(f39(a1),x93901))),f227(x93902,x93901))+P24(f332(f332(f247(a1),x93901),f2(a1))) % 165.28/165.05 [8201]~P92(x82012)+~P118(x82012)+~P24(f332(f332(f246(x82012),f332(f106(x82012),x82011)),f79(x82012)))+P24(f332(f332(f246(a1),x82011),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))) % 165.28/165.05 [8202]~P92(x82022)+~P118(x82022)+~P24(f332(f332(f247(x82022),f332(f106(x82022),x82021)),f79(x82022)))+P24(f332(f332(f247(a1),x82021),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))) % 165.28/165.05 [8464]~P118(x84641)+~P92(x84641)+P24(f332(f332(f246(x84641),f332(f106(x84641),x84642)),f79(x84641)))+~P24(f332(f332(f246(a1),x84642),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))) % 165.28/165.05 [8465]~P118(x84651)+~P92(x84651)+P24(f332(f332(f247(x84651),f332(f106(x84651),x84652)),f79(x84651)))+~P24(f332(f332(f247(a1),x84652),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))) % 165.28/165.05 [8661]~P92(x86612)+~P118(x86612)+~P24(f332(f332(f246(x86612),f79(x86612)),f332(f106(x86612),x86611)))+P24(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),x86611)) % 165.28/165.05 [8662]~P92(x86622)+~P118(x86622)+~P24(f332(f332(f247(x86622),f79(x86622)),f332(f106(x86622),x86621)))+P24(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),x86621)) % 165.28/165.05 [9024]~P118(x90241)+~P92(x90241)+P24(f332(f332(f246(x90241),f79(x90241)),f332(f106(x90241),x90242)))+~P24(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),x90242)) % 165.28/165.05 [9025]~P118(x90251)+~P92(x90251)+P24(f332(f332(f247(x90251),f79(x90251)),f332(f106(x90251),x90252)))+~P24(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),x90252)) % 165.28/165.05 [9515]~P137(x95152)+E(x95151,f79(x95152))+E(x95151,f332(f80(x95152),f79(x95152)))+~E(f332(f332(f257(x95152),x95151),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f79(x95152)) % 165.28/165.05 [9789]~P62(x97891)+~P92(x97891)+~P24(f332(f332(f247(x97891),f2(x97891)),x97892))+P24(f332(f332(f247(x97891),f2(x97891)),f332(f332(f290(x97891),x97892),f332(f106(x97891),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))) % 165.28/165.05 [9850]~P62(x98501)+~P92(x98501)+P24(f332(f332(f247(x98501),f2(x98501)),x98502))+~P24(f332(f332(f247(x98501),f2(x98501)),f332(f332(f290(x98501),x98502),f332(f106(x98501),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))) % 165.28/165.05 [10102]~P138(x101022)+E(x101021,f2(a1))+P24(f332(f332(f247(a1),x101021),f2(a1)))+E(f332(f332(f271(a1,a1,x101022),f332(f332(f7(a1,f875(a1,f875(x101022,x101022)),f875(a1,x101022)),f332(f332(f8(f875(f875(x101022,x101022),x101022),f875(f875(a1,f875(x101022,x101022)),f875(a1,x101022)),a1),f8(f875(x101022,x101022),x101022,a1)),f332(f332(f8(x101022,f875(f875(x101022,x101022),x101022),a1),f87(x101022,x101022)),f105(x101022)))),f332(f332(f7(a1,f875(x101022,x101022),f875(x101022,x101022)),f332(f332(f8(f875(x101022,f875(x101022,x101022)),f875(f875(x101022,x101022),f875(x101022,x101022)),a1),f18(x101022,x101022,x101022)),f332(f332(f7(a1,f875(x101022,x101022),f875(x101022,f875(x101022,x101022))),f332(f332(f8(f875(x101022,f875(x101022,x101022)),f875(f875(x101022,x101022),f875(x101022,f875(x101022,x101022))),a1),f8(x101022,f875(x101022,x101022),x101022)),f332(f332(f8(a862,f875(x101022,f875(x101022,x101022)),a1),f99(x101022)),f332(f332(f7(a1,a1,a862),a329),f2(a1))))),f332(f332(f18(x101022,x101022,x101022),f81(x101022)),f5(x101022))))),f332(f332(f7(x101022,x101022,x101022),f332(f332(f8(x101022,f875(x101022,x101022),x101022),f81(x101022)),f332(f332(f18(x101022,x101022,x101022),f81(x101022)),f5(x101022)))),f79(x101022))))),f46(x101021,f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f105(x101022),x101021)) % 165.28/165.05 [5216]~P59(x52163)+~P39(x52163,x52162,f56(x52163))+E(x52161,f780(x52162,x52163))+~P24(f332(x52162,x52161)) % 165.28/165.05 [5377]~P59(x53771)+P39(x53771,x53772,f56(x53771))+~E(f781(x53772,x53771,x53773),x53773)+~P24(f332(x53772,x53773)) % 165.28/165.05 [4850]~P91(x48503)+~P92(x48503)+E(x48501,x48502)+~E(f332(f106(x48503),x48501),f332(f106(x48503),x48502)) % 165.28/165.05 [6000]~P59(x60001)+P39(x60001,x60002,f56(x60001))+~P24(f332(x60002,x60003))+P24(f332(x60002,f781(x60002,x60001,x60003))) % 165.28/165.05 [6010]~P24(f332(x60101,x60102))+~P24(f332(x60101,x60103))+~P24(f332(f332(f246(a868),x60103),f408(x60102,x60101)))+P24(f332(x60101,f2(a868))) % 165.28/165.05 [6433]P145(x64332,x64333,x64331)+E(x64331,f2(a1))+P24(f332(f332(f246(a1),f2(a1)),f805(x64331,x64333,x64332)))+P24(f332(f332(f247(a1),x64331),f2(a1))) % 165.28/165.05 [6434]P144(x64342,x64343,x64341)+E(x64341,f2(a1))+P24(f332(f332(f246(a1),f2(a1)),f811(x64341,x64343,x64342)))+P24(f332(f332(f247(a1),x64341),f2(a1))) % 165.28/165.05 [6555]P144(x65551,x65552,x65553)+~P24(f332(x65551,x65552))+P24(f332(f332(f246(a1),f2(a1)),f811(x65553,x65552,x65551)))+P24(f332(f332(f247(a1),x65553),f2(a1))) % 165.28/165.05 [6581]P145(x65811,x65812,x65813)+P24(f332(f332(f246(a1),f2(a1)),f805(x65813,x65812,x65811)))+~P24(f332(x65811,f2(a1)))+P24(f332(f332(f247(a1),x65813),f2(a1))) % 165.28/165.05 [6609]P145(x66092,x66093,x66091)+E(x66091,f2(a1))+~P24(f332(x66092,f806(x66091,x66093,x66092)))+P24(f332(f332(f247(a1),x66091),f2(a1))) % 165.28/165.05 [6610]P144(x66102,x66103,x66101)+E(x66101,f2(a1))+~P24(f332(x66102,f811(x66101,x66103,x66102)))+P24(f332(f332(f247(a1),x66101),f2(a1))) % 165.28/165.05 [6709]~P106(x67091)+~P30(x67091)+~P24(f332(f332(f247(x67091),x67092),f40(x67091,x67093)))+P24(f332(f332(f247(x67091),x67092),f637(x67093,x67092,x67091))) % 165.28/165.05 [6718]P144(x67181,x67182,x67183)+~P24(f332(x67181,x67182))+~P24(f332(x67181,f811(x67183,x67182,x67181)))+P24(f332(f332(f247(a1),x67183),f2(a1))) % 165.28/165.05 [6750]P145(x67501,x67502,x67503)+~P24(f332(x67501,f806(x67503,x67502,x67501)))+~P24(f332(x67501,f2(a1)))+P24(f332(f332(f247(a1),x67503),f2(a1))) % 165.28/165.05 [7000]P145(x70002,x70003,x70001)+E(x70001,f2(a1))+P24(f332(f332(f246(a1),f2(a1)),f805(x70001,x70003,x70002)))+P24(f332(f332(f247(a1),x70001),f804(x70001,x70003,x70002))) % 165.28/165.05 [7001]P144(x70012,x70013,x70011)+E(x70011,f2(a1))+P24(f332(f332(f246(a1),f2(a1)),f811(x70011,x70013,x70012)))+P24(f332(f332(f247(a1),x70011),f810(x70011,x70013,x70012))) % 165.28/165.05 [7118]P144(x71181,x71182,x71183)+~P24(f332(x71181,x71182))+P24(f332(f332(f246(a1),f2(a1)),f811(x71183,x71182,x71181)))+P24(f332(f332(f247(a1),x71183),f810(x71183,x71182,x71181))) % 165.28/165.05 [7137]P145(x71371,x71372,x71373)+P24(f332(f332(f246(a1),f2(a1)),f805(x71373,x71372,x71371)))+P24(f332(f332(f247(a1),x71373),f804(x71373,x71372,x71371)))+~P24(f332(x71371,f2(a1))) % 165.28/165.05 [7170]P145(x71702,x71703,x71701)+E(x71701,f2(a1))+~P24(f332(x71702,f806(x71701,x71703,x71702)))+P24(f332(f332(f247(a1),x71701),f804(x71701,x71703,x71702))) % 165.28/165.05 [7171]P144(x71712,x71713,x71711)+E(x71711,f2(a1))+~P24(f332(x71712,f811(x71711,x71713,x71712)))+P24(f332(f332(f247(a1),x71711),f810(x71711,x71713,x71712))) % 165.28/165.05 [7212]P145(x72122,x72123,x72121)+E(x72121,f2(a1))+P24(f332(f332(f246(a1),f2(a1)),f805(x72121,x72123,x72122)))+~P24(f332(x72122,f809(x72121,x72123,x72122))) % 165.28/165.05 [7213]P144(x72132,x72133,x72131)+E(x72131,f2(a1))+P24(f332(f332(f246(a1),f2(a1)),f811(x72131,x72133,x72132)))+~P24(f332(x72132,f810(x72131,x72133,x72132))) % 165.28/165.05 [7301]P144(x73011,x73012,x73013)+~P24(f332(x73011,x73012))+~P24(f332(x73011,f811(x73013,x73012,x73011)))+P24(f332(f332(f247(a1),x73013),f810(x73013,x73012,x73011))) % 165.28/165.05 [7317]P145(x73171,x73172,x73173)+~P24(f332(x73171,f806(x73173,x73172,x73171)))+P24(f332(f332(f247(a1),x73173),f804(x73173,x73172,x73171)))+~P24(f332(x73171,f2(a1))) % 165.28/165.05 [7321]P144(x73211,x73212,x73213)+~P24(f332(x73211,x73212))+P24(f332(f332(f246(a1),f2(a1)),f811(x73213,x73212,x73211)))+~P24(f332(x73211,f810(x73213,x73212,x73211))) % 165.28/165.05 [7337]P145(x73371,x73372,x73373)+P24(f332(f332(f246(a1),f2(a1)),f805(x73373,x73372,x73371)))+~P24(f332(x73371,f809(x73373,x73372,x73371)))+~P24(f332(x73371,f2(a1))) % 165.28/165.05 [7360]P145(x73602,x73603,x73601)+E(x73601,f2(a1))+~P24(f332(x73602,f806(x73601,x73603,x73602)))+~P24(f332(x73602,f809(x73601,x73603,x73602))) % 165.28/165.05 [7361]P144(x73612,x73613,x73611)+E(x73611,f2(a1))+~P24(f332(x73612,f811(x73611,x73613,x73612)))+~P24(f332(x73612,f810(x73611,x73613,x73612))) % 165.28/165.05 [7453]P144(x74531,x74532,x74533)+~P24(f332(x74531,x74532))+~P24(f332(x74531,f811(x74533,x74532,x74531)))+~P24(f332(x74531,f810(x74533,x74532,x74531))) % 165.28/165.05 [7470]P145(x74701,x74702,x74703)+~P24(f332(x74701,f806(x74703,x74702,x74701)))+~P24(f332(x74701,f809(x74703,x74702,x74701)))+~P24(f332(x74701,f2(a1))) % 165.28/165.05 [7519]P145(x75192,x75193,x75191)+E(x75191,f2(a1))+P24(f332(f332(f246(a1),f2(a1)),f805(x75191,x75193,x75192)))+P24(f332(f332(f246(a1),f804(x75191,x75193,x75192)),f2(a1))) % 165.28/165.05 [7520]P144(x75202,x75203,x75201)+E(x75201,f2(a1))+P24(f332(f332(f246(a1),f2(a1)),f811(x75201,x75203,x75202)))+P24(f332(f332(f246(a1),f810(x75201,x75203,x75202)),f2(a1))) % 165.28/165.05 [7521]~P87(x75211)+~P24(f332(f332(f246(x75211),x75213),f2(x75211)))+~P24(f332(f332(f246(x75211),x75212),f2(x75211)))+P24(f332(f332(f246(x75211),f332(f332(f81(x75211),x75212),x75213)),f2(x75211))) % 165.28/165.05 [7522]~P138(x75221)+~P24(f332(f332(f334(x75221),x75223),f112(x75221)))+~P24(f332(f332(f334(x75221),x75222),f112(x75221)))+P24(f332(f332(f334(x75221),f332(f332(f22(x75221),x75222),x75223)),f112(x75221))) % 165.28/165.05 [7523]~P138(x75231)+~P24(f332(f332(f334(x75231),x75233),f112(x75231)))+~P24(f332(f332(f334(x75231),x75232),f112(x75231)))+P24(f332(f332(f334(x75231),f332(f332(f81(x75231),x75232),x75233)),f112(x75231))) % 165.28/165.05 [7524]~P142(x75241)+~P24(f332(f332(f334(x75241),x75243),f194(x75241)))+~P24(f332(f332(f334(x75241),x75242),f194(x75241)))+P24(f332(f332(f334(x75241),f332(f332(f81(x75241),x75242),x75243)),f194(x75241))) % 165.28/165.05 [7525]~P138(x75251)+~P24(f332(f332(f334(x75251),x75253),f112(x75251)))+~P24(f332(f332(f334(x75251),x75252),f112(x75251)))+P24(f332(f332(f334(x75251),f332(f332(f82(x75251),x75252),x75253)),f112(x75251))) % 165.28/165.05 [7526]~P142(x75261)+~P24(f332(f332(f334(x75261),x75263),f194(x75261)))+~P24(f332(f332(f334(x75261),x75262),f194(x75261)))+P24(f332(f332(f334(x75261),f332(f332(f82(x75261),x75262),x75263)),f194(x75261))) % 165.28/165.05 [7527]~P87(x75271)+~P24(f332(f332(f246(x75271),x75273),f2(x75271)))+~P24(f332(f332(f247(x75271),x75272),f2(x75271)))+P24(f332(f332(f247(x75271),f332(f332(f81(x75271),x75272),x75273)),f2(x75271))) % 165.28/165.05 [7528]~P87(x75281)+~P24(f332(f332(f246(x75281),x75282),f2(x75281)))+~P24(f332(f332(f247(x75281),x75283),f2(x75281)))+P24(f332(f332(f247(x75281),f332(f332(f81(x75281),x75282),x75283)),f2(x75281))) % 165.28/165.05 [7529]~P87(x75291)+~P24(f332(f332(f247(x75291),x75293),f2(x75291)))+~P24(f332(f332(f247(x75291),x75292),f2(x75291)))+P24(f332(f332(f247(x75291),f332(f332(f81(x75291),x75292),x75293)),f2(x75291))) % 165.28/165.05 [7555]P145(x75553,x75552,x75551)+E(x75551,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x75551),f806(x75551,x75552,x75553))),f805(x75551,x75552,x75553)),x75552)+P24(f332(f332(f247(a1),x75551),f2(a1))) % 165.28/165.05 [7556]P144(x75563,x75562,x75561)+E(x75561,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x75561),f812(x75561,x75562,x75563))),f811(x75561,x75562,x75563)),x75562)+P24(f332(f332(f247(a1),x75561),f2(a1))) % 165.28/165.05 [7638]P144(x76381,x76382,x76383)+~P24(f332(x76381,x76382))+P24(f332(f332(f246(a1),f2(a1)),f811(x76383,x76382,x76381)))+P24(f332(f332(f246(a1),f810(x76383,x76382,x76381)),f2(a1))) % 165.28/165.05 [7667]P145(x76671,x76672,x76673)+P24(f332(f332(f246(a1),f2(a1)),f805(x76673,x76672,x76671)))+~P24(f332(x76671,f2(a1)))+P24(f332(f332(f246(a1),f804(x76673,x76672,x76671)),f2(a1))) % 165.28/165.05 [7676]P144(x76763,x76762,x76761)+~P24(f332(x76763,x76762))+E(f332(f332(f81(a1),f332(f332(f82(a1),x76761),f812(x76761,x76762,x76763))),f811(x76761,x76762,x76763)),x76762)+P24(f332(f332(f247(a1),x76761),f2(a1))) % 165.28/165.05 [7683]P145(x76832,x76833,x76831)+E(x76831,f2(a1))+~P24(f332(x76832,f806(x76831,x76833,x76832)))+P24(f332(f332(f246(a1),f804(x76831,x76833,x76832)),f2(a1))) % 165.28/165.05 [7684]P144(x76842,x76843,x76841)+E(x76841,f2(a1))+~P24(f332(x76842,f811(x76841,x76843,x76842)))+P24(f332(f332(f246(a1),f810(x76841,x76843,x76842)),f2(a1))) % 165.28/165.05 [7689]P145(x76893,x76892,x76891)+E(f332(f332(f81(a1),f332(f332(f82(a1),x76891),f806(x76891,x76892,x76893))),f805(x76891,x76892,x76893)),x76892)+~P24(f332(x76893,f2(a1)))+P24(f332(f332(f247(a1),x76891),f2(a1))) % 165.28/165.05 [7745]P144(x77451,x77452,x77453)+~P24(f332(x77451,x77452))+~P24(f332(x77451,f811(x77453,x77452,x77451)))+P24(f332(f332(f246(a1),f810(x77453,x77452,x77451)),f2(a1))) % 165.28/165.05 [7749]P145(x77491,x77492,x77493)+~P24(f332(x77491,f806(x77493,x77492,x77491)))+~P24(f332(x77491,f2(a1)))+P24(f332(f332(f246(a1),f804(x77493,x77492,x77491)),f2(a1))) % 165.28/165.05 [7816]~P122(x78161)+~P24(f332(f332(f246(x78161),f332(f332(f82(x78161),x78163),x78162)),f2(x78161)))+P24(f332(f332(f246(x78161),x78162),f2(x78161)))+P24(f332(f332(f246(x78161),x78163),f2(x78161))) % 165.28/165.05 [7817]~P62(x78171)+~P24(f332(f332(f246(x78171),f332(f332(f290(x78171),x78173),x78172)),f2(x78171)))+P24(f332(f332(f246(x78171),x78172),f2(x78171)))+P24(f332(f332(f246(x78171),x78173),f2(x78171))) % 165.28/165.05 [7818]~P62(x78181)+~P24(f332(f332(f247(x78181),f332(f332(f290(x78181),x78183),x78182)),f2(x78181)))+P24(f332(f332(f247(x78181),x78182),f2(x78181)))+P24(f332(f332(f247(x78181),x78183),f2(x78181))) % 165.30/165.05 [7931]P145(x79313,x79312,x79311)+E(x79311,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x79311),f806(x79311,x79312,x79313))),f805(x79311,x79312,x79313)),x79312)+P24(f332(f332(f247(a1),x79311),f804(x79311,x79312,x79313))) % 165.30/165.05 [7932]P144(x79323,x79322,x79321)+E(x79321,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x79321),f812(x79321,x79322,x79323))),f811(x79321,x79322,x79323)),x79322)+P24(f332(f332(f247(a1),x79321),f810(x79321,x79322,x79323))) % 165.30/165.05 [7944]P145(x79443,x79442,x79441)+E(x79441,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x79441),f809(x79441,x79442,x79443))),f804(x79441,x79442,x79443)),x79442)+P24(f332(f332(f246(a1),f2(a1)),f805(x79441,x79442,x79443))) % 165.30/165.05 [7945]P144(x79453,x79452,x79451)+E(x79451,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x79451),f813(x79451,x79452,x79453))),f810(x79451,x79452,x79453)),x79452)+P24(f332(f332(f246(a1),f2(a1)),f811(x79451,x79452,x79453))) % 165.30/165.05 [7987]P144(x79873,x79872,x79871)+~P24(f332(x79873,x79872))+E(f332(f332(f81(a1),f332(f332(f82(a1),x79871),f812(x79871,x79872,x79873))),f811(x79871,x79872,x79873)),x79872)+P24(f332(f332(f247(a1),x79871),f810(x79871,x79872,x79873))) % 165.30/165.05 [7996]P145(x79963,x79962,x79961)+E(f332(f332(f81(a1),f332(f332(f82(a1),x79961),f806(x79961,x79962,x79963))),f805(x79961,x79962,x79963)),x79962)+P24(f332(f332(f247(a1),x79961),f804(x79961,x79962,x79963)))+~P24(f332(x79963,f2(a1))) % 165.30/165.05 [8002]P144(x80023,x80022,x80021)+~P24(f332(x80023,x80022))+E(f332(f332(f81(a1),f332(f332(f82(a1),x80021),f813(x80021,x80022,x80023))),f810(x80021,x80022,x80023)),x80022)+P24(f332(f332(f246(a1),f2(a1)),f811(x80021,x80022,x80023))) % 165.30/165.05 [8008]P145(x80083,x80082,x80081)+E(f332(f332(f81(a1),f332(f332(f82(a1),x80081),f809(x80081,x80082,x80083))),f804(x80081,x80082,x80083)),x80082)+P24(f332(f332(f246(a1),f2(a1)),f805(x80081,x80082,x80083)))+~P24(f332(x80083,f2(a1))) % 165.30/165.05 [8019]P145(x80193,x80192,x80191)+E(x80191,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x80191),f806(x80191,x80192,x80193))),f805(x80191,x80192,x80193)),x80192)+~P24(f332(x80193,f809(x80191,x80192,x80193))) % 165.30/165.05 [8020]P144(x80203,x80202,x80201)+E(x80201,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x80201),f812(x80201,x80202,x80203))),f811(x80201,x80202,x80203)),x80202)+~P24(f332(x80203,f810(x80201,x80202,x80203))) % 165.30/165.05 [8021]P145(x80213,x80212,x80211)+E(x80211,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x80211),f809(x80211,x80212,x80213))),f804(x80211,x80212,x80213)),x80212)+~P24(f332(x80213,f806(x80211,x80212,x80213))) % 165.30/165.05 [8022]P144(x80223,x80222,x80221)+E(x80221,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x80221),f813(x80221,x80222,x80223))),f810(x80221,x80222,x80223)),x80222)+~P24(f332(x80223,f811(x80221,x80222,x80223))) % 165.30/165.05 [8079]P144(x80793,x80792,x80791)+~P24(f332(x80793,x80792))+E(f332(f332(f81(a1),f332(f332(f82(a1),x80791),f812(x80791,x80792,x80793))),f811(x80791,x80792,x80793)),x80792)+~P24(f332(x80793,f810(x80791,x80792,x80793))) % 165.30/165.05 [8080]P144(x80803,x80802,x80801)+~P24(f332(x80803,x80802))+E(f332(f332(f81(a1),f332(f332(f82(a1),x80801),f813(x80801,x80802,x80803))),f810(x80801,x80802,x80803)),x80802)+~P24(f332(x80803,f811(x80801,x80802,x80803))) % 165.30/165.05 [8090]P145(x80903,x80902,x80901)+E(f332(f332(f81(a1),f332(f332(f82(a1),x80901),f806(x80901,x80902,x80903))),f805(x80901,x80902,x80903)),x80902)+~P24(f332(x80903,f809(x80901,x80902,x80903)))+~P24(f332(x80903,f2(a1))) % 165.30/165.05 [8091]P145(x80913,x80912,x80911)+E(f332(f332(f81(a1),f332(f332(f82(a1),x80911),f809(x80911,x80912,x80913))),f804(x80911,x80912,x80913)),x80912)+~P24(f332(x80913,f806(x80911,x80912,x80913)))+~P24(f332(x80913,f2(a1))) % 165.30/165.05 [8194]P145(x81943,x81942,x81941)+E(x81941,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x81941),f806(x81941,x81942,x81943))),f805(x81941,x81942,x81943)),x81942)+P24(f332(f332(f246(a1),f804(x81941,x81942,x81943)),f2(a1))) % 165.30/165.05 [8195]P144(x81953,x81952,x81951)+E(x81951,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x81951),f812(x81951,x81952,x81953))),f811(x81951,x81952,x81953)),x81952)+P24(f332(f332(f246(a1),f810(x81951,x81952,x81953)),f2(a1))) % 165.30/165.05 [8235]P144(x82353,x82352,x82351)+~P24(f332(x82353,x82352))+E(f332(f332(f81(a1),f332(f332(f82(a1),x82351),f812(x82351,x82352,x82353))),f811(x82351,x82352,x82353)),x82352)+P24(f332(f332(f246(a1),f810(x82351,x82352,x82353)),f2(a1))) % 165.30/165.05 [8240]P145(x82403,x82402,x82401)+E(f332(f332(f81(a1),f332(f332(f82(a1),x82401),f806(x82401,x82402,x82403))),f805(x82401,x82402,x82403)),x82402)+~P24(f332(x82403,f2(a1)))+P24(f332(f332(f246(a1),f804(x82401,x82402,x82403)),f2(a1))) % 165.30/165.05 [8367]P145(x83673,x83672,x83671)+E(x83671,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x83671),f809(x83671,x83672,x83673))),f804(x83671,x83672,x83673)),x83672)+E(f332(f332(f81(a1),f332(f332(f82(a1),x83671),f806(x83671,x83672,x83673))),f805(x83671,x83672,x83673)),x83672) % 165.30/165.05 [8368]P144(x83683,x83682,x83681)+E(x83681,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x83681),f813(x83681,x83682,x83683))),f810(x83681,x83682,x83683)),x83682)+E(f332(f332(f81(a1),f332(f332(f82(a1),x83681),f812(x83681,x83682,x83683))),f811(x83681,x83682,x83683)),x83682) % 165.30/165.05 [8388]P144(x83883,x83882,x83881)+~P24(f332(x83883,x83882))+E(f332(f332(f81(a1),f332(f332(f82(a1),x83881),f813(x83881,x83882,x83883))),f810(x83881,x83882,x83883)),x83882)+E(f332(f332(f81(a1),f332(f332(f82(a1),x83881),f812(x83881,x83882,x83883))),f811(x83881,x83882,x83883)),x83882) % 165.30/165.05 [8400]P145(x84003,x84002,x84001)+E(f332(f332(f81(a1),f332(f332(f82(a1),x84001),f809(x84001,x84002,x84003))),f804(x84001,x84002,x84003)),x84002)+E(f332(f332(f81(a1),f332(f332(f82(a1),x84001),f806(x84001,x84002,x84003))),f805(x84001,x84002,x84003)),x84002)+~P24(f332(x84003,f2(a1))) % 165.30/165.05 [9029]~P122(x90291)+~E(x90293,f2(x90291))+~E(x90292,f2(x90291))+P24(f332(f332(f246(x90291),f332(f332(f81(x90291),f332(f332(f82(x90291),x90292),x90292)),f332(f332(f82(x90291),x90293),x90293))),f2(x90291))) % 165.30/165.05 [10052]~P118(x100521)+~E(x100523,f2(x100521))+~E(x100522,f2(x100521))+P24(f332(f332(f246(x100521),f332(f332(f81(x100521),f332(f332(f257(x100521),x100522),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x100521),x100523),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))),f2(x100521))) % 165.30/165.05 [4798]~E(x47983,x47981)+~P116(x47982)+E(x47981,f2(x47982))+E(f332(f332(f290(x47982),x47983),x47981),f79(x47982)) % 165.30/165.05 [4851]~P64(x48511)+~E(x48513,f196(x48511))+~E(x48512,f196(x48511))+E(f332(f332(f113(x48511),x48512),x48513),f196(x48511)) % 165.30/165.05 [4852]~P98(x48521)+~E(x48523,f255(x48521))+~E(x48522,f255(x48521))+E(f332(f332(f104(x48521),x48522),x48523),f255(x48521)) % 165.30/165.05 [4940]~P116(x49403)+E(x49401,x49402)+E(x49402,f2(x49403))+~E(f332(f332(f290(x49403),x49401),x49402),f79(x49403)) % 165.30/165.05 [4959]~P127(x49592)+E(x49591,f2(x49592))+E(x49593,f2(x49592))+~E(f332(f332(f82(x49592),x49593),x49591),f2(x49592)) % 165.30/165.05 [4960]~P139(x49602)+E(x49601,f2(x49602))+E(x49603,f2(x49602))+~E(f332(f332(f82(x49602),x49603),x49601),f2(x49602)) % 165.30/165.05 [5344]~P115(x53443)+E(x53441,x53442)+E(x53441,f332(f80(x53443),x53442))+~E(f332(f332(f82(x53443),x53441),x53441),f332(f332(f82(x53443),x53442),x53442)) % 165.30/165.05 [5384]~P81(x53841)+E(f332(f80(x53841),x53842),x53843)+~E(f332(f332(f113(x53841),x53842),x53843),f255(x53841))+~E(f332(f332(f104(x53841),x53842),x53843),f196(x53841)) % 165.30/165.05 [5463]~P118(x54633)+E(x54631,x54632)+P24(f332(f332(f247(x54633),x54632),x54631))+P24(f332(f332(f247(x54633),x54631),x54632)) % 165.30/165.05 [5464]~P106(x54643)+E(x54641,x54642)+P24(f332(f332(f247(x54643),x54642),x54641))+P24(f332(f332(f247(x54643),x54641),x54642)) % 165.30/165.05 [5465]~E(x54652,x54653)+~P106(x54651)+P24(f332(f332(f247(x54651),x54652),x54653))+P24(f332(f332(f246(x54651),x54652),x54653)) % 165.30/165.05 [5720]~P107(x57203)+E(x57201,x57202)+~P24(f332(f332(f246(x57203),x57202),x57201))+P24(f332(f332(f247(x57203),x57202),x57201)) % 165.30/165.05 [5722]~P106(x57223)+E(x57221,x57222)+~P24(f332(f332(f246(x57223),x57221),x57222))+P24(f332(f332(f247(x57223),x57221),x57222)) % 165.30/165.05 [5728]~P107(x57283)+E(x57281,x57282)+~P24(f332(f332(f246(x57283),x57281),x57282))+P24(f332(f332(f247(x57283),x57281),x57282)) % 165.30/165.05 [5830]P144(x58301,x58302,x58303)+~P24(f332(x58301,x58302))+P24(f332(f332(f247(a1),x58303),f2(a1)))+P24(f332(f332(f247(a1),f2(a1)),x58303)) % 165.30/165.05 [5877]P145(x58771,x58772,x58773)+~P24(f332(x58771,f2(a1)))+P24(f332(f332(f247(a1),x58773),f2(a1)))+P24(f332(f332(f247(a1),f2(a1)),x58773)) % 165.30/165.05 [5881]~P26(x58811)+E(f332(f332(f113(x58811),x58812),f11(x58811,x58813)),x58812)+~P24(f332(f62(x58811),x58813))+~P24(f332(f332(f334(x58811),x58812),x58813)) % 165.30/165.05 [5882]~P26(x58821)+E(f332(f332(f104(x58821),x58822),f10(x58821,x58823)),x58822)+~P24(f332(f62(x58821),x58823))+~P24(f332(f332(f334(x58821),x58822),x58823)) % 165.30/165.05 [5918]~P26(x59181)+E(f332(f332(f113(x59181),x59182),f10(x59181,x59183)),f10(x59181,x59183))+~P24(f332(f62(x59181),x59183))+~P24(f332(f332(f334(x59181),x59182),x59183)) % 165.30/165.05 [5919]~P26(x59191)+E(f332(f332(f104(x59191),x59192),f11(x59191,x59193)),f11(x59191,x59193))+~P24(f332(f62(x59191),x59193))+~P24(f332(f332(f334(x59191),x59192),x59193)) % 165.30/165.05 [5920]~P106(x59201)+E(f332(f332(f244(x59201),x59202),f15(x59201,x59203)),f15(x59201,x59203))+~P24(f332(f62(x59201),x59203))+~P24(f332(f332(f334(x59201),x59202),x59203)) % 165.30/165.05 [5921]~P106(x59211)+E(f332(f332(f245(x59211),x59212),f14(x59211,x59213)),f14(x59211,x59213))+~P24(f332(f62(x59211),x59213))+~P24(f332(f332(f334(x59211),x59212),x59213)) % 165.30/165.05 [5962]E(x59621,x59622)+~P107(x59623)+~P24(f332(f332(f246(x59623),x59622),x59621))+~P24(f332(f332(f246(x59623),x59621),x59622)) % 165.30/165.05 [6105]~P104(x61051)+P24(f332(f332(f247(x61051),x61053),x61052))+~P24(f332(f332(f246(x61051),x61053),x61052))+P24(f332(f332(f246(x61051),x61052),x61053)) % 165.30/165.05 [6128]~P106(x61281)+~P24(f332(f62(x61281),x61283))+P24(f332(f332(f246(x61281),x61282),f14(x61281,x61283)))+~P24(f332(f332(f334(x61281),x61282),x61283)) % 165.30/165.05 [6182]~P106(x61821)+E(f332(f332(f244(x61821),x61822),f13(x61821,f245(x61821),x61823)),x61822)+~P24(f332(f62(x61821),x61823))+~P24(f332(f332(f334(x61821),x61822),x61823)) % 165.30/165.05 [6183]~P106(x61831)+E(f332(f332(f245(x61831),x61832),f12(x61831,f244(x61831),x61833)),x61832)+~P24(f332(f62(x61831),x61833))+~P24(f332(f332(f334(x61831),x61832),x61833)) % 165.30/165.05 [6320]E(x63201,x63202)+~E(f332(f332(f22(a868),x63201),x63203),f332(f332(f22(a868),x63202),x63203))+~P24(f332(f332(f246(a868),x63203),x63201))+~P24(f332(f332(f246(a868),x63203),x63202)) % 165.30/165.05 [6349]~P106(x63491)+~P24(f332(f62(x63491),x63492))+~P24(f332(f332(f334(x63491),x63493),x63492))+P24(f332(f332(f246(x63491),f15(x63491,x63492)),x63493)) % 165.30/165.05 [6412]P145(x64122,x64123,x64121)+E(x64121,f2(a1))+P24(f332(f332(f247(a1),x64121),f804(x64121,x64123,x64122)))+P24(f332(f332(f247(a1),f2(a1)),x64121)) % 165.30/165.05 [6413]P144(x64132,x64133,x64131)+E(x64131,f2(a1))+P24(f332(f332(f247(a1),x64131),f810(x64131,x64133,x64132)))+P24(f332(f332(f247(a1),f2(a1)),x64131)) % 165.30/165.05 [6414]~P106(x64141)+E(f332(f332(f244(x64141),x64142),f12(x64141,f244(x64141),x64143)),f12(x64141,f244(x64141),x64143))+~P24(f332(f62(x64141),x64143))+~P24(f332(f332(f334(x64141),x64142),x64143)) % 165.30/165.05 [6415]~P106(x64151)+E(f332(f332(f245(x64151),x64152),f13(x64151,f245(x64151),x64153)),f13(x64151,f245(x64151),x64153))+~P24(f332(f62(x64151),x64153))+~P24(f332(f332(f334(x64151),x64152),x64153)) % 165.30/165.05 [6421]~P24(f332(x64211,x64212))+P24(f332(x64211,f485(x64212,x64211,x64213)))+P24(f332(x64211,f2(a868)))+~P24(f332(f332(f247(a868),x64212),x64213)) % 165.30/165.05 [6476]~P24(f332(x64761,x64762))+~P24(f332(f62(x64763),x64762))+P24(f332(x64761,f570(x64761,x64762,x64763)))+P24(f332(x64761,f196(f875(x64763,a862)))) % 165.30/165.05 [6489]~P118(x64891)+~P92(x64891)+P24(f332(f332(f246(x64891),f332(f106(x64891),x64892)),f332(f106(x64891),x64893)))+~P24(f332(f332(f246(a1),x64892),x64893)) % 165.30/165.05 [6490]~P118(x64901)+~P92(x64901)+P24(f332(f332(f247(x64901),f332(f106(x64901),x64902)),f332(f106(x64901),x64903)))+~P24(f332(f332(f247(a1),x64902),x64903)) % 165.30/165.05 [6493]~P24(f332(x64931,x64933))+~P24(f332(f62(x64932),x64933))+P24(f332(f62(x64932),f570(x64931,x64933,x64932)))+P24(f332(x64931,f196(f875(x64932,a862)))) % 165.30/165.05 [6527]P144(x65271,x65272,x65273)+~P24(f332(x65271,x65272))+P24(f332(f332(f247(a1),x65273),f810(x65273,x65272,x65271)))+P24(f332(f332(f247(a1),f2(a1)),x65273)) % 165.30/165.05 [6561]P145(x65611,x65612,x65613)+P24(f332(f332(f247(a1),x65613),f804(x65613,x65612,x65611)))+~P24(f332(x65611,f2(a1)))+P24(f332(f332(f247(a1),f2(a1)),x65613)) % 165.30/165.05 [6592]~P105(x65921)+~P93(x65921)+E(f332(f332(f244(x65921),f332(f106(x65921),x65922)),f332(f106(x65921),x65923)),f332(f106(x65921),x65923))+P24(f332(f332(f246(x65921),f332(f106(x65921),x65922)),f332(f106(x65921),x65923))) % 165.30/165.05 [6593]~P105(x65931)+~P93(x65931)+E(f332(f332(f245(x65931),f332(f106(x65931),x65932)),f332(f106(x65931),x65933)),f332(f106(x65931),x65932))+P24(f332(f332(f246(x65931),f332(f106(x65931),x65932)),f332(f106(x65931),x65933))) % 165.30/165.05 [6650]P145(x66502,x66503,x66501)+E(x66501,f2(a1))+~P24(f332(x66502,f809(x66501,x66503,x66502)))+P24(f332(f332(f247(a1),f2(a1)),x66501)) % 165.30/165.05 [6651]P144(x66512,x66513,x66511)+E(x66511,f2(a1))+~P24(f332(x66512,f810(x66511,x66513,x66512)))+P24(f332(f332(f247(a1),f2(a1)),x66511)) % 165.30/165.05 [6655]P24(f332(x66551,x66552))+~P24(f332(f62(x66553),x66552))+P24(f332(x66551,f636(x66551,x66552,x66553)))+~P24(f332(x66551,f196(f875(x66553,a862)))) % 165.30/165.05 [6674]P24(f332(x66741,x66742))+P24(f332(f62(x66743),f636(x66741,x66742,x66743)))+~P24(f332(f62(x66743),x66742))+~P24(f332(x66741,f196(f875(x66743,a862)))) % 165.30/165.05 [6739]P144(x67391,x67392,x67393)+~P24(f332(x67391,x67392))+~P24(f332(x67391,f810(x67393,x67392,x67391)))+P24(f332(f332(f247(a1),f2(a1)),x67393)) % 165.30/165.05 [6769]P145(x67691,x67692,x67693)+~P24(f332(x67691,f809(x67693,x67692,x67691)))+~P24(f332(x67691,f2(a1)))+P24(f332(f332(f247(a1),f2(a1)),x67693)) % 165.30/165.05 [6877]~P92(x68773)+~P118(x68773)+~P24(f332(f332(f246(x68773),f332(f106(x68773),x68771)),f332(f106(x68773),x68772)))+P24(f332(f332(f246(a1),x68771),x68772)) % 165.30/165.05 [6878]~P92(x68783)+~P118(x68783)+~P24(f332(f332(f247(x68783),f332(f106(x68783),x68781)),f332(f106(x68783),x68782)))+P24(f332(f332(f247(a1),x68781),x68782)) % 165.30/165.05 [6905]~P106(x69051)+~P32(x69051,x69053)+P32(x69051,f332(f332(f152(x69051),x69052),x69053))+~P24(f332(f332(f246(x69051),x69052),f611(x69053,x69052,x69051))) % 165.30/165.05 [6906]~P106(x69061)+~P32(x69061,x69063)+P32(x69061,f332(f332(f152(x69061),x69062),x69063))+~P24(f332(f332(f246(x69061),x69062),f612(x69063,x69062,x69061))) % 165.30/165.05 [6907]~P106(x69071)+~P32(x69071,x69073)+P32(x69071,f332(f332(f152(x69071),x69072),x69073))+~P24(f332(f332(f246(x69071),x69072),f709(x69072,x69073,x69071))) % 165.30/165.05 [6991]P145(x69912,x69913,x69911)+E(x69911,f2(a1))+P24(f332(f332(f247(a1),x69911),f2(a1)))+P24(f332(f332(f247(a1),f805(x69911,x69913,x69912)),x69911)) % 165.30/165.05 [6992]P144(x69922,x69923,x69921)+E(x69921,f2(a1))+P24(f332(f332(f247(a1),x69921),f2(a1)))+P24(f332(f332(f247(a1),f811(x69921,x69923,x69922)),x69921)) % 165.30/165.05 [7031]P145(x70312,x70313,x70311)+E(x70311,f2(a1))+P24(f332(f332(f246(a1),f804(x70311,x70313,x70312)),f2(a1)))+P24(f332(f332(f247(a1),f2(a1)),x70311)) % 165.30/165.05 [7032]P144(x70322,x70323,x70321)+E(x70321,f2(a1))+P24(f332(f332(f246(a1),f810(x70321,x70323,x70322)),f2(a1)))+P24(f332(f332(f247(a1),f2(a1)),x70321)) % 165.30/165.05 [7054]~P106(x70541)+~P32(x70541,x70543)+E(f332(f332(f149(x70541,x70541,f5(x70541)),x70542),f172(x70541,x70542,x70543)),x70543)+~P24(f332(f332(f334(x70541),x70542),f332(f174(x70541),x70543))) % 165.30/165.05 [7101]P144(x71011,x71012,x71013)+~P24(f332(x71011,x71012))+P24(f332(f332(f247(a1),x71013),f2(a1)))+P24(f332(f332(f247(a1),f811(x71013,x71012,x71011)),x71013)) % 165.30/165.05 [7107]~P105(x71071)+~P93(x71071)+E(f332(f332(f244(x71071),f332(f106(x71071),x71072)),f332(f106(x71071),x71073)),f332(f106(x71071),x71072))+~P24(f332(f332(f246(x71071),f332(f106(x71071),x71072)),f332(f106(x71071),x71073))) % 165.30/165.05 [7108]~P105(x71081)+~P93(x71081)+E(f332(f332(f245(x71081),f332(f106(x71081),x71082)),f332(f106(x71081),x71083)),f332(f106(x71081),x71083))+~P24(f332(f332(f246(x71081),f332(f106(x71081),x71082)),f332(f106(x71081),x71083))) % 165.30/165.05 [7122]P145(x71221,x71222,x71223)+~P24(f332(x71221,f2(a1)))+P24(f332(f332(f247(a1),x71223),f2(a1)))+P24(f332(f332(f247(a1),f805(x71223,x71222,x71221)),x71223)) % 165.30/165.05 [7130]P144(x71301,x71302,x71303)+~P24(f332(x71301,x71302))+P24(f332(f332(f246(a1),f810(x71303,x71302,x71301)),f2(a1)))+P24(f332(f332(f247(a1),f2(a1)),x71303)) % 165.30/165.05 [7154]P145(x71541,x71542,x71543)+~P24(f332(x71541,f2(a1)))+P24(f332(f332(f246(a1),f804(x71543,x71542,x71541)),f2(a1)))+P24(f332(f332(f247(a1),f2(a1)),x71543)) % 165.30/165.05 [7182]~P24(f332(x71821,x71822))+P24(f332(x71821,f2(a868)))+~P24(f332(f332(f247(a868),x71822),x71823))+P24(f332(f332(f247(a868),f485(x71822,x71821,x71823)),x71823)) % 165.30/165.05 [7199]~P106(x71991)+~P32(x71991,x71993)+P32(x71991,f332(f332(f152(x71991),x71992),x71993))+P24(f332(f332(f334(x71991),f611(x71993,x71992,x71991)),f332(f174(x71991),x71993))) % 165.30/165.05 [7200]~P106(x72001)+~P32(x72001,x72003)+P32(x72001,f332(f332(f152(x72001),x72002),x72003))+P24(f332(f332(f334(x72001),f612(x72003,x72002,x72001)),f332(f174(x72001),x72003))) % 165.30/165.05 [7201]~P106(x72011)+~P32(x72011,x72013)+P32(x72011,f332(f332(f152(x72011),x72012),x72013))+P24(f332(f332(f334(x72011),f709(x72012,x72013,x72011)),f332(f174(x72011),x72013))) % 165.30/165.05 [7305]~P106(x73051)+~P30(x73051)+~P24(f332(f332(f247(x73051),x73053),f40(x73051,x73052)))+P24(f332(f332(f334(x73051),f637(x73052,x73053,x73051)),x73052)) % 165.30/165.05 [7468]~P106(x74681)+~P30(x74681)+~P24(f332(f332(f247(x74681),f41(x74681,x74683)),x74682))+P24(f332(f332(f334(x74681),f643(x74682,x74683,x74681)),x74683)) % 165.30/165.05 [7469]~P106(x74691)+~P30(x74691)+~P24(f332(f332(f247(x74691),f41(x74691,x74693)),x74692))+P24(f332(f332(f247(x74691),f643(x74692,x74693,x74691)),x74692)) % 165.30/165.05 [7484]P145(x74842,x74843,x74841)+E(x74841,f2(a1))+P24(f332(f332(f247(a1),x74841),f804(x74841,x74843,x74842)))+P24(f332(f332(f247(a1),f805(x74841,x74843,x74842)),x74841)) % 165.30/165.05 [7485]P144(x74852,x74853,x74851)+E(x74851,f2(a1))+P24(f332(f332(f247(a1),x74851),f810(x74851,x74853,x74852)))+P24(f332(f332(f247(a1),f811(x74851,x74853,x74852)),x74851)) % 165.30/165.05 [7576]P145(x75763,x75762,x75761)+E(x75761,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x75761),f809(x75761,x75762,x75763))),f804(x75761,x75762,x75763)),x75762)+P24(f332(f332(f247(a1),f2(a1)),x75761)) % 165.30/165.05 [7577]P144(x75773,x75772,x75771)+E(x75771,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x75771),f813(x75771,x75772,x75773))),f810(x75771,x75772,x75773)),x75772)+P24(f332(f332(f247(a1),f2(a1)),x75771)) % 165.30/165.05 [7579]~P122(x75791)+~P24(f332(f332(f246(x75791),x75793),f2(x75791)))+P24(f332(f332(f246(x75791),f332(f332(f82(x75791),x75792),x75793)),f2(x75791)))+~P24(f332(f332(f246(x75791),f2(x75791)),x75792)) % 165.30/165.05 [7580]~P122(x75801)+~P24(f332(f332(f246(x75801),x75802),f2(x75801)))+P24(f332(f332(f246(x75801),f332(f332(f82(x75801),x75802),x75803)),f2(x75801)))+~P24(f332(f332(f246(x75801),f2(x75801)),x75803)) % 165.30/165.05 [7582]~P133(x75821)+~P24(f332(f332(f246(x75821),x75823),f2(x75821)))+P24(f332(f332(f246(x75821),f332(f332(f82(x75821),x75822),x75823)),f2(x75821)))+~P24(f332(f332(f246(x75821),f2(x75821)),x75822)) % 165.30/165.05 [7584]~P133(x75841)+~P24(f332(f332(f246(x75841),x75842),f2(x75841)))+P24(f332(f332(f246(x75841),f332(f332(f82(x75841),x75842),x75843)),f2(x75841)))+~P24(f332(f332(f246(x75841),f2(x75841)),x75843)) % 165.30/165.05 [7585]~P62(x75851)+~P24(f332(f332(f246(x75851),x75853),f2(x75851)))+P24(f332(f332(f246(x75851),f332(f332(f290(x75851),x75852),x75853)),f2(x75851)))+~P24(f332(f332(f246(x75851),f2(x75851)),x75852)) % 165.30/165.05 [7586]~P62(x75861)+~P24(f332(f332(f246(x75861),x75862),f2(x75861)))+P24(f332(f332(f246(x75861),f332(f332(f290(x75861),x75862),x75863)),f2(x75861)))+~P24(f332(f332(f246(x75861),f2(x75861)),x75863)) % 165.30/165.05 [7587]~P63(x75871)+~P24(f332(f332(f246(x75871),x75872),f2(x75871)))+P24(f332(f332(f246(x75871),f332(f332(f290(x75871),x75872),x75873)),f2(x75871)))+~P24(f332(f332(f247(x75871),f2(x75871)),x75873)) % 165.30/165.05 [7588]~P63(x75881)+~P24(f332(f332(f247(x75881),x75883),f2(x75881)))+P24(f332(f332(f246(x75881),f332(f332(f290(x75881),x75882),x75883)),f2(x75881)))+~P24(f332(f332(f246(x75881),f2(x75881)),x75882)) % 165.30/165.05 [7590]~P129(x75901)+~P24(f332(f332(f247(x75901),x75903),f2(x75901)))+P24(f332(f332(f247(x75901),f332(f332(f82(x75901),x75902),x75903)),f2(x75901)))+~P24(f332(f332(f247(x75901),f2(x75901)),x75902)) % 165.30/165.05 [7591]~P129(x75911)+~P24(f332(f332(f247(x75911),x75912),f2(x75911)))+P24(f332(f332(f247(x75911),f332(f332(f82(x75911),x75912),x75913)),f2(x75911)))+~P24(f332(f332(f247(x75911),f2(x75911)),x75913)) % 165.30/165.05 [7592]~P62(x75921)+~P24(f332(f332(f247(x75921),x75923),f2(x75921)))+P24(f332(f332(f247(x75921),f332(f332(f290(x75921),x75922),x75923)),f2(x75921)))+~P24(f332(f332(f247(x75921),f2(x75921)),x75922)) % 165.30/165.05 [7593]~P62(x75931)+~P24(f332(f332(f247(x75931),x75932),f2(x75931)))+P24(f332(f332(f247(x75931),f332(f332(f290(x75931),x75932),x75933)),f2(x75931)))+~P24(f332(f332(f247(x75931),f2(x75931)),x75933)) % 165.30/165.05 [7594]~P63(x75941)+~P24(f332(f332(f247(x75941),x75943),f2(x75941)))+P24(f332(f332(f247(x75941),f332(f332(f290(x75941),x75942),x75943)),f2(x75941)))+~P24(f332(f332(f247(x75941),f2(x75941)),x75942)) % 165.30/165.05 [7595]~P63(x75951)+~P24(f332(f332(f247(x75951),x75952),f2(x75951)))+P24(f332(f332(f247(x75951),f332(f332(f290(x75951),x75952),x75953)),f2(x75951)))+~P24(f332(f332(f247(x75951),f2(x75951)),x75953)) % 165.30/165.05 [7610]P144(x76101,x76102,x76103)+~P24(f332(x76101,x76102))+P24(f332(f332(f247(a1),x76103),f810(x76103,x76102,x76101)))+P24(f332(f332(f247(a1),f811(x76103,x76102,x76101)),x76103)) % 165.30/165.05 [7623]P145(x76231,x76232,x76233)+P24(f332(f332(f247(a1),x76233),f804(x76233,x76232,x76231)))+~P24(f332(x76231,f2(a1)))+P24(f332(f332(f247(a1),f805(x76233,x76232,x76231)),x76233)) % 165.30/165.05 [7674]P145(x76742,x76743,x76741)+E(x76741,f2(a1))+~P24(f332(x76742,f809(x76741,x76743,x76742)))+P24(f332(f332(f247(a1),f805(x76741,x76743,x76742)),x76741)) % 165.30/165.05 [7675]P144(x76752,x76753,x76751)+E(x76751,f2(a1))+~P24(f332(x76752,f810(x76751,x76753,x76752)))+P24(f332(f332(f247(a1),f811(x76751,x76753,x76752)),x76751)) % 165.30/165.05 [7686]P144(x76863,x76862,x76861)+~P24(f332(x76863,x76862))+E(f332(f332(f81(a1),f332(f332(f82(a1),x76861),f813(x76861,x76862,x76863))),f810(x76861,x76862,x76863)),x76862)+P24(f332(f332(f247(a1),f2(a1)),x76861)) % 165.30/165.05 [7703]P145(x77033,x77032,x77031)+E(f332(f332(f81(a1),f332(f332(f82(a1),x77031),f809(x77031,x77032,x77033))),f804(x77031,x77032,x77033)),x77032)+~P24(f332(x77033,f2(a1)))+P24(f332(f332(f247(a1),f2(a1)),x77031)) % 165.30/165.05 [7729]~P24(f332(x77291,x77293))+~P24(f332(f62(x77292),x77293))+P24(f332(f332(f334(x77292),f593(x77291,x77293,x77292)),f570(x77291,x77293,x77292)))+P24(f332(x77291,f196(f875(x77292,a862)))) % 165.30/165.05 [7740]P144(x77401,x77402,x77403)+~P24(f332(x77401,x77402))+~P24(f332(x77401,f810(x77403,x77402,x77401)))+P24(f332(f332(f247(a1),f811(x77403,x77402,x77401)),x77403)) % 165.30/165.05 [7746]P145(x77461,x77462,x77463)+~P24(f332(x77461,f809(x77463,x77462,x77461)))+~P24(f332(x77461,f2(a1)))+P24(f332(f332(f247(a1),f805(x77463,x77462,x77461)),x77463)) % 165.30/165.05 [7847]~P122(x78471)+~P24(f332(f332(f246(x78471),f332(f332(f82(x78471),x78473),x78472)),f2(x78471)))+P24(f332(f332(f246(x78471),x78472),f2(x78471)))+P24(f332(f332(f246(x78471),f2(x78471)),x78472)) % 165.30/165.05 [7848]~P122(x78481)+~P24(f332(f332(f246(x78481),f332(f332(f82(x78481),x78482),x78483)),f2(x78481)))+P24(f332(f332(f246(x78481),x78482),f2(x78481)))+P24(f332(f332(f246(x78481),f2(x78481)),x78482)) % 165.30/165.05 [7849]~P62(x78491)+~P24(f332(f332(f246(x78491),f332(f332(f290(x78491),x78493),x78492)),f2(x78491)))+P24(f332(f332(f246(x78491),x78492),f2(x78491)))+P24(f332(f332(f246(x78491),f2(x78491)),x78492)) % 165.30/165.05 [7850]~P62(x78501)+~P24(f332(f332(f246(x78501),f332(f332(f290(x78501),x78502),x78503)),f2(x78501)))+P24(f332(f332(f246(x78501),x78502),f2(x78501)))+P24(f332(f332(f246(x78501),f2(x78501)),x78502)) % 165.30/165.05 [7851]~P62(x78511)+~P24(f332(f332(f247(x78511),f332(f332(f290(x78511),x78513),x78512)),f2(x78511)))+P24(f332(f332(f247(x78511),x78512),f2(x78511)))+P24(f332(f332(f247(x78511),f2(x78511)),x78512)) % 165.30/165.05 [7852]~P62(x78521)+~P24(f332(f332(f247(x78521),f332(f332(f290(x78521),x78522),x78523)),f2(x78521)))+P24(f332(f332(f247(x78521),x78522),f2(x78521)))+P24(f332(f332(f247(x78521),f2(x78521)),x78522)) % 165.30/165.05 [7875]~P122(x78751)+~P24(f332(f332(f246(x78751),f332(f332(f82(x78751),x78752),x78753)),f2(x78751)))+P24(f332(f332(f246(x78751),f2(x78751)),x78752))+P24(f332(f332(f246(x78751),f2(x78751)),x78753)) % 165.30/165.05 [7876]~P62(x78761)+~P24(f332(f332(f246(x78761),f332(f332(f290(x78761),x78762),x78763)),f2(x78761)))+P24(f332(f332(f246(x78761),f2(x78761)),x78762))+P24(f332(f332(f246(x78761),f2(x78761)),x78763)) % 165.30/165.05 [7877]~P62(x78771)+~P24(f332(f332(f247(x78771),f332(f332(f290(x78771),x78772),x78773)),f2(x78771)))+P24(f332(f332(f247(x78771),f2(x78771)),x78772))+P24(f332(f332(f247(x78771),f2(x78771)),x78773)) % 165.30/165.05 [7898]P145(x78982,x78983,x78981)+E(x78981,f2(a1))+P24(f332(f332(f246(a1),f804(x78981,x78983,x78982)),f2(a1)))+P24(f332(f332(f247(a1),f805(x78981,x78983,x78982)),x78981)) % 165.30/165.05 [7899]P144(x78992,x78993,x78991)+E(x78991,f2(a1))+P24(f332(f332(f246(a1),f810(x78991,x78993,x78992)),f2(a1)))+P24(f332(f332(f247(a1),f811(x78991,x78993,x78992)),x78991)) % 165.30/165.05 [7906]~P112(x79061)+~P24(f332(f332(f247(x79061),x79062),f79(x79061)))+P24(f332(f332(f247(x79061),f332(f332(f257(x79061),x79062),f332(a115,x79063))),f79(x79061)))+~P24(f332(f332(f247(x79061),f2(x79061)),x79062)) % 165.30/165.05 [7961]~P106(x79611)+~E(x79613,f116(x79611))+~P32(x79611,f332(f170(x79611),x79613))+E(f332(f143(x79611,x79611,f332(f7(x79611,x79611,x79611),f245(x79611)),x79612),f332(f170(x79611),x79613)),x79612) % 165.30/165.05 [7964]P144(x79641,x79642,x79643)+~P24(f332(x79641,x79642))+P24(f332(f332(f246(a1),f810(x79643,x79642,x79641)),f2(a1)))+P24(f332(f332(f247(a1),f811(x79643,x79642,x79641)),x79643)) % 165.30/165.05 [7971]P145(x79711,x79712,x79713)+~P24(f332(x79711,f2(a1)))+P24(f332(f332(f246(a1),f804(x79713,x79712,x79711)),f2(a1)))+P24(f332(f332(f247(a1),f805(x79713,x79712,x79711)),x79713)) % 165.30/165.05 [8189]P145(x81893,x81892,x81891)+E(x81891,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x81891),f809(x81891,x81892,x81893))),f804(x81891,x81892,x81893)),x81892)+P24(f332(f332(f247(a1),f805(x81891,x81892,x81893)),x81891)) % 165.30/165.05 [8190]P144(x81903,x81902,x81901)+E(x81901,f2(a1))+E(f332(f332(f81(a1),f332(f332(f82(a1),x81901),f813(x81901,x81902,x81903))),f810(x81901,x81902,x81903)),x81902)+P24(f332(f332(f247(a1),f811(x81901,x81902,x81903)),x81901)) % 165.30/165.05 [8226]P144(x82263,x82262,x82261)+~P24(f332(x82263,x82262))+E(f332(f332(f81(a1),f332(f332(f82(a1),x82261),f813(x82261,x82262,x82263))),f810(x82261,x82262,x82263)),x82262)+P24(f332(f332(f247(a1),f811(x82261,x82262,x82263)),x82261)) % 165.30/165.05 [8227]~P73(x82271)+~P74(x82271)+~P42(x82273)+E(f332(f332(f6(a868,x82271),f332(f332(f8(a1,x82271,a868),x82272),f103(a1))),f332(f311(a1,a868,a107),x82273)),f332(f332(f6(a1,x82271),x82272),x82273)) % 165.30/165.05 [8228]~P73(x82281)+~P74(x82281)+~P42(x82283)+E(f332(f332(f9(a868,x82281),f332(f332(f8(a1,x82281,a868),x82282),f103(a1))),f332(f311(a1,a868,a107),x82283)),f332(f332(f9(a1,x82281),x82282),x82283)) % 165.30/165.05 [8237]P145(x82373,x82372,x82371)+E(f332(f332(f81(a1),f332(f332(f82(a1),x82371),f809(x82371,x82372,x82373))),f804(x82371,x82372,x82373)),x82372)+~P24(f332(x82373,f2(a1)))+P24(f332(f332(f247(a1),f805(x82371,x82372,x82373)),x82371)) % 165.30/165.05 [8256]~E(x82562,f2(a868))+~E(f332(f266(a868,a868),x82563),f2(a868))+~E(x82561,f332(f332(f81(a868),f332(f332(f82(a868),f332(f266(a868,a868),x82563)),x82562)),f332(f270(a868,a868),x82563)))+P24(f332(f48(x82561,x82562),x82563)) % 165.30/165.05 [8308]P24(f332(x83081,x83082))+~P24(f332(f332(f334(x83083),f626(x83081,x83082,x83083)),f636(x83081,x83082,x83083)))+~P24(f332(f62(x83083),x83082))+~P24(f332(x83081,f196(f875(x83083,a862)))) % 165.30/165.05 [8904]P24(f332(x89041,x89042))+~P24(f332(f62(x89043),x89042))+~P24(f332(x89041,f332(f332(f310(x89043),f626(x89041,x89042,x89043)),f636(x89041,x89042,x89043))))+~P24(f332(x89041,f196(f875(x89043,a862)))) % 165.30/165.05 [9131]P24(f332(f332(f246(a1),x91311),f2(a1)))+~P24(f332(f332(f247(a1),f332(f332(f81(a1),f332(f332(f82(a1),x91313),x91311)),x91312)),f2(a1)))+~P24(f332(f332(f246(a1),f2(a1)),x91312))+~P24(f332(f332(f247(a1),f2(a1)),x91313)) % 165.30/165.05 [5791]~P26(x57912)+E(x57911,f196(f875(x57912,a862)))+~P24(f332(f62(x57912),x57911))+E(f10(x57912,f332(f332(f310(x57912),x57913),x57911)),f332(f332(f113(x57912),x57913),f10(x57912,x57911))) % 165.30/165.05 [5792]~P26(x57922)+E(x57921,f196(f875(x57922,a862)))+~P24(f332(f62(x57922),x57921))+E(f11(x57922,f332(f332(f310(x57922),x57923),x57921)),f332(f332(f104(x57922),x57923),f11(x57922,x57921))) % 165.30/165.05 [5793]~P106(x57932)+E(x57931,f196(f875(x57932,a862)))+~P24(f332(f62(x57932),x57931))+E(f14(x57932,f332(f332(f310(x57932),x57933),x57931)),f332(f332(f245(x57932),x57933),f14(x57932,x57931))) % 165.30/165.05 [5794]~P106(x57942)+E(x57941,f196(f875(x57942,a862)))+~P24(f332(f62(x57942),x57941))+E(f15(x57942,f332(f332(f310(x57942),x57943),x57941)),f332(f332(f244(x57942),x57943),f15(x57942,x57941))) % 165.30/165.05 [6102]~P122(x61021)+~E(x61023,f2(x61021))+~E(x61022,f2(x61021))+E(f332(f332(f81(x61021),f332(f332(f82(x61021),x61022),x61022)),f332(f332(f82(x61021),x61023),x61023)),f2(x61021)) % 165.30/165.05 [6175]~P95(x61752)+E(x61751,f196(f875(x61752,a862)))+~P24(f332(f62(x61752),x61751))+E(f332(f64(x61752,f82(x61752)),f332(f332(f310(x61752),x61753),x61751)),f332(f332(f82(x61752),x61753),f332(f64(x61752,f82(x61752)),x61751))) % 165.30/165.05 [6299]~P106(x62992)+E(x62991,f196(f875(x62992,a862)))+~P24(f332(f62(x62992),x62991))+E(f12(x62992,f244(x62992),f332(f332(f310(x62992),x62993),x62991)),f332(f332(f244(x62992),x62993),f12(x62992,f244(x62992),x62991))) % 165.30/165.05 [6300]~P106(x63002)+E(x63001,f196(f875(x63002,a862)))+~P24(f332(f62(x63002),x63001))+E(f13(x63002,f245(x63002),f332(f332(f310(x63002),x63003),x63001)),f332(f332(f245(x63002),x63003),f13(x63002,f245(x63002),x63001))) % 165.30/165.05 [6804]~P71(x68041)+~P24(f332(f62(x68041),x68043))+E(f332(f64(x68041,f82(x68041)),f332(f332(f310(x68041),x68042),x68043)),f332(f332(f65(x68041,x68041,f82(x68041)),x68042),x68043))+P24(f332(f332(f334(x68041),x68042),x68043)) % 165.30/165.05 [6885]~E(f332(f332(f81(a1),x68852),f332(f332(f82(a1),x68853),x68851)),x68853)+~P24(f332(f332(f247(a1),f2(a1)),x68853))+P24(f332(f332(f246(a1),f79(a1)),x68851))+~P24(f332(f332(f247(a1),x68852),x68853)) % 165.30/165.05 [6912]~E(f332(f332(f81(a1),x69122),f332(f332(f82(a1),x69123),x69121)),x69123)+P24(f332(f332(f246(a1),x69121),f79(a1)))+~P24(f332(f332(f246(a1),f2(a1)),x69122))+~P24(f332(f332(f247(a1),f2(a1)),x69123)) % 165.30/165.05 [6928]E(x69281,f2(a868))+~P24(f332(f48(x69283,x69281),x69282))+~P24(f332(f332(f247(a868),f2(a868)),x69281))+P24(f332(f332(f247(a868),f332(f270(a868,a868),x69282)),x69281)) % 165.30/165.05 [6958]~P136(x69581)+~P24(f332(f332(f246(x69581),x69582),f2(x69581)))+~P24(f332(f332(f246(x69581),x69583),f2(x69581)))+E(f332(f332(f82(x69581),f332(f76(x69581),x69582)),f332(f76(x69581),x69583)),f332(f76(x69581),f332(f332(f82(x69581),x69582),x69583))) % 165.30/165.05 [7008]~P136(x70081)+~P24(f332(f332(f246(x70081),x70082),f2(x70081)))+E(f332(f332(f82(x70081),f332(f76(x70081),x70082)),f332(f76(x70081),x70083)),f332(f76(x70081),f332(f332(f82(x70081),x70082),x70083)))+~P24(f332(f332(f246(x70081),f2(x70081)),x70083)) % 165.30/165.05 [7009]~P136(x70091)+~P24(f332(f332(f246(x70091),x70093),f2(x70091)))+E(f332(f332(f82(x70091),f332(f76(x70091),x70092)),f332(f76(x70091),x70093)),f332(f76(x70091),f332(f332(f82(x70091),x70092),x70093)))+~P24(f332(f332(f246(x70091),f2(x70091)),x70092)) % 165.30/165.05 [7063]~P136(x70631)+E(f332(f332(f82(x70631),f332(f76(x70631),x70632)),f332(f76(x70631),x70633)),f332(f76(x70631),f332(f332(f82(x70631),x70632),x70633)))+~P24(f332(f332(f246(x70631),f2(x70631)),x70632))+~P24(f332(f332(f246(x70631),f2(x70631)),x70633)) % 165.30/165.05 [7080]~P126(x70801)+~P24(f332(f332(f246(x70801),x70803),f2(x70801)))+~P24(f332(f332(f246(x70801),x70802),f2(x70801)))+P24(f332(f332(f246(x70801),f2(x70801)),f332(f332(f82(x70801),x70802),x70803))) % 165.30/165.05 [7081]~P122(x70811)+~P24(f332(f332(f246(x70811),x70813),f2(x70811)))+~P24(f332(f332(f246(x70811),x70812),f2(x70811)))+P24(f332(f332(f246(x70811),f2(x70811)),f332(f332(f82(x70811),x70812),x70813))) % 165.30/165.05 [7082]~P62(x70821)+~P24(f332(f332(f246(x70821),x70823),f2(x70821)))+~P24(f332(f332(f246(x70821),x70822),f2(x70821)))+P24(f332(f332(f246(x70821),f2(x70821)),f332(f332(f290(x70821),x70822),x70823))) % 165.30/165.05 [7083]~P63(x70831)+~P24(f332(f332(f247(x70831),x70833),f2(x70831)))+~P24(f332(f332(f246(x70831),x70832),f2(x70831)))+P24(f332(f332(f246(x70831),f2(x70831)),f332(f332(f290(x70831),x70832),x70833))) % 165.30/165.05 [7084]~P122(x70841)+~P24(f332(f332(f247(x70841),x70843),f2(x70841)))+~P24(f332(f332(f247(x70841),x70842),f2(x70841)))+P24(f332(f332(f247(x70841),f2(x70841)),f332(f332(f82(x70841),x70842),x70843))) % 165.30/165.05 [7085]~P62(x70851)+~P24(f332(f332(f247(x70851),x70853),f2(x70851)))+~P24(f332(f332(f247(x70851),x70852),f2(x70851)))+P24(f332(f332(f247(x70851),f2(x70851)),f332(f332(f290(x70851),x70852),x70853))) % 165.30/165.05 [7086]~P63(x70861)+~P24(f332(f332(f247(x70861),x70863),f2(x70861)))+~P24(f332(f332(f247(x70861),x70862),f2(x70861)))+P24(f332(f332(f247(x70861),f2(x70861)),f332(f332(f290(x70861),x70862),x70863))) % 165.30/165.05 [7087]~P112(x70871)+~P24(f332(f332(f247(a868),f2(a868)),x70873))+~P24(f332(f332(f247(x70871),f79(x70871)),x70872))+P24(f332(f332(f247(x70871),f79(x70871)),f332(f332(f257(x70871),x70872),x70873))) % 165.30/165.05 [7184]~P126(x71841)+~P24(f332(f332(f246(x71841),f2(x71841)),x71843))+~P24(f332(f332(f246(x71841),f2(x71841)),x71842))+P24(f332(f332(f246(x71841),f2(x71841)),f332(f332(f82(x71841),x71842),x71843))) % 165.30/165.05 [7185]~P122(x71851)+~P24(f332(f332(f246(x71851),f2(x71851)),x71853))+~P24(f332(f332(f246(x71851),f2(x71851)),x71852))+P24(f332(f332(f246(x71851),f2(x71851)),f332(f332(f82(x71851),x71852),x71853))) % 165.30/165.05 [7186]~P133(x71861)+~P24(f332(f332(f246(x71861),f2(x71861)),x71863))+~P24(f332(f332(f246(x71861),f2(x71861)),x71862))+P24(f332(f332(f246(x71861),f2(x71861)),f332(f332(f82(x71861),x71862),x71863))) % 165.30/165.05 [7187]~P62(x71871)+~P24(f332(f332(f246(x71871),f2(x71871)),x71873))+~P24(f332(f332(f246(x71871),f2(x71871)),x71872))+P24(f332(f332(f246(x71871),f2(x71871)),f332(f332(f290(x71871),x71872),x71873))) % 165.30/165.05 [7188]~P63(x71881)+~P24(f332(f332(f247(x71881),f2(x71881)),x71883))+~P24(f332(f332(f246(x71881),f2(x71881)),x71882))+P24(f332(f332(f246(x71881),f2(x71881)),f332(f332(f290(x71881),x71882),x71883))) % 165.30/165.05 [7189]~P112(x71891)+~P24(f332(f332(f247(x71891),f79(x71891)),x71893))+~P24(f332(f332(f247(x71891),f79(x71891)),x71892))+P24(f332(f332(f247(x71891),f79(x71891)),f332(f332(f82(x71891),x71892),x71893))) % 165.30/165.05 [7192]~P87(x71921)+~P24(f332(f332(f247(x71921),f2(x71921)),x71923))+~P24(f332(f332(f247(x71921),f2(x71921)),x71922))+P24(f332(f332(f247(x71921),f2(x71921)),f332(f332(f81(x71921),x71922),x71923))) % 165.30/165.05 [7193]~P129(x71931)+~P24(f332(f332(f247(x71931),f2(x71931)),x71933))+~P24(f332(f332(f247(x71931),f2(x71931)),x71932))+P24(f332(f332(f247(x71931),f2(x71931)),f332(f332(f82(x71931),x71932),x71933))) % 165.30/165.05 [7194]~P62(x71941)+~P24(f332(f332(f247(x71941),f2(x71941)),x71943))+~P24(f332(f332(f247(x71941),f2(x71941)),x71942))+P24(f332(f332(f247(x71941),f2(x71941)),f332(f332(f290(x71941),x71942),x71943))) % 165.30/165.05 [7195]~P63(x71951)+~P24(f332(f332(f247(x71951),f2(x71951)),x71953))+~P24(f332(f332(f247(x71951),f2(x71951)),x71952))+P24(f332(f332(f247(x71951),f2(x71951)),f332(f332(f290(x71951),x71952),x71953))) % 165.30/165.05 [7266]~P26(x72661)+~P24(f332(f62(x72661),x72663))+E(f10(x72661,f332(f332(f310(x72661),x72662),x72663)),x72662)+~E(f332(f332(f22(f875(x72661,a862)),x72663),f332(f332(f310(x72661),x72662),f196(f875(x72661,a862)))),f196(f875(x72661,a862))) % 165.30/165.05 [7267]~P26(x72671)+~P24(f332(f62(x72671),x72673))+E(f11(x72671,f332(f332(f310(x72671),x72672),x72673)),x72672)+~E(f332(f332(f22(f875(x72671,a862)),x72673),f332(f332(f310(x72671),x72672),f196(f875(x72671,a862)))),f196(f875(x72671,a862))) % 165.30/165.05 [7268]~P106(x72681)+~P24(f332(f62(x72681),x72683))+E(f14(x72681,f332(f332(f310(x72681),x72682),x72683)),x72682)+~E(f332(f332(f22(f875(x72681,a862)),x72683),f332(f332(f310(x72681),x72682),f196(f875(x72681,a862)))),f196(f875(x72681,a862))) % 165.30/165.05 [7269]~P106(x72691)+~P24(f332(f62(x72691),x72693))+E(f15(x72691,f332(f332(f310(x72691),x72692),x72693)),x72692)+~E(f332(f332(f22(f875(x72691,a862)),x72693),f332(f332(f310(x72691),x72692),f196(f875(x72691,a862)))),f196(f875(x72691,a862))) % 165.30/165.05 [7270]~P122(x72701)+P24(f332(f332(f246(x72701),x72702),f2(x72701)))+P24(f332(f332(f246(x72701),f2(x72701)),x72703))+~P24(f332(f332(f246(x72701),f2(x72701)),f332(f332(f82(x72701),x72703),x72702))) % 165.30/165.05 [7271]~P122(x72711)+P24(f332(f332(f246(x72711),x72712),f2(x72711)))+P24(f332(f332(f246(x72711),f2(x72711)),x72713))+~P24(f332(f332(f246(x72711),f2(x72711)),f332(f332(f82(x72711),x72712),x72713))) % 165.30/165.05 [7272]~P62(x72721)+P24(f332(f332(f246(x72721),x72722),f2(x72721)))+P24(f332(f332(f246(x72721),f2(x72721)),x72723))+~P24(f332(f332(f246(x72721),f2(x72721)),f332(f332(f290(x72721),x72723),x72722))) % 165.30/165.05 [7273]~P62(x72731)+P24(f332(f332(f246(x72731),x72732),f2(x72731)))+P24(f332(f332(f246(x72731),f2(x72731)),x72733))+~P24(f332(f332(f246(x72731),f2(x72731)),f332(f332(f290(x72731),x72732),x72733))) % 165.30/165.05 [7274]~P122(x72741)+P24(f332(f332(f246(x72741),x72742),f2(x72741)))+P24(f332(f332(f246(x72741),f2(x72741)),x72742))+~P24(f332(f332(f246(x72741),f2(x72741)),f332(f332(f82(x72741),x72743),x72742))) % 165.30/165.05 [7275]~P122(x72751)+P24(f332(f332(f246(x72751),x72752),f2(x72751)))+P24(f332(f332(f246(x72751),f2(x72751)),x72752))+~P24(f332(f332(f246(x72751),f2(x72751)),f332(f332(f82(x72751),x72752),x72753))) % 165.30/165.05 [7276]~P62(x72761)+P24(f332(f332(f246(x72761),x72762),f2(x72761)))+P24(f332(f332(f246(x72761),f2(x72761)),x72762))+~P24(f332(f332(f246(x72761),f2(x72761)),f332(f332(f290(x72761),x72763),x72762))) % 165.30/165.05 [7277]~P62(x72771)+P24(f332(f332(f246(x72771),x72772),f2(x72771)))+P24(f332(f332(f246(x72771),f2(x72771)),x72772))+~P24(f332(f332(f246(x72771),f2(x72771)),f332(f332(f290(x72771),x72772),x72773))) % 165.30/165.05 [7278]~P62(x72781)+P24(f332(f332(f247(x72781),x72782),f2(x72781)))+P24(f332(f332(f247(x72781),f2(x72781)),x72783))+~P24(f332(f332(f247(x72781),f2(x72781)),f332(f332(f290(x72781),x72783),x72782))) % 165.30/165.05 [7279]~P62(x72791)+P24(f332(f332(f247(x72791),x72792),f2(x72791)))+P24(f332(f332(f247(x72791),f2(x72791)),x72793))+~P24(f332(f332(f247(x72791),f2(x72791)),f332(f332(f290(x72791),x72792),x72793))) % 165.30/165.05 [7280]~P62(x72801)+P24(f332(f332(f247(x72801),x72802),f2(x72801)))+P24(f332(f332(f247(x72801),f2(x72801)),x72802))+~P24(f332(f332(f247(x72801),f2(x72801)),f332(f332(f290(x72801),x72803),x72802))) % 165.30/165.05 [7281]~P62(x72811)+P24(f332(f332(f247(x72811),x72812),f2(x72811)))+P24(f332(f332(f247(x72811),f2(x72811)),x72812))+~P24(f332(f332(f247(x72811),f2(x72811)),f332(f332(f290(x72811),x72812),x72813))) % 165.30/165.05 [7368]~E(f332(f332(f104(f875(x73681,a862)),f332(f174(x73681),x73682)),f332(f174(x73681),x73683)),f196(f875(x73681,a862)))+~P24(f332(f138(x73681),x73683))+~P24(f332(f138(x73681),x73682))+P24(f332(f138(x73681),f332(f332(f135(x73681),x73682),x73683))) % 165.30/165.05 [7369]~P106(x73691)+~P24(f332(f62(x73691),x73693))+E(f12(x73691,f244(x73691),f332(f332(f310(x73691),x73692),x73693)),x73692)+~E(f332(f332(f22(f875(x73691,a862)),x73693),f332(f332(f310(x73691),x73692),f196(f875(x73691,a862)))),f196(f875(x73691,a862))) % 165.30/165.05 [7370]~P106(x73701)+~P24(f332(f62(x73701),x73703))+E(f13(x73701,f245(x73701),f332(f332(f310(x73701),x73702),x73703)),x73702)+~E(f332(f332(f22(f875(x73701,a862)),x73703),f332(f332(f310(x73701),x73702),f196(f875(x73701,a862)))),f196(f875(x73701,a862))) % 165.30/165.05 [7387]~P85(x73871)+~P24(f332(f332(f246(x73871),x73872),x73873))+~P24(f332(f332(f246(x73871),f332(f80(x73871),x73872)),x73873))+P24(f332(f332(f246(x73871),f332(f76(x73871),x73872)),x73873)) % 165.30/165.05 [7388]~P118(x73881)+~P24(f332(f332(f247(x73881),x73882),x73883))+~P24(f332(f332(f247(x73881),f332(f80(x73881),x73882)),x73883))+P24(f332(f332(f247(x73881),f332(f76(x73881),x73882)),x73883)) % 165.30/165.05 [7458]~P129(x74581)+P24(f332(f332(f247(x74581),f2(x74581)),x74582))+~P24(f332(f332(f247(x74581),f2(x74581)),x74583))+~P24(f332(f332(f247(x74581),f2(x74581)),f332(f332(f82(x74581),x74583),x74582))) % 165.30/165.05 [7459]~P129(x74591)+P24(f332(f332(f247(x74591),f2(x74591)),x74592))+~P24(f332(f332(f247(x74591),f2(x74591)),x74593))+~P24(f332(f332(f247(x74591),f2(x74591)),f332(f332(f82(x74591),x74592),x74593))) % 165.30/165.05 [7762]E(x77621,x77622)+~P24(f332(f62(x77623),x77621))+~P24(f332(f332(f246(a868),f332(f38(x77623),x77621)),f332(f38(x77623),x77622)))+~P24(f332(f332(f246(f875(x77623,a862)),x77622),x77621)) % 165.30/165.05 [7902]~P24(f332(f332(f247(a1),x79021),f2(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x79022))+~P24(f332(f332(f246(a1),x79022),x79023))+P24(f332(f332(f246(a1),f332(f332(f39(a1),x79021),x79022)),f332(f332(f39(a1),x79021),x79023))) % 165.30/165.05 [7914]~P24(f332(f332(f246(a1),f2(a1)),x79141))+~P24(f332(f332(f247(a1),f2(a1)),x79143))+~P24(f332(f332(f246(a1),x79143),x79142))+P24(f332(f332(f246(a1),f332(f332(f39(a1),x79141),x79142)),f332(f332(f39(a1),x79141),x79143))) % 165.30/165.05 [8047]E(f332(x80471,f429(x80472,x80471,x80473)),x80472)+~P24(f332(f332(f246(a1),x80472),f332(x80471,x80473)))+P24(f332(f332(f247(a868),f430(x80472,x80471,x80473)),x80473))+~P24(f332(f332(f246(a1),f332(x80471,f2(a868))),x80472)) % 165.30/165.05 [8048]E(f332(x80481,f454(x80482,x80481,x80483)),x80482)+~P24(f332(f332(f246(a1),x80482),f332(x80481,x80483)))+P24(f332(f332(f247(a868),f455(x80482,x80481,x80483)),x80483))+~P24(f332(f332(f246(a1),f332(x80481,f2(a868))),x80482)) % 165.30/165.05 [8149]~P24(f332(f62(x81491),x81493))+~P24(f332(f332(f247(a868),f332(f38(x81491),x81492)),f332(f38(x81491),x81493)))+~P24(f332(f332(f246(f875(x81491,a862)),x81492),x81493))+P24(f332(f332(f247(f875(x81491,a862)),x81492),x81493)) % 165.30/165.05 [8178]E(f332(f332(f81(a1),f375(x81783,x81781,x81782)),f376(x81783,x81781,x81782)),x81781)+E(f332(f332(f22(a1),x81781),x81782),x81781)+~P24(f332(f332(f247(a1),f2(a1)),x81782))+~P24(f332(f332(f334(a1),f332(f332(f22(a1),x81781),f79(a1))),x81783)) % 165.30/165.05 [8179]E(f332(f332(f22(a1),f383(x81793,x81791,x81792)),f381(x81793,x81791,x81792)),x81791)+E(f332(f332(f81(a1),x81791),x81792),x81791)+~P24(f332(f332(f247(a1),f2(a1)),x81792))+~P24(f332(f332(f334(a1),f332(f332(f81(a1),x81791),f79(a1))),x81793)) % 165.30/165.05 [8232]~P24(f332(f332(f246(a868),x82323),x82321))+P24(f332(f332(f246(a868),x82321),x82322))+~P24(f332(f332(f246(a868),x82323),x82322))+~P24(f332(f332(f246(a868),f332(f332(f22(a868),x82321),x82323)),f332(f332(f22(a868),x82322),x82323))) % 165.30/165.05 [8233]~P24(f332(f332(f246(a868),x82333),x82331))+P24(f332(f332(f247(a868),x82331),x82332))+~P24(f332(f332(f246(a868),x82333),x82332))+~P24(f332(f332(f247(a868),f332(f332(f22(a868),x82331),x82333)),f332(f332(f22(a868),x82332),x82333))) % 165.30/165.05 [8249]~P106(x82492)+E(x82491,f116(x82492))+~P32(x82492,f332(f170(x82492),x82491))+E(f332(f143(x82492,x82492,f332(f7(x82492,x82492,x82492),f245(x82492)),x82493),f332(f170(x82492),x82491)),f332(f332(f245(x82492),f332(f332(f166(x82492),x82491),f2(a868))),x82493)) % 165.30/165.05 [8313]E(f332(f332(f22(a1),x83131),x83132),x83131)+~P24(f332(f332(f247(a1),f2(a1)),x83132))+P24(f332(f332(f334(a1),f375(x83133,x83131,x83132)),x83133))+~P24(f332(f332(f334(a1),f332(f332(f22(a1),x83131),f79(a1))),x83133)) % 165.30/165.05 [8314]E(f332(f332(f81(a1),x83141),x83142),x83141)+~P24(f332(f332(f247(a1),f2(a1)),x83142))+P24(f332(f332(f334(a1),f383(x83143,x83141,x83142)),x83143))+~P24(f332(f332(f334(a1),f332(f332(f81(a1),x83141),f79(a1))),x83143)) % 165.30/165.05 [8386]~P24(f332(f332(f246(a1),x83861),f332(x83862,x83863)))+P24(f332(f332(f247(a868),f430(x83861,x83862,x83863)),x83863))+P24(f332(f332(f246(a868),f429(x83861,x83862,x83863)),x83863))+~P24(f332(f332(f246(a1),f332(x83862,f2(a868))),x83861)) % 165.30/165.05 [8387]~P24(f332(f332(f246(a1),x83871),f332(x83872,x83873)))+P24(f332(f332(f247(a868),f455(x83871,x83872,x83873)),x83873))+P24(f332(f332(f246(a868),f454(x83871,x83872,x83873)),x83873))+~P24(f332(f332(f246(a1),f332(x83872,f2(a868))),x83871)) % 165.30/165.05 [8458]E(f332(f332(f22(a1),x84581),x84582),x84581)+~P24(f332(f332(f247(a1),f2(a1)),x84582))+P24(f332(f332(f334(a1),f376(x84583,x84581,x84582)),f303(a1,f79(a1),x84582)))+~P24(f332(f332(f334(a1),f332(f332(f22(a1),x84581),f79(a1))),x84583)) % 165.30/165.05 [8459]E(f332(f332(f81(a1),x84591),x84592),x84591)+~P24(f332(f332(f247(a1),f2(a1)),x84592))+P24(f332(f332(f334(a1),f381(x84593,x84591,x84592)),f303(a1,f79(a1),x84592)))+~P24(f332(f332(f334(a1),f332(f332(f81(a1),x84591),f79(a1))),x84593)) % 165.30/165.05 [8585]~P112(x85851)+~P24(f332(f332(f247(x85851),x85852),f79(x85851)))+~P24(f332(f332(f247(x85851),f2(x85851)),x85852))+P24(f332(f332(f247(x85851),f332(f332(f82(x85851),x85852),f332(f332(f257(x85851),x85852),x85853))),f332(f332(f257(x85851),x85852),x85853))) % 165.30/165.05 [8668]~P24(f332(x86681,x86682))+P24(f332(x86681,f2(a868)))+~P24(f332(f332(f247(a868),x86682),x86683))+~P24(f332(x86681,f45(a868,f332(a115,f485(x86682,x86681,x86683)),x86683))) % 165.30/165.05 [8806]E(f514(x88061,x88062,x88063),f2(a868))+P24(f332(f332(x88061,x88063),x88062))+P24(f332(f332(x88061,f514(x88061,x88062,x88063)),f45(a868,f513(x88061,x88062,x88063),f514(x88061,x88062,x88063))))+~P24(f332(f320(f874(a868,a868),a231),f332(f332(f267(a868,a868),x88063),x88062))) % 165.30/165.05 [8844]~P21(x88441,x88441,x88442,x88443)+E(f332(f311(x88441,x88441,x88442),x88443),x88443)+~P24(f332(f62(x88441),x88443))+~P24(f332(f332(f246(f875(x88441,a862)),f332(f311(x88441,x88441,x88442),x88443)),x88443)) % 165.30/165.05 [9058]P24(f332(f332(x90581,x90582),x90583))+P24(f332(f332(f247(a1),f802(x90581,x90583,x90582)),f803(x90581,x90583,x90582)))+P24(f332(f332(x90581,f802(x90581,x90583,x90582)),f332(f332(f81(a1),f803(x90581,x90583,x90582)),f79(a1))))+~P24(f332(f320(f874(a1,a1),a134),f332(f332(f267(a1,a1),x90582),x90583))) % 165.30/165.05 [9075]P24(f332(f332(x90751,x90752),x90753))+~P24(f332(f332(f247(a1),f512(x90751,x90753,x90752)),f2(a1)))+P24(f332(f332(x90751,f332(f80(a1),f511(x90751,x90753,x90752))),f332(f80(a1),f512(x90751,x90753,x90752))))+~P24(f332(f320(f874(a1,a1),a236),f332(f332(f267(a1,a1),x90752),x90753))) % 165.30/165.05 [9249]P24(f332(f332(x92491,x92492),x92493))+P24(f332(f332(x92491,f332(f332(f81(a1),f580(x92491,x92493,x92492)),f79(a1))),f581(x92491,x92493,x92492)))+~P24(f332(f332(f246(a1),f580(x92491,x92493,x92492)),f581(x92491,x92493,x92492)))+~P24(f332(f320(f874(a1,a1),a185),f332(f332(f267(a1,a1),x92492),x92493))) % 165.30/165.05 [9666]~P59(x96662)+~P59(x96661)+~P24(f332(f59(f874(x96661,x96662)),x96663))+P24(f332(f59(x96661),f332(f332(f8(f875(x96662,a862),a862,x96661),f59(x96662)),f332(f332(f8(f875(x96662,f874(x96661,x96662)),f875(x96662,a862),x96661),f332(f8(f874(x96661,x96662),a862,x96662),x96663)),f267(x96661,x96662))))) % 165.30/165.05 [9667]~P59(x96672)+~P59(x96671)+~P24(f332(f58(f874(x96671,x96672)),x96673))+P24(f332(f58(x96671),f332(f332(f8(f875(x96672,a862),a862,x96671),f58(x96672)),f332(f332(f8(f875(x96672,f874(x96671,x96672)),f875(x96672,a862),x96671),f332(f8(f874(x96671,x96672),a862,x96672),x96673)),f267(x96671,x96672))))) % 165.30/165.05 [9770]~P59(x97702)+~P59(x97701)+P24(f332(f59(f874(x97701,x97702)),x97703))+~P24(f332(f59(x97701),f332(f332(f8(f875(x97702,a862),a862,x97701),f59(x97702)),f332(f332(f8(f875(x97702,f874(x97701,x97702)),f875(x97702,a862),x97701),f332(f8(f874(x97701,x97702),a862,x97702),x97703)),f267(x97701,x97702))))) % 165.30/165.05 [9771]~P59(x97712)+~P59(x97711)+P24(f332(f58(f874(x97711,x97712)),x97713))+~P24(f332(f58(x97711),f332(f332(f8(f875(x97712,a862),a862,x97711),f58(x97712)),f332(f332(f8(f875(x97712,f874(x97711,x97712)),f875(x97712,a862),x97711),f332(f8(f874(x97711,x97712),a862,x97712),x97713)),f267(x97711,x97712))))) % 165.30/165.05 [9939]E(f332(x99391,f429(x99392,x99391,x99393)),x99392)+~P24(f332(f332(f246(a1),x99392),f332(x99391,x99393)))+~P24(f332(f332(f246(a1),f332(f76(a1),f332(f332(f22(a1),f332(x99391,f332(f332(f81(a868),f430(x99392,x99391,x99393)),f79(a868)))),f332(x99391,f430(x99392,x99391,x99393))))),f79(a1)))+~P24(f332(f332(f246(a1),f332(x99391,f2(a868))),x99392)) % 165.30/165.05 [9940]E(f332(x99401,f454(x99402,x99401,x99403)),x99402)+~P24(f332(f332(f246(a1),x99402),f332(x99401,x99403)))+~P24(f332(f332(f246(a1),f332(f76(a1),f332(f332(f22(a1),f332(x99401,f332(f332(f81(a868),f455(x99402,x99401,x99403)),f79(a868)))),f332(x99401,f455(x99402,x99401,x99403))))),f79(a1)))+~P24(f332(f332(f246(a1),f332(x99401,f2(a868))),x99402)) % 165.30/165.05 [9944]~P24(f332(f332(f246(a1),x99441),f332(x99442,x99443)))+~P24(f332(f332(f246(a1),f332(f76(a1),f332(f332(f22(a1),f332(x99442,f332(f332(f81(a868),f430(x99441,x99442,x99443)),f79(a868)))),f332(x99442,f430(x99441,x99442,x99443))))),f79(a1)))+P24(f332(f332(f246(a868),f429(x99441,x99442,x99443)),x99443))+~P24(f332(f332(f246(a1),f332(x99442,f2(a868))),x99441)) % 165.30/165.05 [9945]~P24(f332(f332(f246(a1),x99451),f332(x99452,x99453)))+~P24(f332(f332(f246(a1),f332(f76(a1),f332(f332(f22(a1),f332(x99452,f332(f332(f81(a868),f455(x99451,x99452,x99453)),f79(a868)))),f332(x99452,f455(x99451,x99452,x99453))))),f79(a1)))+P24(f332(f332(f246(a868),f454(x99451,x99452,x99453)),x99453))+~P24(f332(f332(f246(a1),f332(x99452,f2(a868))),x99451)) % 165.30/165.05 [10000]E(x100001,x100002)+~E(f332(f143(f869(x100003),f869(x100003),f135(x100003),f116(x100003)),x100001),f332(f143(f869(x100003),f869(x100003),f135(x100003),f116(x100003)),x100002))+~E(f332(f197(f869(f869(x100003))),x100001),f332(f197(f869(f869(x100003))),x100002))+~P24(f332(f332(f271(f869(x100003),f869(x100003),a862),f332(f332(f7(f869(x100003),f875(f869(x100003),a868),f875(f869(x100003),a862)),f332(f332(f8(f875(a868,a862),f875(f875(f869(x100003),a868),f875(f869(x100003),a862)),f869(x100003)),f8(a868,a862,f869(x100003))),f332(f332(f8(a868,f875(a868,a862),f869(x100003)),a329),f197(f869(x100003))))),f197(f869(x100003)))),f621(x100002,x100001,x100003))) % 165.30/165.05 [10001]E(x100011,x100012)+~E(f332(f143(f869(x100013),f869(x100013),f135(x100013),f116(x100013)),x100011),f332(f143(f869(x100013),f869(x100013),f135(x100013),f116(x100013)),x100012))+~E(f332(f197(f869(f869(x100013))),x100011),f332(f197(f869(f869(x100013))),x100012))+~P24(f332(f332(f271(f869(x100013),f869(x100013),a862),f332(f332(f7(f869(x100013),f875(f869(x100013),a868),f875(f869(x100013),a862)),f332(f332(f8(f875(a868,a862),f875(f875(f869(x100013),a868),f875(f869(x100013),a862)),f869(x100013)),f8(a868,a862,f869(x100013))),f332(f332(f8(a868,f875(a868,a862),f869(x100013)),a329),f197(f869(x100013))))),f197(f869(x100013)))),f622(x100011,x100012,x100013))) % 165.30/165.05 [6791]~E(f79(a868),f2(a868))+~P24(f332(f62(x67911),x67913))+~P24(f332(f62(x67911),x67912))+E(f332(f332(f81(a868),f332(f38(x67911),x67912)),f332(f38(x67911),x67913)),f332(f38(x67911),f332(f332(f113(f875(x67911,a862)),x67912),x67913))) % 165.30/165.05 [7202]~P100(x72021)+~P24(f332(f62(x72021),x72022))+~P24(f332(f332(f334(x72021),x72023),x72022))+P24(f332(f332(f246(x72021),f332(f64(x72021,f104(x72021)),x72022)),x72023)) % 165.30/165.05 [7203]~P106(x72031)+~P24(f332(f62(x72031),x72032))+~P24(f332(f332(f334(x72031),x72033),x72032))+P24(f332(f332(f246(x72031),f332(f64(x72031,f244(x72031)),x72032)),x72033)) % 165.30/165.05 [7452]~P24(f332(f62(x74521),x74523))+~P24(f332(f62(x74521),x74522))+~E(f332(f332(f104(f875(x74521,a862)),x74522),x74523),f196(f875(x74521,a862)))+E(f332(f332(f81(a868),f332(f38(x74521),x74522)),f332(f38(x74521),x74523)),f332(f38(x74521),f332(f332(f113(f875(x74521,a862)),x74522),x74523))) % 165.30/165.05 [8238]~P41(x82381,x82383)+~P41(x82381,x82382)+~E(f332(f332(f104(f875(x82381,a862)),f332(f265(x82381,x82381),x82382)),f332(f263(x82381,x82381),x82383)),f196(f875(x82381,a862)))+P41(x82381,f332(f332(f113(f875(f874(x82381,x82381),a862)),x82382),x82383)) % 165.30/165.05 [8328]E(x83281,f332(f332(f39(a868),x83282),x83283))+~P24(f332(f332(f247(a868),f2(a868)),x83283))+~P24(f332(f332(f247(a868),x83282),f332(f332(f82(a868),x83283),f332(a115,x83281))))+~P24(f332(f332(f246(a868),f332(f332(f82(a868),x83283),x83281)),x83282)) % 165.30/165.05 [8456]~P24(f332(f62(x84561),x84562))+~P24(f332(f62(x84561),x84563))+E(f332(f332(f81(a868),f332(f38(x84561),x84562)),f332(f38(x84561),x84563)),f332(f38(x84561),f332(f332(f113(f875(x84561,a862)),x84562),x84563)))+P24(f332(f332(f334(x84561),f854(x84563,x84562,x84561)),f332(f332(f104(f875(x84561,a862)),x84562),x84563))) % 165.30/165.05 [8818]~P122(x88182)+~E(x88181,f2(x88182))+~E(x88183,f2(x88182))+~P24(f332(f332(f247(x88182),f2(x88182)),f332(f332(f81(x88182),f332(f332(f82(x88182),x88183),x88183)),f332(f332(f82(x88182),x88181),x88181)))) % 165.30/165.05 [9327]~P41(x93271,x93273)+~P41(x93271,x93272)+P41(x93271,f332(f332(f113(f875(f874(x93271,x93271),a862)),x93272),x93273))+~P24(f332(f332(f246(f875(f874(x93271,x93271),a862)),f332(f332(f289(x93271,x93271,x93271),x93272),x93273)),x93272)) % 165.30/165.05 [9446]~P24(f332(x94461,x94463))+~P24(f332(f62(x94462),x94463))+P24(f332(x94461,f196(f875(x94462,a862))))+~P24(f332(x94461,f332(f332(f22(f875(x94462,a862)),f570(x94461,x94463,x94462)),f332(f332(f310(x94462),f593(x94461,x94463,x94462)),f196(f875(x94462,a862)))))) % 165.30/165.05 [9696]~P59(x96961)+~P59(x96962)+P8(x96961,f332(f332(f8(f875(x96962,x96961),a862,f869(x96961)),x96963),f332(f332(f8(f875(x96962,f872(x96961)),f875(x96962,x96961),f869(x96961)),f74(f872(x96961),x96961,x96962,f243(x96961))),f332(f332(f8(f869(f874(x96962,x96961)),f875(x96962,f872(x96961)),f869(x96961)),f180(x96962,x96961)),f332(f184(x96962,x96961),f56(x96962))))),f332(f197(f869(x96962)),f56(x96962)))+~P24(f332(f59(f875(x96962,x96961)),x96963)) % 165.30/165.05 [9697]~P59(x96971)+~P59(x96972)+P7(x96971,f332(f332(f8(f875(x96972,x96971),a862,f869(x96971)),x96973),f332(f332(f8(f875(x96972,f872(x96971)),f875(x96972,x96971),f869(x96971)),f74(f872(x96971),x96971,x96972,f243(x96971))),f332(f332(f8(f869(f874(x96972,x96971)),f875(x96972,f872(x96971)),f869(x96971)),f180(x96972,x96971)),f332(f184(x96972,x96971),f56(x96972))))),f332(f197(f869(x96972)),f56(x96972)))+~P24(f332(f58(f875(x96972,x96971)),x96973)) % 165.30/165.05 [9792]~P59(x97921)+~P59(x97922)+~P8(x97922,f332(f332(f8(f875(x97921,x97922),a862,f869(x97922)),x97923),f332(f332(f8(f875(x97921,f872(x97922)),f875(x97921,x97922),f869(x97922)),f74(f872(x97922),x97922,x97921,f243(x97922))),f332(f332(f8(f869(f874(x97921,x97922)),f875(x97921,f872(x97922)),f869(x97922)),f180(x97921,x97922)),f332(f184(x97921,x97922),f56(x97921))))),f332(f197(f869(x97921)),f56(x97921)))+P24(f332(f59(f875(x97921,x97922)),x97923)) % 165.30/165.05 [9793]~P59(x97931)+~P59(x97932)+~P7(x97932,f332(f332(f8(f875(x97931,x97932),a862,f869(x97932)),x97933),f332(f332(f8(f875(x97931,f872(x97932)),f875(x97931,x97932),f869(x97932)),f74(f872(x97932),x97932,x97931,f243(x97932))),f332(f332(f8(f869(f874(x97931,x97932)),f875(x97931,f872(x97932)),f869(x97932)),f180(x97931,x97932)),f332(f184(x97931,x97932),f56(x97931))))),f332(f197(f869(x97931)),f56(x97931)))+P24(f332(f58(f875(x97931,x97932)),x97933)) % 165.30/165.05 [8619]~P24(f332(f332(f247(a1),f2(a1)),x86193))+P24(f332(f332(f246(a1),f2(a1)),x86191))+~P24(f332(f332(f247(a1),x86192),x86193))+~P24(f332(f332(f246(a1),f2(a1)),f332(f332(f81(a1),f332(f332(f82(a1),x86193),x86191)),x86192))) % 165.30/165.05 [8642]~P26(x86421)+~P24(f332(f62(x86421),x86422))+E(f332(f332(f22(f875(x86421,a862)),x86422),f332(f332(f310(x86421),x86423),f196(f875(x86421,a862)))),f196(f875(x86421,a862)))+E(f332(f332(f113(x86421),x86423),f10(x86421,f332(f332(f22(f875(x86421,a862)),x86422),f332(f332(f310(x86421),x86423),f196(f875(x86421,a862)))))),f10(x86421,f332(f332(f310(x86421),x86423),x86422))) % 165.30/165.05 [8643]~P26(x86431)+~P24(f332(f62(x86431),x86432))+E(f332(f332(f22(f875(x86431,a862)),x86432),f332(f332(f310(x86431),x86433),f196(f875(x86431,a862)))),f196(f875(x86431,a862)))+E(f332(f332(f104(x86431),x86433),f11(x86431,f332(f332(f22(f875(x86431,a862)),x86432),f332(f332(f310(x86431),x86433),f196(f875(x86431,a862)))))),f11(x86431,f332(f332(f310(x86431),x86433),x86432))) % 165.30/165.05 [8644]~P106(x86441)+~P24(f332(f62(x86441),x86442))+E(f332(f332(f22(f875(x86441,a862)),x86442),f332(f332(f310(x86441),x86443),f196(f875(x86441,a862)))),f196(f875(x86441,a862)))+E(f332(f332(f245(x86441),x86443),f14(x86441,f332(f332(f22(f875(x86441,a862)),x86442),f332(f332(f310(x86441),x86443),f196(f875(x86441,a862)))))),f14(x86441,f332(f332(f310(x86441),x86443),x86442))) % 165.30/165.05 [8645]~P106(x86451)+~P24(f332(f62(x86451),x86452))+E(f332(f332(f22(f875(x86451,a862)),x86452),f332(f332(f310(x86451),x86453),f196(f875(x86451,a862)))),f196(f875(x86451,a862)))+E(f332(f332(f244(x86451),x86453),f15(x86451,f332(f332(f22(f875(x86451,a862)),x86452),f332(f332(f310(x86451),x86453),f196(f875(x86451,a862)))))),f15(x86451,f332(f332(f310(x86451),x86453),x86452))) % 165.30/165.05 [8709]~P106(x87091)+~P24(f332(f62(x87091),x87092))+E(f332(f332(f22(f875(x87091,a862)),x87092),f332(f332(f310(x87091),x87093),f196(f875(x87091,a862)))),f196(f875(x87091,a862)))+E(f332(f332(f244(x87091),x87093),f12(x87091,f244(x87091),f332(f332(f22(f875(x87091,a862)),x87092),f332(f332(f310(x87091),x87093),f196(f875(x87091,a862)))))),f12(x87091,f244(x87091),f332(f332(f310(x87091),x87093),x87092))) % 165.30/165.05 [8710]~P106(x87101)+~P24(f332(f62(x87101),x87102))+E(f332(f332(f22(f875(x87101,a862)),x87102),f332(f332(f310(x87101),x87103),f196(f875(x87101,a862)))),f196(f875(x87101,a862)))+E(f332(f332(f245(x87101),x87103),f13(x87101,f245(x87101),f332(f332(f22(f875(x87101,a862)),x87102),f332(f332(f310(x87101),x87103),f196(f875(x87101,a862)))))),f13(x87101,f245(x87101),f332(f332(f310(x87101),x87103),x87102))) % 165.30/165.05 [9269]E(x92691,x92692)+~E(f332(f143(f869(x92693),f869(x92693),f135(x92693),f116(x92693)),x92691),f332(f143(f869(x92693),f869(x92693),f135(x92693),f116(x92693)),x92692))+~E(f332(f197(f869(f869(x92693))),x92691),f332(f197(f869(f869(x92693))),x92692))+P24(f332(f332(f334(f874(f869(x92693),f869(x92693))),f621(x92692,x92691,x92693)),f332(f174(f874(f869(x92693),f869(x92693))),f332(f332(f184(f869(x92693),f869(x92693)),x92691),x92692)))) % 165.30/165.05 [9270]E(x92701,x92702)+~E(f332(f143(f869(x92703),f869(x92703),f135(x92703),f116(x92703)),x92701),f332(f143(f869(x92703),f869(x92703),f135(x92703),f116(x92703)),x92702))+~E(f332(f197(f869(f869(x92703))),x92701),f332(f197(f869(f869(x92703))),x92702))+P24(f332(f332(f334(f874(f869(x92703),f869(x92703))),f622(x92701,x92702,x92703)),f332(f174(f874(f869(x92703),f869(x92703))),f332(f332(f184(f869(x92703),f869(x92703)),x92702),x92701)))) % 165.30/165.05 [10084]~P97(x100842)+E(x100841,f196(f875(x100842,a862)))+~P24(f332(f62(x100842),x100841))+E(f11(x100842,f332(f252(x100842),f332(f332(f8(f875(x100842,a862),a862,x100842),f88(x100842)),f332(f332(f7(x100842,f875(x100842,a862),f875(x100842,a862)),f332(f332(f8(f875(x100842,f875(a862,a862)),f875(f875(x100842,a862),f875(x100842,a862)),x100842),f18(x100842,a862,a862)),f332(f332(f8(f875(x100842,a862),f875(x100842,f875(a862,a862)),x100842),f332(f8(a862,f875(a862,a862),x100842),a330)),f332(f332(f7(x100842,f875(x100842,x100842),f875(x100842,a862)),f332(f332(f8(f875(x100842,a862),f875(f875(x100842,x100842),f875(x100842,a862)),x100842),f8(x100842,a862,x100842)),a329)),f332(f113(x100842),x100843))))),f332(f332(f7(x100842,f875(x100842,a862),a862),f334(x100842)),x100841))))),f332(f332(f113(x100842),x100843),f11(x100842,x100841))) % 165.30/165.05 [10085]~P97(x100852)+E(x100851,f196(f875(x100852,a862)))+~P24(f332(f62(x100852),x100851))+E(f10(x100852,f332(f252(x100852),f332(f332(f8(f875(x100852,a862),a862,x100852),f88(x100852)),f332(f332(f7(x100852,f875(x100852,a862),f875(x100852,a862)),f332(f332(f8(f875(x100852,f875(a862,a862)),f875(f875(x100852,a862),f875(x100852,a862)),x100852),f18(x100852,a862,a862)),f332(f332(f8(f875(x100852,a862),f875(x100852,f875(a862,a862)),x100852),f332(f8(a862,f875(a862,a862),x100852),a330)),f332(f332(f7(x100852,f875(x100852,x100852),f875(x100852,a862)),f332(f332(f8(f875(x100852,a862),f875(f875(x100852,x100852),f875(x100852,a862)),x100852),f8(x100852,a862,x100852)),a329)),f332(f104(x100852),x100853))))),f332(f332(f7(x100852,f875(x100852,a862),a862),f334(x100852)),x100851))))),f332(f332(f104(x100852),x100853),f10(x100852,x100851))) % 165.30/165.05 [10086]~P76(x100862)+E(x100861,f196(f875(x100862,a862)))+~P24(f332(f62(x100862),x100861))+E(f14(x100862,f332(f252(x100862),f332(f332(f8(f875(x100862,a862),a862,x100862),f88(x100862)),f332(f332(f7(x100862,f875(x100862,a862),f875(x100862,a862)),f332(f332(f8(f875(x100862,f875(a862,a862)),f875(f875(x100862,a862),f875(x100862,a862)),x100862),f18(x100862,a862,a862)),f332(f332(f8(f875(x100862,a862),f875(x100862,f875(a862,a862)),x100862),f332(f8(a862,f875(a862,a862),x100862),a330)),f332(f332(f7(x100862,f875(x100862,x100862),f875(x100862,a862)),f332(f332(f8(f875(x100862,a862),f875(f875(x100862,x100862),f875(x100862,a862)),x100862),f8(x100862,a862,x100862)),a329)),f332(f81(x100862),x100863))))),f332(f332(f7(x100862,f875(x100862,a862),a862),f334(x100862)),x100861))))),f332(f332(f81(x100862),x100863),f14(x100862,x100861))) % 165.30/165.05 [10087]~P76(x100872)+E(x100871,f196(f875(x100872,a862)))+~P24(f332(f62(x100872),x100871))+E(f15(x100872,f332(f252(x100872),f332(f332(f8(f875(x100872,a862),a862,x100872),f88(x100872)),f332(f332(f7(x100872,f875(x100872,a862),f875(x100872,a862)),f332(f332(f8(f875(x100872,f875(a862,a862)),f875(f875(x100872,a862),f875(x100872,a862)),x100872),f18(x100872,a862,a862)),f332(f332(f8(f875(x100872,a862),f875(x100872,f875(a862,a862)),x100872),f332(f8(a862,f875(a862,a862),x100872),a330)),f332(f332(f7(x100872,f875(x100872,x100872),f875(x100872,a862)),f332(f332(f8(f875(x100872,a862),f875(f875(x100872,x100872),f875(x100872,a862)),x100872),f8(x100872,a862,x100872)),a329)),f332(f81(x100872),x100873))))),f332(f332(f7(x100872,f875(x100872,a862),a862),f334(x100872)),x100871))))),f332(f332(f81(x100872),x100873),f15(x100872,x100871))) % 165.30/165.05 [10088]~P106(x100882)+E(x100881,f196(f875(x100882,a862)))+~P24(f332(f62(x100882),x100881))+E(f13(x100882,f245(x100882),f332(f252(x100882),f332(f332(f8(f875(x100882,a862),a862,x100882),f88(x100882)),f332(f332(f7(x100882,f875(x100882,a862),f875(x100882,a862)),f332(f332(f8(f875(x100882,f875(a862,a862)),f875(f875(x100882,a862),f875(x100882,a862)),x100882),f18(x100882,a862,a862)),f332(f332(f8(f875(x100882,a862),f875(x100882,f875(a862,a862)),x100882),f332(f8(a862,f875(a862,a862),x100882),a330)),f332(f332(f7(x100882,f875(x100882,x100882),f875(x100882,a862)),f332(f332(f8(f875(x100882,a862),f875(f875(x100882,x100882),f875(x100882,a862)),x100882),f8(x100882,a862,x100882)),a329)),f332(f244(x100882),x100883))))),f332(f332(f7(x100882,f875(x100882,a862),a862),f334(x100882)),x100881))))),f332(f332(f244(x100882),x100883),f13(x100882,f245(x100882),x100881))) % 165.30/165.05 [10089]~P106(x100892)+E(x100891,f196(f875(x100892,a862)))+~P24(f332(f62(x100892),x100891))+E(f12(x100892,f244(x100892),f332(f252(x100892),f332(f332(f8(f875(x100892,a862),a862,x100892),f88(x100892)),f332(f332(f7(x100892,f875(x100892,a862),f875(x100892,a862)),f332(f332(f8(f875(x100892,f875(a862,a862)),f875(f875(x100892,a862),f875(x100892,a862)),x100892),f18(x100892,a862,a862)),f332(f332(f8(f875(x100892,a862),f875(x100892,f875(a862,a862)),x100892),f332(f8(a862,f875(a862,a862),x100892),a330)),f332(f332(f7(x100892,f875(x100892,x100892),f875(x100892,a862)),f332(f332(f8(f875(x100892,a862),f875(f875(x100892,x100892),f875(x100892,a862)),x100892),f8(x100892,a862,x100892)),a329)),f332(f245(x100892),x100893))))),f332(f332(f7(x100892,f875(x100892,a862),a862),f334(x100892)),x100891))))),f332(f332(f245(x100892),x100893),f12(x100892,f244(x100892),x100891))) % 165.30/165.05 [9843]~P118(x98431)+~E(x98433,f2(x98431))+~E(x98432,f2(x98431))+E(f332(f332(f81(x98431),f332(f332(f257(x98431),x98432),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x98431),x98433),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f2(x98431)) % 165.30/165.05 [9984]~P112(x99841)+~P24(f332(f332(f246(x99841),f2(x99841)),x99843))+P24(f332(f332(f246(x99841),x99842),x99843))+~P24(f332(f332(f246(x99841),f332(f332(f257(x99841),x99842),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x99841),x99843),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))))) % 165.30/165.05 [10030]~P118(x100302)+~E(x100301,f2(x100302))+~E(x100303,f2(x100302))+~P24(f332(f332(f247(x100302),f2(x100302)),f332(f332(f81(x100302),f332(f332(f257(x100302),x100303),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))),f332(f332(f257(x100302),x100301),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))))) % 165.30/165.05 [9233]E(x92331,x92332)+~E(f553(x92331,x92332,x92334,x92333),f554(x92331,x92332,x92334,x92333))+P24(f332(f332(f334(f874(f869(x92333),f869(x92333))),f332(f332(f267(f869(x92333),f869(x92333)),x92332),x92331)),f148(x92333,x92334)))+P24(f332(f332(f334(f874(f869(x92333),f869(x92333))),f332(f332(f267(f869(x92333),f869(x92333)),x92331),x92332)),f148(x92333,x92334))) % 165.30/165.05 [4837]~P60(x48372)+~E(x48374,f2(x48372))+~E(x48371,f2(x48372))+E(x48371,f332(f332(f290(x48372),x48373),x48374)) % 165.30/165.05 [4838]~P60(x48381)+~E(x48383,f2(x48381))+~E(x48384,f2(x48381))+E(f332(f332(f290(x48381),x48382),x48383),x48384) % 165.30/165.05 [4949]~P60(x49492)+E(x49491,f2(x49492))+~E(x49493,f2(x49492))+~E(x49491,f332(f332(f290(x49492),x49494),x49493)) % 165.30/165.05 [4950]~P60(x49502)+E(x49501,f2(x49502))+~E(x49503,f2(x49502))+~E(f332(f332(f290(x49502),x49504),x49503),x49501) % 165.30/165.05 [5128]~P116(x51282)+E(x51281,f2(x51282))+~E(f332(f332(f290(x51282),x51283),x51281),x51284)+E(x51283,f332(f332(f82(x51282),x51284),x51281)) % 165.30/165.05 [5130]~P116(x51302)+E(x51301,f2(x51302))+~E(f332(f332(f82(x51302),x51303),x51301),x51304)+E(x51303,f332(f332(f290(x51302),x51304),x51301)) % 165.30/165.05 [5131]~P60(x51312)+E(x51311,f2(x51312))+~E(f332(f332(f290(x51312),x51313),x51311),x51314)+E(x51313,f332(f332(f82(x51312),x51314),x51311)) % 165.30/165.05 [5132]~P60(x51322)+E(x51321,f2(x51322))+~E(f332(f332(f82(x51322),x51323),x51321),x51324)+E(x51323,f332(f332(f290(x51322),x51324),x51321)) % 165.30/165.05 [5133]~P116(x51332)+E(x51331,f2(x51332))+~E(x51333,f332(f332(f290(x51332),x51334),x51331))+E(f332(f332(f82(x51332),x51333),x51331),x51334) % 165.30/165.05 [5135]~P116(x51352)+E(x51351,f2(x51352))+~E(x51353,f332(f332(f82(x51352),x51354),x51351))+E(f332(f332(f290(x51352),x51353),x51351),x51354) % 165.30/165.05 [5136]~P60(x51362)+E(x51361,f2(x51362))+~E(x51363,f332(f332(f290(x51362),x51364),x51361))+E(f332(f332(f82(x51362),x51363),x51361),x51364) % 165.30/165.05 [5137]~P60(x51372)+E(x51371,f2(x51372))+~E(x51373,f332(f332(f82(x51372),x51374),x51371))+E(f332(f332(f290(x51372),x51373),x51371),x51374) % 165.30/165.05 [5169]~P60(x51692)+~E(x51691,f2(x51692))+~E(f332(f332(f82(x51692),x51691),x51694),x51693)+E(x51691,f332(f332(f290(x51692),x51693),x51694)) % 165.30/165.05 [5170]~P60(x51701)+~E(x51704,f2(x51701))+~E(x51702,f332(f332(f82(x51701),x51704),x51703))+E(f332(f332(f290(x51701),x51702),x51703),x51704) % 165.30/165.05 [5244]~E(x52443,x52444)+~E(x52442,x52443)+~P107(x52441)+E(f303(x52441,x52442,x52443),f332(f332(f310(x52441),x52444),f196(f875(x52441,a862)))) % 165.30/165.05 [5453]~E(f117(x54532,x54531),x54533)+~E(f145(x54532,x54531),x54534)+E(x54531,f116(x54532))+E(f332(f332(f135(x54532),x54533),f332(f332(f152(x54532),x54534),f116(x54532))),x54531) % 165.30/165.05 [6070]~P112(x60703)+E(x60701,x60702)+~E(f332(f332(f257(x60703),x60704),x60701),f332(f332(f257(x60703),x60704),x60702))+~P24(f332(f332(f247(x60703),f79(x60703)),x60704)) % 165.30/165.05 [6071]E(x60711,x60712)+~E(f332(f332(f310(x60713),x60714),x60711),f332(f332(f310(x60713),x60714),x60712))+P24(f332(f332(f334(x60713),x60714),x60712))+P24(f332(f332(f334(x60713),x60714),x60711)) % 165.30/165.05 [6109]E(f332(x61091,x61092),f79(a868))+~E(f332(f332(f9(x61093,a868),x61091),x61094),f79(a868))+~P24(f332(f62(x61093),x61094))+~P24(f332(f332(f334(x61093),x61092),x61094)) % 165.30/165.05 [6110]E(f332(x61101,x61102),f2(a868))+~E(f332(f332(f6(x61103,a868),x61101),x61104),f2(a868))+~P24(f332(f62(x61103),x61104))+~P24(f332(f332(f334(x61103),x61102),x61104)) % 165.30/165.05 [6332]~P107(x63321)+~P24(f332(f332(f246(x63321),x63324),x63323))+P24(f332(f332(f246(x63321),x63322),x63323))+~P24(f332(f332(f246(x63321),x63322),x63324)) % 165.30/165.05 [6333]~P104(x63331)+~P24(f332(f332(f246(x63331),x63332),x63334))+P24(f332(f332(f246(x63331),x63332),x63333))+~P24(f332(f332(f246(x63331),x63334),x63333)) % 165.30/165.05 [6334]~P107(x63341)+~P24(f332(f332(f247(x63341),x63344),x63343))+P24(f332(f332(f247(x63341),x63342),x63343))+~P24(f332(f332(f246(x63341),x63342),x63344)) % 165.30/165.05 [6335]~P107(x63351)+~P24(f332(f332(f247(x63351),x63352),x63354))+P24(f332(f332(f247(x63351),x63352),x63353))+~P24(f332(f332(f246(x63351),x63354),x63353)) % 165.30/165.05 [6336]~P107(x63361)+~P24(f332(f332(f247(x63361),x63364),x63363))+P24(f332(f332(f247(x63361),x63362),x63363))+~P24(f332(f332(f247(x63361),x63362),x63364)) % 165.30/165.05 [6337]~P104(x63371)+~P24(f332(f332(f247(x63371),x63372),x63374))+P24(f332(f332(f247(x63371),x63372),x63373))+~P24(f332(f332(f246(x63371),x63374),x63373)) % 165.30/165.05 [6338]~P104(x63381)+~P24(f332(f332(f247(x63381),x63384),x63383))+P24(f332(f332(f247(x63381),x63382),x63383))+~P24(f332(f332(f246(x63381),x63382),x63384)) % 165.30/165.05 [6339]~P104(x63391)+~P24(f332(f332(f247(x63391),x63392),x63394))+P24(f332(f332(f247(x63391),x63392),x63393))+~P24(f332(f332(f247(x63391),x63394),x63393)) % 165.30/165.05 [6422]~P39(x64224,x64223,x64222)+E(x64221,f794(x64222,x64223,x64224))+~P24(f332(x64223,x64221))+~P24(f332(f332(f334(x64224),x64221),f332(f174(x64224),x64222))) % 165.30/165.05 [6567]~P30(x65671)+~P24(f332(f332(f246(x65671),x65672),f41(x65671,x65674)))+P24(f332(f332(f246(x65671),x65672),x65673))+~P24(f332(f332(f334(x65671),x65673),x65674)) % 165.30/165.05 [6712]~P106(x67121)+~P32(x67121,f332(f332(f152(x67121),x67122),x67124))+~P24(f332(f332(f334(x67121),x67123),f332(f174(x67121),x67124)))+P24(f332(f332(f246(x67121),x67122),x67123)) % 165.30/165.05 [6802]~P30(x68021)+~P24(f332(f332(f246(x68021),f40(x68021,x68024)),x68023))+P24(f332(f332(f246(x68021),x68022),x68023))+~P24(f332(f332(f334(x68021),x68022),x68024)) % 165.30/165.05 [7205]~P106(x72051)+E(f332(f332(f113(f875(x72051,a862)),f332(f302(x72051,x72052),x72053)),f332(f302(x72051,x72053),x72054)),f332(f302(x72051,x72052),x72054))+~P24(f332(f332(f246(x72051),x72053),x72054))+~P24(f332(f332(f246(x72051),x72052),x72053)) % 165.30/165.05 [7242]P39(x72421,x72422,x72423)+~E(f797(x72423,x72422,x72421,x72424),x72424)+~P24(f332(x72422,x72424))+~P24(f332(f332(f334(x72421),x72424),f332(f174(x72421),x72423))) % 165.30/165.05 [7316]~P106(x73161)+E(f332(f332(f113(f875(x73161,a862)),f332(f302(x73161,x73162),x73163)),f303(x73161,x73163,x73164)),f303(x73161,x73162,x73164))+~P24(f332(f332(f246(x73161),x73163),x73164))+~P24(f332(f332(f246(x73161),x73162),x73163)) % 165.30/165.05 [7379]~P106(x73791)+E(f332(f332(f113(f875(x73791,a862)),f306(x73791,x73792,x73793)),f332(f302(x73791,x73793),x73794)),f306(x73791,x73792,x73794))+~P24(f332(f332(f246(x73791),x73793),x73794))+~P24(f332(f332(f247(x73791),x73792),x73793)) % 165.30/165.05 [7400]~P106(x74001)+E(f332(f332(f113(f875(x74001,a862)),f303(x74001,x74002,x74003)),f306(x74001,x74003,x74004)),f332(f302(x74001,x74002),x74004))+~P24(f332(f332(f246(x74001),x74002),x74003))+~P24(f332(f332(f247(x74001),x74003),x74004)) % 165.30/165.05 [7432]~P106(x74321)+E(f332(f332(f113(f875(x74321,a862)),f306(x74321,x74322,x74323)),f303(x74321,x74323,x74324)),f305(x74321,x74322,x74324))+~P24(f332(f332(f246(x74321),x74323),x74324))+~P24(f332(f332(f247(x74321),x74322),x74323)) % 165.30/165.05 [7433]~P106(x74331)+E(f332(f332(f113(f875(x74331,a862)),f305(x74331,x74332,x74333)),f306(x74331,x74333,x74334)),f306(x74331,x74332,x74334))+~P24(f332(f332(f246(x74331),x74332),x74333))+~P24(f332(f332(f247(x74331),x74333),x74334)) % 165.30/165.05 [7434]~P106(x74341)+E(f332(f332(f113(f875(x74341,a862)),f305(x74341,x74342,x74343)),f305(x74341,x74343,x74344)),f305(x74341,x74342,x74344))+~P24(f332(f332(f246(x74341),x74343),x74344))+~P24(f332(f332(f246(x74341),x74342),x74343)) % 165.30/165.05 [7435]~P106(x74351)+E(f332(f332(f113(f875(x74351,a862)),f303(x74351,x74352,x74353)),f305(x74351,x74353,x74354)),f303(x74351,x74352,x74354))+~P24(f332(f332(f246(x74351),x74353),x74354))+~P24(f332(f332(f246(x74351),x74352),x74353)) % 165.30/165.05 [8222]P21(x82221,x82222,f711(x82223,x82222,x82224,x82221),x82224)+~P24(f332(f62(x82222),x82223))+~P24(f332(f62(x82221),x82224))+~P24(f332(f332(f246(a868),f332(f38(x82221),x82224)),f332(f38(x82222),x82223))) % 165.30/165.05 [8243]P39(x82431,x82432,x82433)+~P24(f332(x82432,x82434))+P24(f332(x82432,f797(x82433,x82432,x82431,x82434)))+~P24(f332(f332(f334(x82431),x82434),f332(f174(x82431),x82433))) % 165.30/165.05 [8292]~P73(x82921)+~E(f332(x82923,f483(x82923,x82924,x82922,x82921)),f79(x82921))+E(f332(f332(f332(f66(x82921,x82922,f82(x82921)),x82923),f79(x82921)),x82924),f79(x82921))+~P24(f332(f62(x82922),x82924)) % 165.30/165.05 [8552]~P112(x85521)+~P24(f332(f332(f246(x85521),f2(x85521)),x85523))+P24(f332(f332(f246(x85521),x85522),x85523))+~P24(f332(f332(f246(x85521),f332(f332(f257(x85521),x85522),f332(a115,x85524))),f332(f332(f257(x85521),x85523),f332(a115,x85524)))) % 165.30/165.05 [8845]P39(x88451,x88452,x88453)+~P24(f332(x88452,x88454))+~P24(f332(f332(f334(x88451),x88454),f332(f174(x88451),x88453)))+P24(f332(f332(f334(x88451),f797(x88453,x88452,x88451,x88454)),f332(f174(x88451),x88453))) % 165.30/165.05 [8922]~P73(x89221)+E(f332(f332(f332(f66(x89221,x89222,f82(x89221)),x89223),f79(x89221)),x89224),f79(x89221))+~P24(f332(f62(x89222),x89224))+P24(f332(f332(f334(x89222),f483(x89223,x89224,x89222,x89221)),x89224)) % 165.30/165.05 [9391]~P24(f332(f332(f246(a1),x93914),f2(a1)))+P24(f332(f332(f246(a1),f332(f332(f81(a1),f332(f332(f82(a1),x93911),f45(a1,x93912,x93913))),x93914)),f2(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x93913))+~P24(f332(f332(f247(a1),x93911),x93914)) % 165.30/165.05 [9836]~P24(f332(f62(x98361),x98362))+~P24(f332(f332(f334(x98361),x98364),x98362))+~P24(f332(f332(f334(x98361),x98363),x98362))+P24(f332(f332(f247(a868),f332(f38(x98361),f332(f332(f22(f875(x98361,a862)),f332(f332(f22(f875(x98361,a862)),x98362),f332(f332(f310(x98361),x98363),f196(f875(x98361,a862))))),f332(f332(f310(x98361),x98364),f196(f875(x98361,a862)))))),f332(f38(x98361),x98362))) % 165.30/165.05 [6917]~P100(x69171)+~P24(f332(f332(f246(x69171),x69172),x69174))+~P24(f332(f332(f246(x69171),x69172),x69173))+P24(f332(f332(f246(x69171),x69172),f332(f332(f104(x69171),x69173),x69174))) % 165.30/165.05 [6920]~P106(x69201)+~P24(f332(f332(f246(x69201),x69202),x69204))+~P24(f332(f332(f246(x69201),x69202),x69203))+P24(f332(f332(f246(x69201),x69202),f332(f332(f244(x69201),x69203),x69204))) % 165.30/165.05 [6921]~P106(x69211)+~P24(f332(f332(f247(x69211),x69212),x69214))+~P24(f332(f332(f247(x69211),x69212),x69213))+P24(f332(f332(f247(x69211),x69212),f332(f332(f244(x69211),x69213),x69214))) % 165.30/165.05 [6940]~P61(x69402)+E(x69401,f2(x69402))+E(f332(f332(f290(x69402),f332(f332(f257(x69402),x69401),x69403)),f332(f332(f257(x69402),x69401),x69404)),f332(f332(f257(x69402),x69401),f332(f332(f22(a868),x69403),x69404)))+~P24(f332(f332(f246(a868),x69404),x69403)) % 165.30/165.05 [6985]~P106(x69851)+~P32(x69851,f332(f332(f152(x69851),x69853),x69854))+P32(x69851,f332(f332(f152(x69851),x69852),f332(f332(f152(x69851),x69853),x69854)))+~P24(f332(f332(f246(x69851),x69852),x69853)) % 165.30/165.05 [7024]~P87(x70241)+~P24(f332(f332(f246(x70241),f2(x70241)),x70244))+~P24(f332(f332(f246(x70241),x70242),x70243))+P24(f332(f332(f246(x70241),x70242),f332(f332(f81(x70241),x70243),x70244))) % 165.30/165.05 [7025]~P87(x70251)+~P24(f332(f332(f246(x70251),f2(x70251)),x70253))+~P24(f332(f332(f246(x70251),x70252),x70254))+P24(f332(f332(f246(x70251),x70252),f332(f332(f81(x70251),x70253),x70254))) % 165.30/165.05 [7026]~P112(x70261)+~P24(f332(f332(f247(x70261),f2(x70261)),x70263))+~P24(f332(f332(f247(x70261),x70262),x70264))+P24(f332(f332(f247(x70261),x70262),f332(f332(f81(x70261),x70263),x70264))) % 165.30/165.05 [7027]~P87(x70271)+~P24(f332(f332(f246(x70271),x70272),x70274))+~P24(f332(f332(f247(x70271),f2(x70271)),x70273))+P24(f332(f332(f247(x70271),x70272),f332(f332(f81(x70271),x70273),x70274))) % 165.30/165.05 [7028]~P87(x70281)+~P24(f332(f332(f246(x70281),f2(x70281)),x70283))+~P24(f332(f332(f247(x70281),x70282),x70284))+P24(f332(f332(f247(x70281),x70282),f332(f332(f81(x70281),x70283),x70284))) % 165.30/165.05 [7067]~P106(x70671)+P24(f332(f332(f246(x70671),x70672),x70673))+P24(f332(f332(f246(x70671),x70672),x70674))+~P24(f332(f332(f246(x70671),x70672),f332(f332(f245(x70671),x70674),x70673))) % 165.30/165.05 [7068]~P106(x70681)+P24(f332(f332(f247(x70681),x70682),x70683))+P24(f332(f332(f247(x70681),x70682),x70684))+~P24(f332(f332(f247(x70681),x70682),f332(f332(f245(x70681),x70684),x70683))) % 165.30/165.05 [7352]~P107(x73522)+~P59(x73521)+~P24(f332(f332(f247(f875(x73521,x73522)),x73523),x73524))+P24(f332(f332(f246(f875(x73521,x73522)),x73523),x73524)) % 165.30/165.05 [7722]~P63(x77221)+~P24(f332(f332(f247(x77221),x77224),f2(x77221)))+~P24(f332(f332(f246(x77221),x77223),f332(f332(f290(x77221),x77222),x77224)))+P24(f332(f332(f246(x77221),x77222),f332(f332(f82(x77221),x77223),x77224))) % 165.30/165.05 [7723]~P63(x77231)+~P24(f332(f332(f247(x77231),x77234),f2(x77231)))+~P24(f332(f332(f246(x77231),x77233),f332(f332(f82(x77231),x77232),x77234)))+P24(f332(f332(f246(x77231),x77232),f332(f332(f290(x77231),x77233),x77234))) % 165.30/165.05 [7724]~P63(x77241)+~P24(f332(f332(f247(x77241),x77244),f2(x77241)))+~P24(f332(f332(f247(x77241),x77243),f332(f332(f290(x77241),x77242),x77244)))+P24(f332(f332(f247(x77241),x77242),f332(f332(f82(x77241),x77243),x77244))) % 165.30/165.05 [7725]~P63(x77251)+~P24(f332(f332(f247(x77251),x77254),f2(x77251)))+~P24(f332(f332(f247(x77251),x77253),f332(f332(f82(x77251),x77252),x77254)))+P24(f332(f332(f247(x77251),x77252),f332(f332(f290(x77251),x77253),x77254))) % 165.30/165.05 [7830]~P126(x78301)+~P24(f332(f332(f246(x78301),x78302),f2(x78301)))+~P24(f332(f332(f246(x78301),x78304),x78303))+P24(f332(f332(f246(x78301),f332(f332(f82(x78301),x78302),x78303)),f332(f332(f82(x78301),x78302),x78304))) % 165.30/165.05 [7831]~P122(x78311)+~P24(f332(f332(f247(x78311),x78312),f2(x78311)))+~P24(f332(f332(f246(x78311),x78314),x78313))+P24(f332(f332(f246(x78311),f332(f332(f82(x78311),x78312),x78313)),f332(f332(f82(x78311),x78312),x78314))) % 165.30/165.05 [7832]~P126(x78321)+~P24(f332(f332(f246(x78321),x78323),f2(x78321)))+~P24(f332(f332(f246(x78321),x78324),x78322))+P24(f332(f332(f246(x78321),f332(f332(f82(x78321),x78322),x78323)),f332(f332(f82(x78321),x78324),x78323))) % 165.30/165.05 [7833]~P62(x78331)+~P24(f332(f332(f246(x78331),x78333),f2(x78331)))+~P24(f332(f332(f246(x78331),x78334),x78332))+P24(f332(f332(f246(x78331),f332(f332(f290(x78331),x78332),x78333)),f332(f332(f290(x78331),x78334),x78333))) % 165.30/165.05 [7837]~P122(x78371)+~P24(f332(f332(f247(x78371),x78373),f2(x78371)))+~P24(f332(f332(f247(x78371),x78374),x78372))+P24(f332(f332(f247(x78371),f332(f332(f82(x78371),x78372),x78373)),f332(f332(f82(x78371),x78374),x78373))) % 165.30/165.05 [7838]~P122(x78381)+~P24(f332(f332(f247(x78381),x78382),f2(x78381)))+~P24(f332(f332(f247(x78381),x78384),x78383))+P24(f332(f332(f247(x78381),f332(f332(f82(x78381),x78382),x78383)),f332(f332(f82(x78381),x78382),x78384))) % 165.30/165.05 [7839]~P63(x78391)+~P24(f332(f332(f247(x78391),x78393),f2(x78391)))+~P24(f332(f332(f247(x78391),x78394),x78392))+P24(f332(f332(f247(x78391),f332(f332(f290(x78391),x78392),x78393)),f332(f332(f290(x78391),x78394),x78393))) % 165.30/165.05 [7840]~P112(x78401)+~P24(f332(f332(f247(x78401),f79(x78401)),x78402))+~P24(f332(f332(f246(a868),x78403),x78404))+P24(f332(f332(f246(x78401),f332(f332(f257(x78401),x78402),x78403)),f332(f332(f257(x78401),x78402),x78404))) % 165.30/165.05 [7841]~P112(x78411)+~P24(f332(f332(f246(x78411),f79(x78411)),x78412))+~P24(f332(f332(f246(a868),x78413),x78414))+P24(f332(f332(f246(x78411),f332(f332(f257(x78411),x78412),x78413)),f332(f332(f257(x78411),x78412),x78414))) % 165.30/165.05 [7843]~P112(x78431)+~P24(f332(f332(f247(x78431),f79(x78431)),x78432))+~P24(f332(f332(f247(a868),x78433),x78434))+P24(f332(f332(f247(x78431),f332(f332(f257(x78431),x78432),x78433)),f332(f332(f257(x78431),x78432),x78434))) % 165.30/165.05 [7870]P24(f332(f332(f247(a868),f2(a868)),f332(x78701,x78702)))+~P24(f332(f62(x78703),x78704))+~P24(f332(f332(f334(x78703),x78702),x78704))+~P24(f332(f332(f247(a868),f2(a868)),f332(f332(f9(x78703,a868),x78701),x78704))) % 165.30/165.05 [7878]~P122(x78781)+~P24(f332(f332(f247(x78781),f2(x78781)),x78782))+~P24(f332(f332(f246(x78781),x78783),x78784))+P24(f332(f332(f246(x78781),f332(f332(f82(x78781),x78782),x78783)),f332(f332(f82(x78781),x78782),x78784))) % 165.30/165.05 [7879]~P135(x78791)+~P24(f332(f332(f246(x78791),x78793),x78794))+~P24(f332(f332(f246(x78791),f2(x78791)),x78792))+P24(f332(f332(f246(x78791),f332(f332(f82(x78791),x78792),x78793)),f332(f332(f82(x78791),x78792),x78794))) % 165.30/165.05 [7880]~P134(x78801)+~P24(f332(f332(f246(x78801),x78803),x78804))+~P24(f332(f332(f246(x78801),f2(x78801)),x78802))+P24(f332(f332(f246(x78801),f332(f332(f82(x78801),x78802),x78803)),f332(f332(f82(x78801),x78802),x78804))) % 165.30/165.05 [7881]~P135(x78811)+~P24(f332(f332(f246(x78811),x78812),x78814))+~P24(f332(f332(f246(x78811),f2(x78811)),x78813))+P24(f332(f332(f246(x78811),f332(f332(f82(x78811),x78812),x78813)),f332(f332(f82(x78811),x78814),x78813))) % 165.30/165.05 [7882]~P112(x78821)+~P24(f332(f332(f246(x78821),x78822),x78824))+~P24(f332(f332(f246(x78821),f2(x78821)),x78822))+P24(f332(f332(f246(x78821),f332(f332(f257(x78821),x78822),x78823)),f332(f332(f257(x78821),x78824),x78823))) % 165.30/165.05 [7883]~P62(x78831)+~P24(f332(f332(f246(x78831),x78832),x78834))+~P24(f332(f332(f246(x78831),f2(x78831)),x78833))+P24(f332(f332(f246(x78831),f332(f332(f290(x78831),x78832),x78833)),f332(f332(f290(x78831),x78834),x78833))) % 165.30/165.05 [7885]~P129(x78851)+~P24(f332(f332(f247(x78851),x78853),x78854))+~P24(f332(f332(f247(x78851),f2(x78851)),x78852))+P24(f332(f332(f247(x78851),f332(f332(f82(x78851),x78852),x78853)),f332(f332(f82(x78851),x78852),x78854))) % 165.30/165.05 [7886]~P119(x78861)+~P24(f332(f332(f247(x78861),x78863),x78864))+~P24(f332(f332(f247(x78861),f2(x78861)),x78862))+P24(f332(f332(f247(x78861),f332(f332(f82(x78861),x78862),x78863)),f332(f332(f82(x78861),x78862),x78864))) % 165.30/165.05 [7887]~P122(x78871)+~P24(f332(f332(f247(x78871),x78872),x78874))+~P24(f332(f332(f247(x78871),f2(x78871)),x78873))+P24(f332(f332(f247(x78871),f332(f332(f82(x78871),x78872),x78873)),f332(f332(f82(x78871),x78874),x78873))) % 165.30/165.05 [7888]~P129(x78881)+~P24(f332(f332(f247(x78881),x78882),x78884))+~P24(f332(f332(f247(x78881),f2(x78881)),x78883))+P24(f332(f332(f247(x78881),f332(f332(f82(x78881),x78882),x78883)),f332(f332(f82(x78881),x78884),x78883))) % 165.30/165.05 [7889]~P122(x78891)+~P24(f332(f332(f247(x78891),x78893),x78894))+~P24(f332(f332(f247(x78891),f2(x78891)),x78892))+P24(f332(f332(f247(x78891),f332(f332(f82(x78891),x78892),x78893)),f332(f332(f82(x78891),x78892),x78894))) % 165.30/165.05 [7890]~P63(x78901)+~P24(f332(f332(f247(x78901),x78902),x78904))+~P24(f332(f332(f247(x78901),f2(x78901)),x78903))+P24(f332(f332(f247(x78901),f332(f332(f290(x78901),x78902),x78903)),f332(f332(f290(x78901),x78904),x78903))) % 165.30/165.05 [7933]~P105(x79332)+P24(f332(f332(f247(f875(x79331,x79332)),x79334),x79333))+~P24(f332(f332(f246(f875(x79331,x79332)),x79334),x79333))+P24(f332(f332(f246(f875(x79331,x79332)),x79333),x79334)) % 165.30/165.05 [7973]P24(f332(f332(f334(x79731),x79732),x79733))+P24(f332(f332(f334(x79731),x79732),x79734))+~P24(f332(f332(f246(f875(x79731,a862)),x79734),x79733))+P24(f332(f332(f247(f875(x79731,a862)),x79734),f332(f332(f310(x79731),x79732),x79733))) % 165.30/165.05 [8128]P24(f332(f332(f334(x81281),x81282),x81283))+P24(f332(f332(f334(x81281),x81282),x81284))+~P24(f332(f332(f247(f875(x81281,a862)),x81284),f332(f332(f310(x81281),x81282),x81283)))+P24(f332(f332(f246(f875(x81281,a862)),x81284),x81283)) % 165.30/165.05 [8136]~P59(x81361)+P7(x81361,x81362,x81363)+~P24(f332(x81362,x81364))+~P24(f332(f332(f334(f869(x81361)),x81364),f332(f174(f869(x81361)),f55(x81361,x81363,f56(x81361))))) % 165.30/165.05 [8146]~P8(x81463,x81461,x81464)+~P59(x81463)+P24(f332(x81461,x81462))+~P24(f332(f332(f334(f869(x81463)),x81462),f332(f174(f869(x81463)),f55(x81463,x81464,f56(x81463))))) % 165.30/165.05 [8199]~P122(x81991)+P24(f332(f332(f247(x81991),x81993),x81992))+P24(f332(f332(f247(x81991),x81992),x81993))+~P24(f332(f332(f247(x81991),f332(f332(f82(x81991),x81994),x81992)),f332(f332(f82(x81991),x81994),x81993))) % 165.30/165.05 [8200]~P122(x82001)+P24(f332(f332(f247(x82001),x82003),x82002))+P24(f332(f332(f247(x82001),x82002),x82003))+~P24(f332(f332(f247(x82001),f332(f332(f82(x82001),x82002),x82004)),f332(f332(f82(x82001),x82003),x82004))) % 165.30/165.05 [8211]~P122(x82111)+P24(f332(f332(f247(x82111),x82114),f2(x82111)))+P24(f332(f332(f247(x82111),x82112),x82113))+~P24(f332(f332(f247(x82111),f332(f332(f82(x82111),x82112),x82114)),f332(f332(f82(x82111),x82113),x82114))) % 165.30/165.05 [8212]~P122(x82121)+P24(f332(f332(f247(x82121),x82124),f2(x82121)))+P24(f332(f332(f247(x82121),x82122),x82123))+~P24(f332(f332(f247(x82121),f332(f332(f82(x82121),x82124),x82122)),f332(f332(f82(x82121),x82124),x82123))) % 165.30/165.05 [8216]~P122(x82161)+P24(f332(f332(f247(x82161),x82162),x82163))+P24(f332(f332(f247(x82161),f2(x82161)),x82164))+~P24(f332(f332(f247(x82161),f332(f332(f82(x82161),x82164),x82163)),f332(f332(f82(x82161),x82164),x82162))) % 165.30/165.05 [8217]~P122(x82171)+P24(f332(f332(f247(x82171),x82172),x82173))+P24(f332(f332(f247(x82171),f2(x82171)),x82174))+~P24(f332(f332(f247(x82171),f332(f332(f82(x82171),x82173),x82174)),f332(f332(f82(x82171),x82172),x82174))) % 165.30/165.05 [8230]~P122(x82301)+P24(f332(f332(f247(x82301),x82302),f2(x82301)))+P24(f332(f332(f247(x82301),f2(x82301)),x82302))+~P24(f332(f332(f247(x82301),f332(f332(f82(x82301),x82303),x82302)),f332(f332(f82(x82301),x82304),x82302))) % 165.30/165.05 [8231]~P122(x82311)+P24(f332(f332(f247(x82311),x82312),f2(x82311)))+P24(f332(f332(f247(x82311),f2(x82311)),x82312))+~P24(f332(f332(f247(x82311),f332(f332(f82(x82311),x82312),x82313)),f332(f332(f82(x82311),x82312),x82314))) % 165.30/165.05 [8257]~P122(x82571)+~P24(f332(f332(f247(x82571),x82574),f2(x82571)))+P24(f332(f332(f246(x82571),x82572),x82573))+~P24(f332(f332(f246(x82571),f332(f332(f82(x82571),x82574),x82573)),f332(f332(f82(x82571),x82574),x82572))) % 165.30/165.05 [8258]~P122(x82581)+~P24(f332(f332(f247(x82581),x82584),f2(x82581)))+P24(f332(f332(f247(x82581),x82582),x82583))+~P24(f332(f332(f247(x82581),f332(f332(f82(x82581),x82584),x82583)),f332(f332(f82(x82581),x82584),x82582))) % 165.30/165.05 [8268]~P112(x82683)+~P24(f332(f332(f247(x82683),f79(x82683)),x82684))+P24(f332(f332(f246(a868),x82681),x82682))+~P24(f332(f332(f246(x82683),f332(f332(f257(x82683),x82684),x82681)),f332(f332(f257(x82683),x82684),x82682))) % 165.30/165.05 [8270]~P112(x82703)+~P24(f332(f332(f247(x82703),f79(x82703)),x82704))+P24(f332(f332(f247(a868),x82701),x82702))+~P24(f332(f332(f247(x82703),f332(f332(f257(x82703),x82704),x82701)),f332(f332(f257(x82703),x82704),x82702))) % 165.30/165.05 [8280]~P122(x82801)+P24(f332(f332(f246(x82801),x82802),x82803))+~P24(f332(f332(f247(x82801),f2(x82801)),x82804))+~P24(f332(f332(f246(x82801),f332(f332(f82(x82801),x82804),x82802)),f332(f332(f82(x82801),x82804),x82803))) % 165.30/165.05 [8281]~P129(x82811)+P24(f332(f332(f246(x82811),x82812),x82813))+~P24(f332(f332(f247(x82811),f2(x82811)),x82814))+~P24(f332(f332(f246(x82811),f332(f332(f82(x82811),x82814),x82812)),f332(f332(f82(x82811),x82814),x82813))) % 165.30/165.05 [8282]~P129(x82821)+P24(f332(f332(f246(x82821),x82822),x82823))+~P24(f332(f332(f247(x82821),f2(x82821)),x82824))+~P24(f332(f332(f246(x82821),f332(f332(f82(x82821),x82822),x82824)),f332(f332(f82(x82821),x82823),x82824))) % 165.30/165.05 [8283]~P122(x82831)+P24(f332(f332(f247(x82831),x82832),x82833))+~P24(f332(f332(f247(x82831),f2(x82831)),x82834))+~P24(f332(f332(f247(x82831),f332(f332(f82(x82831),x82834),x82832)),f332(f332(f82(x82831),x82834),x82833))) % 165.30/165.05 [8284]~P129(x82841)+P24(f332(f332(f247(x82841),x82842),x82843))+~P24(f332(f332(f246(x82841),f2(x82841)),x82844))+~P24(f332(f332(f247(x82841),f332(f332(f82(x82841),x82844),x82842)),f332(f332(f82(x82841),x82844),x82843))) % 165.30/165.05 [8285]~P130(x82851)+P24(f332(f332(f247(x82851),x82852),x82853))+~P24(f332(f332(f246(x82851),f2(x82851)),x82854))+~P24(f332(f332(f247(x82851),f332(f332(f82(x82851),x82854),x82852)),f332(f332(f82(x82851),x82854),x82853))) % 165.30/165.05 [8286]~P112(x82861)+~P24(f332(f332(f246(x82861),f2(x82861)),x82863))+P24(f332(f332(f247(x82861),x82862),x82863))+~P24(f332(f332(f247(x82861),f332(f332(f257(x82861),x82862),x82864)),f332(f332(f257(x82861),x82863),x82864))) % 165.30/165.05 [8287]~P129(x82871)+P24(f332(f332(f247(x82871),x82872),x82873))+~P24(f332(f332(f246(x82871),f2(x82871)),x82874))+~P24(f332(f332(f247(x82871),f332(f332(f82(x82871),x82872),x82874)),f332(f332(f82(x82871),x82873),x82874))) % 165.30/165.05 [8288]~P130(x82881)+P24(f332(f332(f247(x82881),x82882),x82883))+~P24(f332(f332(f246(x82881),f2(x82881)),x82884))+~P24(f332(f332(f247(x82881),f332(f332(f82(x82881),x82882),x82884)),f332(f332(f82(x82881),x82883),x82884))) % 165.30/165.05 [8331]P24(f332(f332(f334(x83311),x83312),x83313))+~P24(f332(f332(f246(f875(x83311,a862)),x83313),x83314))+~P24(f332(f332(f247(f875(x83311,a862)),x83313),x83314))+P24(f332(f332(f247(f875(x83311,a862)),x83313),f332(f332(f310(x83311),x83312),x83314))) % 165.30/165.05 [8575]~P59(x85751)+~P94(x85752)+~E(f332(x85753,f800(x85754,x85753,x85751,x85752)),f332(x85754,f800(x85754,x85753,x85751,x85752)))+P24(f332(f332(f92(f875(x85751,x85752)),x85753),x85754)) % 165.30/165.05 [8689]E(f332(f332(f22(a1),f399(x86891,x86892,x86893,x86894)),f390(x86891,x86892,x86893,x86894)),x86894)+~P24(f332(f332(f247(a1),f2(a1)),x86893))+~P24(f332(f332(f246(a1),x86891),x86894))+P24(f332(f332(f246(a1),x86891),f332(f332(f81(a1),x86894),x86893))) % 165.30/165.05 [8690]E(f332(f332(f22(a1),f409(x86901,x86902,x86903,x86904)),f405(x86901,x86902,x86903,x86904)),x86904)+~P24(f332(f332(f247(a1),f2(a1)),x86903))+~P24(f332(f332(f247(a1),x86901),x86904))+P24(f332(f332(f247(a1),x86901),f332(f332(f81(a1),x86904),x86903))) % 165.30/165.05 [8825]~E(f332(f332(f166(x88251),x88253),f559(x88254,x88253,x88251,x88252)),f332(f332(f166(x88251),x88254),f559(x88254,x88253,x88251,x88252)))+E(f332(f332(f177(x88251),x88252),x88253),f332(f332(f177(x88251),x88252),x88254))+~P24(f332(f332(f246(a868),x88252),f332(f197(f869(x88251)),x88253)))+~P24(f332(f332(f246(a868),x88252),f332(f197(f869(x88251)),x88254))) % 165.30/165.05 [8894]~P24(f332(f332(f247(a1),f2(a1)),x88943))+~P24(f332(f332(f246(a1),x88941),x88944))+P24(f332(f332(f334(a1),f399(x88941,x88942,x88943,x88944)),x88942))+P24(f332(f332(f246(a1),x88941),f332(f332(f81(a1),x88944),x88943))) % 165.30/165.05 [8895]~P24(f332(f332(f247(a1),f2(a1)),x88953))+~P24(f332(f332(f247(a1),x88951),x88954))+P24(f332(f332(f334(a1),f409(x88951,x88952,x88953,x88954)),x88952))+P24(f332(f332(f247(a1),x88951),f332(f332(f81(a1),x88954),x88953))) % 165.30/165.05 [8931]~P100(x89311)+~P24(f332(f62(x89311),x89313))+~P24(f332(f332(f334(x89311),x89314),x89313))+P24(f332(f332(f246(x89311),f332(f332(f65(x89311,x89311,f104(x89311)),x89312),x89313)),f332(f332(f104(x89311),x89314),x89312))) % 165.30/165.05 [8932]~P106(x89321)+~P24(f332(f62(x89321),x89323))+~P24(f332(f332(f334(x89321),x89324),x89323))+P24(f332(f332(f246(x89321),f332(f332(f65(x89321,x89321,f244(x89321)),x89322),x89323)),f332(f332(f244(x89321),x89324),x89322))) % 165.30/165.05 [8978]E(f332(f332(f177(x89781),x89782),x89783),f332(f332(f177(x89781),x89782),x89784))+P24(f332(f332(f247(a868),f559(x89783,x89784,x89781,x89782)),x89782))+~P24(f332(f332(f246(a868),x89782),f332(f197(f869(x89781)),x89783)))+~P24(f332(f332(f246(a868),x89782),f332(f197(f869(x89781)),x89784))) % 165.30/165.05 [8983]~P24(f332(f332(f247(a1),f2(a1)),x89833))+~P24(f332(f332(f246(a1),x89831),x89832))+P24(f332(f332(f334(a1),f390(x89831,x89834,x89833,x89832)),f303(a1,f79(a1),x89833)))+P24(f332(f332(f246(a1),x89831),f332(f332(f81(a1),x89832),x89833))) % 165.30/165.05 [8984]~P24(f332(f332(f247(a1),f2(a1)),x89843))+~P24(f332(f332(f247(a1),x89841),x89842))+P24(f332(f332(f334(a1),f405(x89841,x89844,x89843,x89842)),f303(a1,f79(a1),x89843)))+P24(f332(f332(f247(a1),x89841),f332(f332(f81(a1),x89842),x89843))) % 165.30/165.05 [9144]~E(f332(f180(x91441,x91442),x91443),f332(f180(x91441,x91442),x91444))+E(f332(f174(f874(x91441,x91442)),x91443),f332(f174(f874(x91441,x91442)),x91444))+~P24(f332(f138(x91441),f332(f332(f155(f874(x91441,x91442),x91441),f266(x91441,x91442)),x91444)))+~P24(f332(f138(x91441),f332(f332(f155(f874(x91441,x91442),x91441),f266(x91441,x91442)),x91443))) % 165.30/165.05 [9156]E(f332(f180(x91561,x91562),x91563),f332(f180(x91561,x91562),x91564))+~E(f332(f174(f874(x91561,x91562)),x91563),f332(f174(f874(x91561,x91562)),x91564))+~P24(f332(f138(x91561),f332(f332(f155(f874(x91561,x91562),x91561),f266(x91561,x91562)),x91564)))+~P24(f332(f138(x91561),f332(f332(f155(f874(x91561,x91562),x91561),f266(x91561,x91562)),x91563))) % 165.30/165.05 [9289]~P106(x92891)+~P24(f332(f62(x92891),x92894))+P24(f332(f332(f334(x92891),f767(x92892,x92893,x92894,x92891)),x92894))+P24(f332(f332(f246(x92891),f332(f332(f65(x92891,x92891,f245(x92891)),x92892),x92894)),f332(f332(f245(x92891),x92893),x92892))) % 165.30/165.05 [9290]~P99(x92901)+~P24(f332(f62(x92901),x92904))+P24(f332(f332(f334(x92901),f770(x92902,x92903,x92904,x92901)),x92904))+P24(f332(f332(f246(x92901),f332(f332(f65(x92901,x92901,f113(x92901)),x92902),x92904)),f332(f332(f113(x92901),x92903),x92902))) % 165.30/165.05 [9409]~P99(x94091)+~P24(f332(f62(x94091),x94093))+~P24(f332(f332(f246(x94091),f770(x94092,x94094,x94093,x94091)),x94094))+P24(f332(f332(f246(x94091),f332(f332(f65(x94091,x94091,f113(x94091)),x94092),x94093)),f332(f332(f113(x94091),x94094),x94092))) % 165.30/165.05 [9410]~P106(x94101)+~P24(f332(f62(x94101),x94103))+~P24(f332(f332(f246(x94101),f767(x94102,x94104,x94103,x94101)),x94104))+P24(f332(f332(f246(x94101),f332(f332(f65(x94101,x94101,f245(x94101)),x94102),x94103)),f332(f332(f245(x94101),x94104),x94102))) % 165.30/165.05 [9413]~P24(f332(f332(f246(a1),f2(a1)),x94134))+~P24(f332(f332(f247(a1),f2(a1)),x94133))+~P24(f332(f332(f247(a1),x94134),x94131))+P24(f332(f332(f247(a1),f332(f332(f81(a1),f332(f332(f82(a1),x94131),f45(a1,x94132,x94133))),x94134)),f332(f332(f82(a1),x94131),x94133))) % 165.30/165.05 [9804]E(x98041,x98042)+P24(f332(f332(f334(f874(f869(x98043),f869(x98043))),f332(f332(f267(f869(x98043),f869(x98043)),x98042),x98041)),f148(x98043,x98044)))+P24(f332(f332(f334(f874(f869(x98043),f869(x98043))),f332(f332(f267(f869(x98043),f869(x98043)),x98041),x98042)),f148(x98043,x98044)))+~P24(f332(f332(f334(f874(x98043,x98043)),f332(f332(f267(x98043,x98043),f553(x98041,x98042,x98044,x98043)),f554(x98041,x98042,x98044,x98043))),x98044)) % 165.30/165.05 [9805]E(x98051,x98052)+P24(f332(f332(f334(f874(f869(x98053),f869(x98053))),f332(f332(f267(f869(x98053),f869(x98053)),x98052),x98051)),f148(x98053,x98054)))+P24(f332(f332(f334(f874(f869(x98053),f869(x98053))),f332(f332(f267(f869(x98053),f869(x98053)),x98051),x98052)),f148(x98053,x98054)))+~P24(f332(f332(f334(f874(x98053,x98053)),f332(f332(f267(x98053,x98053),f554(x98051,x98052,x98054,x98053)),f553(x98051,x98052,x98054,x98053))),x98054)) % 165.30/165.05 [7422]~P99(x74221)+~P24(f332(f332(f246(x74221),x74223),x74224))+~P24(f332(f332(f246(x74221),x74222),x74224))+P24(f332(f332(f246(x74221),f332(f332(f113(x74221),x74222),x74223)),x74224)) % 165.30/165.05 [7425]~P106(x74251)+~P24(f332(f332(f246(x74251),x74253),x74254))+~P24(f332(f332(f246(x74251),x74252),x74254))+P24(f332(f332(f246(x74251),f332(f332(f245(x74251),x74252),x74253)),x74254)) % 165.30/165.05 [7426]~P106(x74261)+~P24(f332(f332(f247(x74261),x74263),x74264))+~P24(f332(f332(f247(x74261),x74262),x74264))+P24(f332(f332(f247(x74261),f332(f332(f245(x74261),x74262),x74263)),x74264)) % 165.30/165.05 [7747]~E(x77471,x77473)+E(f140(a868,f332(f302(a868,x77471),x77472)),f332(f332(f152(a868),x77473),x77474))+~E(f140(a868,f332(f302(a868,f332(f332(f81(a868),x77471),f79(a868))),x77472)),x77474)+~P24(f332(f332(f247(a868),x77471),x77472)) % 165.30/165.05 [7756]~P106(x77561)+P24(f332(f332(f246(x77561),x77562),x77563))+P24(f332(f332(f246(x77561),x77564),x77563))+~P24(f332(f332(f246(x77561),f332(f332(f244(x77561),x77564),x77562)),x77563)) % 165.30/165.05 [7757]~P106(x77571)+P24(f332(f332(f247(x77571),x77572),x77573))+P24(f332(f332(f247(x77571),x77574),x77573))+~P24(f332(f332(f247(x77571),f332(f332(f244(x77571),x77574),x77572)),x77573)) % 165.30/165.05 [8029]~P62(x80291)+~P24(f332(f332(f247(x80291),f2(x80291)),x80293))+~P24(f332(f332(f246(x80291),x80292),f332(f332(f290(x80291),x80294),x80293)))+P24(f332(f332(f246(x80291),f332(f332(f82(x80291),x80292),x80293)),x80294)) % 165.30/165.05 [8030]~P63(x80301)+~P24(f332(f332(f247(x80301),f2(x80301)),x80303))+~P24(f332(f332(f246(x80301),x80302),f332(f332(f290(x80301),x80304),x80303)))+P24(f332(f332(f246(x80301),f332(f332(f82(x80301),x80302),x80303)),x80304)) % 165.30/165.05 [8031]~P62(x80311)+~P24(f332(f332(f247(x80311),f2(x80311)),x80313))+~P24(f332(f332(f246(x80311),x80312),f332(f332(f82(x80311),x80314),x80313)))+P24(f332(f332(f246(x80311),f332(f332(f290(x80311),x80312),x80313)),x80314)) % 165.30/165.05 [8033]~P63(x80331)+~P24(f332(f332(f247(x80331),f2(x80331)),x80333))+~P24(f332(f332(f246(x80331),x80332),f332(f332(f82(x80331),x80334),x80333)))+P24(f332(f332(f246(x80331),f332(f332(f290(x80331),x80332),x80333)),x80334)) % 165.30/165.05 [8034]~P62(x80341)+~P24(f332(f332(f247(x80341),f2(x80341)),x80343))+~P24(f332(f332(f247(x80341),x80342),f332(f332(f290(x80341),x80344),x80343)))+P24(f332(f332(f247(x80341),f332(f332(f82(x80341),x80342),x80343)),x80344)) % 165.30/165.05 [8035]~P63(x80351)+~P24(f332(f332(f247(x80351),f2(x80351)),x80353))+~P24(f332(f332(f247(x80351),x80352),f332(f332(f290(x80351),x80354),x80353)))+P24(f332(f332(f247(x80351),f332(f332(f82(x80351),x80352),x80353)),x80354)) % 165.30/165.05 [8036]~P62(x80361)+~P24(f332(f332(f247(x80361),f2(x80361)),x80363))+~P24(f332(f332(f247(x80361),x80362),f332(f332(f82(x80361),x80364),x80363)))+P24(f332(f332(f247(x80361),f332(f332(f290(x80361),x80362),x80363)),x80364)) % 165.30/165.05 [8038]~P63(x80381)+~P24(f332(f332(f247(x80381),f2(x80381)),x80383))+~P24(f332(f332(f247(x80381),x80382),f332(f332(f82(x80381),x80384),x80383)))+P24(f332(f332(f247(x80381),f332(f332(f290(x80381),x80382),x80383)),x80384)) % 165.30/165.05 [8168]~P62(x81681)+~P24(f332(f332(f247(x81681),f2(x81681)),x81684))+P24(f332(f332(f246(x81681),x81682),f332(f332(f82(x81681),x81683),x81684)))+~P24(f332(f332(f246(x81681),f332(f332(f290(x81681),x81682),x81684)),x81683)) % 165.30/165.05 [8169]~P62(x81691)+~P24(f332(f332(f247(x81691),f2(x81691)),x81694))+P24(f332(f332(f246(x81691),x81692),f332(f332(f290(x81691),x81693),x81694)))+~P24(f332(f332(f246(x81691),f332(f332(f82(x81691),x81692),x81694)),x81693)) % 165.30/165.05 [8171]~P63(x81711)+~P24(f332(f332(f247(x81711),f2(x81711)),x81714))+P24(f332(f332(f246(x81711),x81712),f332(f332(f82(x81711),x81713),x81714)))+~P24(f332(f332(f246(x81711),f332(f332(f290(x81711),x81712),x81714)),x81713)) % 165.30/165.05 [8172]~P63(x81721)+~P24(f332(f332(f247(x81721),f2(x81721)),x81724))+P24(f332(f332(f246(x81721),x81722),f332(f332(f290(x81721),x81723),x81724)))+~P24(f332(f332(f246(x81721),f332(f332(f82(x81721),x81722),x81724)),x81723)) % 165.30/165.05 [8173]~P62(x81731)+~P24(f332(f332(f247(x81731),f2(x81731)),x81734))+P24(f332(f332(f247(x81731),x81732),f332(f332(f82(x81731),x81733),x81734)))+~P24(f332(f332(f247(x81731),f332(f332(f290(x81731),x81732),x81734)),x81733)) % 165.30/165.05 [8174]~P62(x81741)+~P24(f332(f332(f247(x81741),f2(x81741)),x81744))+P24(f332(f332(f247(x81741),x81742),f332(f332(f290(x81741),x81743),x81744)))+~P24(f332(f332(f247(x81741),f332(f332(f82(x81741),x81742),x81744)),x81743)) % 165.30/165.05 [8176]~P63(x81761)+~P24(f332(f332(f247(x81761),f2(x81761)),x81764))+P24(f332(f332(f247(x81761),x81762),f332(f332(f82(x81761),x81763),x81764)))+~P24(f332(f332(f247(x81761),f332(f332(f290(x81761),x81762),x81764)),x81763)) % 165.30/165.05 [8177]~P63(x81771)+~P24(f332(f332(f247(x81771),f2(x81771)),x81774))+P24(f332(f332(f247(x81771),x81772),f332(f332(f290(x81771),x81773),x81774)))+~P24(f332(f332(f247(x81771),f332(f332(f82(x81771),x81772),x81774)),x81773)) % 165.30/165.05 [8335]~P63(x83351)+~P24(f332(f332(f247(x83351),x83353),f2(x83351)))+~P24(f332(f332(f246(x83351),f332(f332(f290(x83351),x83354),x83353)),x83352))+P24(f332(f332(f246(x83351),f332(f332(f82(x83351),x83352),x83353)),x83354)) % 165.30/165.05 [8336]~P63(x83361)+~P24(f332(f332(f247(x83361),x83363),f2(x83361)))+~P24(f332(f332(f246(x83361),f332(f332(f82(x83361),x83364),x83363)),x83362))+P24(f332(f332(f246(x83361),f332(f332(f290(x83361),x83362),x83363)),x83364)) % 165.30/165.05 [8337]~P63(x83371)+~P24(f332(f332(f247(x83371),x83373),f2(x83371)))+~P24(f332(f332(f247(x83371),f332(f332(f290(x83371),x83374),x83373)),x83372))+P24(f332(f332(f247(x83371),f332(f332(f82(x83371),x83372),x83373)),x83374)) % 165.30/165.05 [8338]~P63(x83381)+~P24(f332(f332(f247(x83381),x83383),f2(x83381)))+~P24(f332(f332(f247(x83381),f332(f332(f82(x83381),x83384),x83383)),x83382))+P24(f332(f332(f247(x83381),f332(f332(f290(x83381),x83382),x83383)),x83384)) % 165.30/165.05 [8348]~P24(f332(x83481,x83484))+~P24(f332(f332(f247(a868),x83482),f332(f332(f82(a868),x83483),f332(a115,x83484))))+P24(f332(x83481,f332(f332(f39(a868),x83482),x83483)))+~P24(f332(f332(f246(a868),f332(f332(f82(a868),x83483),x83484)),x83482)) % 165.30/165.05 [8549]~P99(x85491)+~P24(f332(f62(x85491),x85494))+~P24(f332(f332(f334(x85491),x85492),x85494))+P24(f332(f332(f246(x85491),f332(f332(f113(x85491),x85492),x85493)),f332(f332(f65(x85491,x85491,f113(x85491)),x85493),x85494))) % 165.30/165.05 [8550]~P106(x85501)+~P24(f332(f62(x85501),x85504))+~P24(f332(f332(f334(x85501),x85502),x85504))+P24(f332(f332(f246(x85501),f332(f332(f245(x85501),x85502),x85503)),f332(f332(f65(x85501,x85501,f245(x85501)),x85503),x85504))) % 165.30/165.05 [8691]~P24(f332(f62(x86911),x86912))+E(f332(f38(x86911),f332(f332(f22(f875(x86911,a862)),x86912),f332(f332(f310(x86911),x86913),x86914))),f332(f332(f22(a868),f332(f38(x86911),f332(f332(f22(f875(x86911,a862)),x86912),x86914))),f79(a868)))+P24(f332(f332(f334(x86911),x86913),x86914))+~P24(f332(f332(f334(x86911),x86913),x86912)) % 165.30/165.05 [8761]E(f332(f332(f81(a1),f400(x87611,x87612,x87613,x87614)),f401(x87611,x87612,x87613,x87614)),x87614)+~P24(f332(f332(f247(a1),f2(a1)),x87613))+~P24(f332(f332(f246(a1),x87614),x87611))+P24(f332(f332(f246(a1),f332(f332(f22(a1),x87614),x87613)),x87611)) % 165.30/165.05 [8762]E(f332(f332(f81(a1),f406(x87621,x87622,x87623,x87624)),f407(x87621,x87622,x87623,x87624)),x87624)+~P24(f332(f332(f247(a1),f2(a1)),x87623))+~P24(f332(f332(f247(a1),x87624),x87621))+P24(f332(f332(f247(a1),f332(f332(f22(a1),x87624),x87623)),x87621)) % 165.30/165.05 [8963]~P24(f332(f332(f247(a1),f2(a1)),x89633))+~P24(f332(f332(f246(a1),x89634),x89631))+P24(f332(f332(f334(a1),f400(x89631,x89632,x89633,x89634)),x89632))+P24(f332(f332(f246(a1),f332(f332(f22(a1),x89634),x89633)),x89631)) % 165.30/165.05 [8964]~P24(f332(f332(f247(a1),f2(a1)),x89643))+~P24(f332(f332(f247(a1),x89644),x89641))+P24(f332(f332(f334(a1),f406(x89641,x89642,x89643,x89644)),x89642))+P24(f332(f332(f247(a1),f332(f332(f22(a1),x89644),x89643)),x89641)) % 165.30/165.05 [9048]~P24(f332(f332(f247(a1),f2(a1)),x90482))+~P24(f332(f332(f246(a1),x90481),x90483))+P24(f332(f332(f334(a1),f401(x90483,x90484,x90482,x90481)),f303(a1,f79(a1),x90482)))+P24(f332(f332(f246(a1),f332(f332(f22(a1),x90481),x90482)),x90483)) % 165.30/165.05 [9049]~P24(f332(f332(f247(a1),f2(a1)),x90492))+~P24(f332(f332(f247(a1),x90491),x90493))+P24(f332(f332(f334(a1),f407(x90493,x90494,x90492,x90491)),f303(a1,f79(a1),x90492)))+P24(f332(f332(f247(a1),f332(f332(f22(a1),x90491),x90492)),x90493)) % 165.30/165.05 [9066]~P24(f332(f332(f246(a1),f2(a1)),x90664))+~P24(f332(f332(f247(a1),f2(a1)),x90663))+~P24(f332(f332(f247(a1),x90664),x90661))+P24(f332(f332(f246(a1),f2(a1)),f332(f332(f81(a1),f332(f332(f82(a1),x90661),f45(a1,x90662,x90663))),x90664))) % 165.30/165.05 [9127]~P100(x91271)+~P24(f332(f62(x91271),x91274))+~P24(f332(f332(f246(x91271),x91272),f765(x91273,x91272,x91274,x91271)))+P24(f332(f332(f246(x91271),f332(f332(f104(x91271),x91272),x91273)),f332(f332(f65(x91271,x91271,f104(x91271)),x91273),x91274))) % 165.30/165.05 [9128]~P106(x91281)+~P24(f332(f62(x91281),x91284))+~P24(f332(f332(f246(x91281),x91282),f766(x91283,x91282,x91284,x91281)))+P24(f332(f332(f246(x91281),f332(f332(f244(x91281),x91282),x91283)),f332(f332(f65(x91281,x91281,f244(x91281)),x91283),x91284))) % 165.30/165.05 [9143]~P24(f332(f332(f246(a1),x91434),f2(a1)))+~P24(f332(f332(f247(a1),f2(a1)),x91432))+~P24(f332(f332(f247(a1),x91431),x91434))+P24(f332(f332(f247(a1),f332(f332(f82(a1),x91431),x91432)),f332(f332(f81(a1),f332(f332(f82(a1),x91431),f45(a1,x91433,x91432))),x91434))) % 165.30/165.05 [9165]P24(f332(f62(x91651),x91652))+~P24(f332(f62(x91651),x91653))+~P24(f332(f332(f334(f875(x91651,a862)),x91652),f332(f332(f61(x91651),x91653),x91654)))+~P24(f332(f332(f246(f875(f874(x91651,x91651),a862)),x91654),f332(f332(f269(x91651,x91651),x91653),f332(f16(f875(x91651,a862),x91651),x91653)))) % 165.30/165.05 [9187]~P106(x91871)+~P24(f332(f62(x91871),x91874))+P24(f332(f332(f334(x91871),f766(x91872,x91873,x91874,x91871)),x91874))+P24(f332(f332(f246(x91871),f332(f332(f244(x91871),x91873),x91872)),f332(f332(f65(x91871,x91871,f244(x91871)),x91872),x91874))) % 165.30/165.05 [9188]~P100(x91881)+~P24(f332(f62(x91881),x91884))+P24(f332(f332(f334(x91881),f765(x91882,x91883,x91884,x91881)),x91884))+P24(f332(f332(f246(x91881),f332(f332(f104(x91881),x91883),x91882)),f332(f332(f65(x91881,x91881,f104(x91881)),x91882),x91884))) % 165.30/165.05 [9571]~P24(f332(f62(x95712),x95714))+~P24(f332(f62(x95711),x95713))+~P24(f332(f332(f246(a868),f332(f38(x95712),x95714)),f332(f38(x95711),x95713)))+P24(f332(f332(f246(f875(x95711,a862)),f332(f311(x95712,x95711,f711(x95713,x95711,x95714,x95712)),x95714)),x95713)) % 165.30/165.05 [9232]~P24(f332(f332(f334(x92321),x92322),x92324))+P24(f332(f332(f334(x92321),x92322),x92323))+~P24(f332(f332(f247(f875(x92321,a862)),x92324),f332(f332(f310(x92321),x92322),x92323)))+P24(f332(f332(f247(f875(x92321,a862)),f332(f332(f22(f875(x92321,a862)),x92324),f332(f332(f310(x92321),x92322),f196(f875(x92321,a862))))),x92323)) % 165.30/165.05 [9387]~P24(f332(f332(f334(x93871),x93872),x93874))+P24(f332(f332(f334(x93871),x93872),x93873))+P24(f332(f332(f247(f875(x93871,a862)),x93874),f332(f332(f310(x93871),x93872),x93873)))+~P24(f332(f332(f247(f875(x93871,a862)),f332(f332(f22(f875(x93871,a862)),x93874),f332(f332(f310(x93871),x93872),f196(f875(x93871,a862))))),x93873)) % 165.30/165.05 [9416]P24(f332(f332(f334(x94161),x94162),x94163))+~P24(f332(f332(f246(f875(x94161,a862)),x94164),x94163))+P24(f332(f332(f247(f875(x94161,a862)),x94164),f332(f332(f310(x94161),x94162),x94163)))+~P24(f332(f332(f247(f875(x94161,a862)),f332(f332(f22(f875(x94161,a862)),x94164),f332(f332(f310(x94161),x94162),f196(f875(x94161,a862))))),x94163)) % 165.30/165.05 [9421]~P24(f332(f332(f334(x94211),x94213),x94212))+~P24(f332(f332(f247(f875(x94211,a862)),x94212),x94214))+P24(f332(f332(f247(f875(x94211,a862)),x94212),f332(f332(f310(x94211),x94213),x94214)))+~P24(f332(f332(f247(f875(x94211,a862)),f332(f332(f22(f875(x94211,a862)),x94212),f332(f332(f310(x94211),x94213),f196(f875(x94211,a862))))),x94214)) % 165.30/165.05 [9433]~P24(f332(f332(f246(f875(x94331,a862)),x94332),x94334))+~P24(f332(f332(f247(f875(x94331,a862)),x94332),x94334))+P24(f332(f332(f247(f875(x94331,a862)),x94332),f332(f332(f310(x94331),x94333),x94334)))+~P24(f332(f332(f247(f875(x94331,a862)),f332(f332(f22(f875(x94331,a862)),x94332),f332(f332(f310(x94331),x94333),f196(f875(x94331,a862))))),x94334)) % 165.30/165.05 [9474]~P107(x94742)+~P59(x94741)+~P24(f332(f332(f246(f875(x94741,x94742)),x94743),x94744))+P24(f332(f59(x94741),f332(f332(f18(x94741,x94742,a862),f332(f332(f8(x94742,f875(x94742,a862),x94741),f246(x94742)),x94743)),x94744))) % 165.30/165.05 [9618]~P107(x96182)+~P59(x96181)+P24(f332(f332(f246(f875(x96181,x96182)),x96183),x96184))+~P24(f332(f59(x96181),f332(f332(f18(x96181,x96182,a862),f332(f332(f8(x96182,f875(x96182,a862),x96181),f246(x96182)),x96183)),x96184))) % 165.30/165.05 [9790]E(f332(f332(f166(x97901),f332(f332(f166(f869(x97901)),f182(x97901,x97902)),x97903)),x97904),f332(f332(f166(x97901),f332(f332(f166(f869(x97901)),x97902),x97904)),x97903))+~P24(f332(f332(f247(a868),x97903),f332(f197(f869(f869(x97901))),f182(x97901,x97902))))+~P32(a868,f332(f170(a868),f332(f332(f155(f869(x97901),a868),f197(f869(x97901))),x97902)))+~P24(f332(f332(f247(a868),x97904),f332(f197(f869(f869(x97901))),f332(f137(f869(x97901),f332(f332(f8(a868,a862,f869(x97901)),f332(f247(a868),x97903)),f197(f869(x97901)))),x97902)))) % 165.30/165.05 [9818]~P24(f332(f332(f334(f874(a868,a868)),x98184),x98181))+~P24(f332(f332(f334(f874(f874(a868,a868),f874(a868,a868))),f332(f332(f267(f874(a868,a868),f874(a868,a868)),x98184),x98182)),a36))+~P24(f332(f332(f334(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),x98181),x98183)),a69))+P24(f332(f332(f334(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),x98181),f332(f332(f310(f874(a868,a868)),x98182),x98183))),a69)) % 165.30/165.05 [9819]~P24(f332(f332(f334(f874(a868,a868)),x98194),x98191))+~P24(f332(f332(f334(f874(f874(a868,a868),f874(a868,a868))),f332(f332(f267(f874(a868,a868),f874(a868,a868)),x98194),x98192)),a71))+~P24(f332(f332(f334(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),x98191),x98193)),a72))+P24(f332(f332(f334(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),x98191),f332(f332(f310(f874(a868,a868)),x98192),x98193))),a72)) % 165.30/165.05 [9703]~P107(x97032)+~P59(x97031)+~P24(f332(f332(f247(f875(x97031,x97032)),x97033),x97034))+P24(f332(f58(x97031),f332(f332(f8(a862,a862,x97031),a327),f332(f332(f18(x97031,x97032,a862),f332(f332(f8(x97032,f875(x97032,a862),x97031),a329),x97033)),x97034)))) % 165.30/165.05 [9832]~P24(f332(f332(f334(f874(a868,a868)),x98324),x98323))+~P24(f332(f332(f334(f874(f874(a868,a868),f874(a868,a868))),f332(f332(f267(f874(a868,a868),f874(a868,a868)),x98321),x98324)),a36))+~P24(f332(f332(f334(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),x98322),x98323)),a37))+P24(f332(f332(f334(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),f332(f332(f310(f874(a868,a868)),x98321),x98322)),x98323)),a37)) % 165.30/165.05 [9833]~P24(f332(f332(f334(f874(a868,a868)),x98334),x98333))+~P24(f332(f332(f334(f874(f874(a868,a868),f874(a868,a868))),f332(f332(f267(f874(a868,a868),f874(a868,a868)),x98331),x98334)),a71))+~P24(f332(f332(f334(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),x98332),x98333)),a70))+P24(f332(f332(f334(f874(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862))),f332(f332(f267(f875(f874(a868,a868),a862),f875(f874(a868,a868),a862)),f332(f332(f310(f874(a868,a868)),x98331),x98332)),x98333)),a70)) % 165.30/165.05 [6019]~P5(x60194,x60191)+~P24(f332(f332(x60191,x60192),x60195))+P24(f332(f332(x60191,x60192),x60193))+~P24(f332(f332(x60191,x60195),x60193)) % 165.30/165.05 [5279]~P66(x52795)+E(x52791,x52792)+~E(x52793,x52794)+~E(f332(f332(f22(x52795),x52793),x52794),f332(f332(f22(x52795),x52791),x52792)) % 165.30/165.05 [6129]~P13(x61295,x61291,x61293)+E(f332(f332(x61291,x61292),f332(x61293,x61294)),f332(x61293,x61294))+~P24(f332(f62(x61295),x61294))+~P24(f332(f332(f334(x61295),x61292),x61294)) % 165.30/165.05 [6323]~P77(x63231)+~E(f332(f332(f22(x63231),x63234),x63235),f332(f332(f22(x63231),x63232),x63233))+~P24(f332(f332(f246(x63231),x63234),x63235))+P24(f332(f332(f246(x63231),x63232),x63233)) % 165.30/165.05 [6325]~P77(x63251)+~E(f332(f332(f22(x63251),x63254),x63255),f332(f332(f22(x63251),x63252),x63253))+~P24(f332(f332(f247(x63251),x63254),x63255))+P24(f332(f332(f247(x63251),x63252),x63253)) % 165.30/165.05 [7283]~E(x72832,f332(f332(f152(x72831),x72834),x72835))+P24(f332(f332(f334(f869(x72831)),x72832),f162(x72831,x72833)))+~P24(f332(f332(f334(f869(x72831)),x72835),f162(x72831,x72833)))+~P24(f332(f332(f334(x72831),x72834),x72833)) % 165.30/165.05 [7698]~E(f332(f197(f869(x76981)),x76983),f332(f197(f869(x76982)),x76984))+~E(f332(f332(f155(f874(x76981,x76982),x76982),f270(x76981,x76982)),x76985),x76984)+~E(f332(f332(f155(f874(x76981,x76982),x76981),f266(x76981,x76982)),x76985),x76983)+E(f332(f332(f184(x76981,x76982),x76983),x76984),x76985) % 165.30/165.05 [8026]~P107(x80261)+P24(f332(f332(f247(f875(x80261,a862)),f303(x80261,x80262,x80263)),f303(x80261,x80264,x80265)))+~P24(f332(f332(f246(x80261),x80264),x80265))+P24(f332(f332(f246(x80261),x80262),x80263)) % 165.30/165.05 [8120]~P107(x81201)+P24(f332(f332(f246(f875(x81201,a862)),f303(x81201,x81202,x81203)),f303(x81201,x81204,x81205)))+~P24(f332(f332(f246(x81201),x81203),x81205))+~P24(f332(f332(f246(x81201),x81204),x81202)) % 165.30/165.05 [8245]~P106(x82451)+P24(f332(f332(f246(x82451),x82452),x82453))+P24(f332(f332(f246(x82451),x82454),x82453))+~P24(f332(f332(f246(f875(x82451,a862)),f332(f302(x82451,x82453),x82452)),f332(f302(x82451,x82454),x82455))) % 165.30/165.05 [8246]~P106(x82461)+P24(f332(f332(f246(x82461),x82462),x82463))+P24(f332(f332(f246(x82461),x82462),x82464))+~P24(f332(f332(f246(f875(x82461,a862)),f332(f302(x82461,x82463),x82462)),f332(f302(x82461,x82465),x82464))) % 165.30/165.05 [8470]~P107(x84701)+~P24(f332(f332(f246(f875(x84701,a862)),f303(x84701,x84704,x84702)),f303(x84701,x84705,x84703)))+P24(f332(f332(f246(x84701),x84702),x84703))+~P24(f332(f332(f246(x84701),x84704),x84702)) % 165.30/165.05 [8471]~P107(x84711)+~P24(f332(f332(f247(f875(x84711,a862)),f303(x84711,x84714,x84712)),f303(x84711,x84715,x84713)))+P24(f332(f332(f246(x84711),x84712),x84713))+~P24(f332(f332(f246(x84711),x84714),x84712)) % 165.30/165.05 [8472]~P107(x84721)+~P24(f332(f332(f246(f875(x84721,a862)),f303(x84721,x84723,x84724)),f303(x84721,x84722,x84725)))+P24(f332(f332(f246(x84721),x84722),x84723))+~P24(f332(f332(f246(x84721),x84723),x84724)) % 165.30/165.05 [8473]~P107(x84731)+~P24(f332(f332(f247(f875(x84731,a862)),f303(x84731,x84733,x84734)),f303(x84731,x84732,x84735)))+P24(f332(f332(f246(x84731),x84732),x84733))+~P24(f332(f332(f246(x84731),x84733),x84734)) % 165.30/165.05 [6018]~P13(x60182,x60185,x60183)+E(x60181,f196(f875(x60182,a862)))+~P24(f332(f62(x60182),x60181))+E(f332(x60183,f332(f332(f310(x60182),x60184),x60181)),f332(f332(x60185,x60184),f332(x60183,x60181))) % 165.30/165.05 [6789]~E(x67891,x67892)+~E(f332(f332(f104(f875(x67893,a862)),x67894),x67895),f196(f875(x67893,a862)))+~P24(f332(f332(f334(x67893),x67892),x67895))+~P24(f332(f332(f334(x67893),x67891),x67894)) % 165.30/165.05 [6871]~P14(x68712,x68715,x68711)+~P24(f332(f62(x68712),x68714))+E(f332(x68711,f332(f332(f310(x68712),x68713),x68714)),f332(f332(f65(x68712,x68712,x68715),x68713),x68714))+P24(f332(f332(f334(x68712),x68713),x68714)) % 165.30/165.05 [6936]~P74(x69362)+~P24(f332(f62(x69361),x69365))+E(f332(f332(f6(x69361,x69362),x69363),f332(f332(f310(x69361),x69364),x69365)),f332(f332(f81(x69362),f332(x69363,x69364)),f332(f332(f6(x69361,x69362),x69363),x69365)))+P24(f332(f332(f334(x69361),x69364),x69365)) % 165.30/165.05 [6938]~P73(x69382)+~P24(f332(f62(x69381),x69385))+E(f332(f332(f9(x69381,x69382),x69383),f332(f332(f310(x69381),x69384),x69385)),f332(f332(f82(x69382),f332(x69383,x69384)),f332(f332(f9(x69381,x69382),x69383),x69385)))+P24(f332(f332(f334(x69381),x69384),x69385)) % 165.30/165.05 [7437]~P14(x74372,x74375,x74371)+~P24(f332(f62(x74372),x74374))+E(f332(x74371,f332(f332(f310(x74372),x74373),x74374)),x74373)+~E(f332(f332(f22(f875(x74372,a862)),x74374),f332(f332(f310(x74372),x74373),f196(f875(x74372,a862)))),f196(f875(x74372,a862))) % 165.30/165.05 [7800]~P99(x78001)+~P24(f332(f332(f246(x78001),x78003),x78005))+~P24(f332(f332(f246(x78001),x78002),x78004))+P24(f332(f332(f246(x78001),f332(f332(f113(x78001),x78002),x78003)),f332(f332(f113(x78001),x78004),x78005))) % 165.30/165.05 [7801]~P100(x78011)+~P24(f332(f332(f246(x78011),x78013),x78015))+~P24(f332(f332(f246(x78011),x78012),x78014))+P24(f332(f332(f246(x78011),f332(f332(f104(x78011),x78012),x78013)),f332(f332(f104(x78011),x78014),x78015))) % 165.30/165.05 [7802]~P84(x78021)+~P24(f332(f332(f246(x78021),x78023),x78025))+~P24(f332(f332(f246(x78021),x78022),x78024))+P24(f332(f332(f246(x78021),f332(f332(f81(x78021),x78022),x78023)),f332(f332(f81(x78021),x78024),x78025))) % 165.30/165.05 [7803]~P106(x78031)+~P24(f332(f332(f246(x78031),x78033),x78035))+~P24(f332(f332(f246(x78031),x78032),x78034))+P24(f332(f332(f246(x78031),f332(f332(f244(x78031),x78032),x78033)),f332(f332(f244(x78031),x78034),x78035))) % 165.30/165.05 [7804]~P106(x78041)+~P24(f332(f332(f246(x78041),x78043),x78045))+~P24(f332(f332(f246(x78041),x78042),x78044))+P24(f332(f332(f246(x78041),f332(f332(f245(x78041),x78042),x78043)),f332(f332(f245(x78041),x78044),x78045))) % 165.30/165.05 [7805]~P86(x78051)+~P24(f332(f332(f246(x78051),x78053),x78055))+~P24(f332(f332(f247(x78051),x78052),x78054))+P24(f332(f332(f247(x78051),f332(f332(f81(x78051),x78052),x78053)),f332(f332(f81(x78051),x78054),x78055))) % 165.30/165.05 [7806]~P86(x78061)+~P24(f332(f332(f246(x78061),x78062),x78064))+~P24(f332(f332(f247(x78061),x78063),x78065))+P24(f332(f332(f247(x78061),f332(f332(f81(x78061),x78062),x78063)),f332(f332(f81(x78061),x78064),x78065))) % 165.30/165.05 [7807]~P86(x78071)+~P24(f332(f332(f247(x78071),x78073),x78075))+~P24(f332(f332(f247(x78071),x78072),x78074))+P24(f332(f332(f247(x78071),f332(f332(f81(x78071),x78072),x78073)),f332(f332(f81(x78071),x78074),x78075))) % 165.30/165.05 [7943]~P123(x79435)+E(x79431,x79432)+E(x79433,x79434)+~E(f332(f332(f81(x79435),f332(f332(f82(x79435),x79433),x79431)),f332(f332(f82(x79435),x79434),x79432)),f332(f332(f81(x79435),f332(f332(f82(x79435),x79433),x79432)),f332(f332(f82(x79435),x79434),x79431))) % 165.30/165.05 [8076]P33(x80761,x80762,x80763)+~P23(x80761,x80764,x80765)+~P33(x80761,x80762,f551(x80765,x80764,x80761,x80762))+~P24(f332(f332(f334(f867(x80761)),x80763),x80765)) % 165.30/165.05 [8143]~P106(x81434)+~P24(f332(f138(x81431),x81433))+P24(f332(f332(f334(x81431),x81432),f332(f174(x81431),x81433)))+P24(f332(f138(x81431),f332(f332(f149(x81431,x81434,x81435),x81432),x81433))) % 165.30/165.05 [8289]~P66(x82891)+E(f332(f332(f22(x82891),f332(f332(f6(a868,x82891),x82892),f332(f302(a868,x82893),x82894))),f332(f332(f6(a868,x82891),x82892),f332(f302(a868,x82893),x82895))),f332(f332(f6(a868,x82891),x82892),f332(f302(a868,x82895),x82894)))+~P24(f332(f332(f246(a868),x82895),x82894))+~P24(f332(f332(f246(a868),x82893),x82895)) % 165.30/165.05 [8290]~P74(x82901)+E(f332(f332(f81(x82901),f332(f332(f6(a868,x82901),x82902),f332(f302(a868,x82903),x82904))),f332(f332(f6(a868,x82901),x82902),f332(f302(a868,x82904),x82905))),f332(f332(f6(a868,x82901),x82902),f332(f302(a868,x82903),x82905)))+~P24(f332(f332(f246(a868),x82904),x82905))+~P24(f332(f332(f246(a868),x82903),x82904)) % 165.30/165.05 [8605]~P61(x86052)+E(x86051,f2(x86052))+E(x86053,f2(x86052))+E(f332(f332(f290(x86052),f332(f332(f22(x86052),f332(f332(f82(x86052),x86054),x86051)),f332(f332(f82(x86052),x86055),x86053))),f332(f332(f82(x86052),x86053),x86051)),f332(f332(f22(x86052),f332(f332(f290(x86052),x86054),x86053)),f332(f332(f290(x86052),x86055),x86051))) % 165.30/165.05 [8606]~P61(x86062)+E(x86061,f2(x86062))+E(x86063,f2(x86062))+E(f332(f332(f290(x86062),f332(f332(f81(x86062),f332(f332(f82(x86062),x86064),x86061)),f332(f332(f82(x86062),x86065),x86063))),f332(f332(f82(x86062),x86063),x86061)),f332(f332(f81(x86062),f332(f332(f290(x86062),x86064),x86063)),f332(f332(f290(x86062),x86065),x86061))) % 165.30/165.05 [8615]~E(x86152,f332(x86153,x86151))+E(x86151,f826(x86152,x86153,x86154,x86155))+~P21(x86155,x86154,x86153,f255(f875(x86155,a862)))+~P24(f332(f332(f334(x86154),x86152),f332(f311(x86155,x86154,x86153),f255(f875(x86155,a862))))) % 165.30/165.05 [8810]~P118(x88101)+~P24(f332(f332(f247(x88101),f332(f76(x88101),x88102)),x88104))+P24(f332(f332(f247(x88101),f332(f332(f82(x88101),f332(f76(x88101),x88102)),f332(f76(x88101),x88103))),f332(f332(f82(x88101),x88104),x88105)))+~P24(f332(f332(f247(x88101),f332(f76(x88101),x88103)),x88105)) % 165.30/165.05 [8827]~P23(x88271,x88275,x88274)+P33(x88271,x88272,x88273)+P24(f332(f332(f334(f867(x88271)),f551(x88274,x88275,x88271,x88272)),x88275))+~P24(f332(f332(f334(f867(x88271)),x88273),x88274)) % 165.30/165.05 [8923]~P21(x89231,x89233,x89235,x89232)+~P24(f332(f62(x89233),x89234))+P24(f332(f332(f246(a868),f332(f38(x89231),x89232)),f332(f38(x89233),x89234)))+~P24(f332(f332(f246(f875(x89233,a862)),f332(f311(x89231,x89233,x89235),x89232)),x89234)) % 165.30/165.05 [8992]~P74(x89922)+~P21(x89921,x89921,x89924,x89925)+~P24(f332(f62(x89921),x89925))+E(f332(f332(f6(x89921,x89922),f332(f74(x89921,x89922,x89921,x89923),x89924)),x89925),f332(f332(f6(x89921,x89922),x89923),f332(f311(x89921,x89921,x89924),x89925))) % 165.30/165.05 [8993]~P73(x89932)+~P21(x89931,x89931,x89934,x89935)+~P24(f332(f62(x89931),x89935))+E(f332(f332(f9(x89931,x89932),f332(f74(x89931,x89932,x89931,x89933),x89934)),x89935),f332(f332(f9(x89931,x89932),x89933),f332(f311(x89931,x89931,x89934),x89935))) % 165.30/165.05 [9106]~P41(x91061,x91062)+~P24(f332(f332(f334(x91061),x91063),x91064))+~P24(f332(f332(f334(x91061),x91065),x91064))+~P24(f332(f332(f334(f874(x91061,x91061)),f332(f332(f267(x91061,x91061),x91065),f739(x91062,x91061,x91064))),x91062)) % 165.30/165.05 [9142]~P21(x91422,x91423,x91425,x91421)+E(x91421,f196(f875(x91422,a862)))+E(f332(f311(x91423,x91422,f726(x91424,x91423,x91422,x91421)),x91424),x91421)+~P24(f332(f332(f246(f875(x91423,a862)),f332(f311(x91422,x91423,x91425),x91421)),x91424)) % 165.30/165.05 [9600]~P106(x96005)+~P30(x96005)+P24(f332(f332(f334(x96001),f471(x96002,x96003,x96001,x96004,x96005)),x96003))+~P24(f332(f332(f247(x96005),x96004),f332(f332(f42(x96001,x96005),x96003),x96002))) % 165.30/165.05 [9605]~P106(x96051)+~P30(x96051)+P24(f332(f332(f247(x96051),x96052),f332(x96053,f471(x96053,x96054,x96055,x96052,x96051))))+~P24(f332(f332(f247(x96051),x96052),f332(f332(f42(x96055,x96051),x96054),x96053))) % 165.30/165.05 [9683]~P71(x96831)+~P24(f332(f67(x96831,x96831,f82(x96831),x96832,x96833),x96835))+P24(f332(f332(f334(x96831),x96832),x96833))+P24(f332(f67(x96831,x96831,f82(x96831),x96834,f332(f332(f310(x96831),x96832),x96833)),f332(f332(f82(x96831),x96834),x96835))) % 165.30/165.05 [9900]~P74(x99002)+~P24(f332(f62(x99001),x99005))+E(f332(f332(f6(x99001,x99002),f332(f332(f7(x99001,x99002,x99002),f332(f332(f18(x99001,x99002,f875(x99002,x99002)),f332(f332(f8(a862,f875(x99002,f875(x99002,x99002)),x99001),f99(x99002)),f332(a329,x99003))),x99004)),f2(x99002))),x99005),f2(x99002))+P24(f332(f332(f334(x99001),x99003),x99005)) % 165.30/165.05 [9901]~P73(x99012)+~P24(f332(f62(x99011),x99015))+E(f332(f332(f9(x99011,x99012),f332(f332(f7(x99011,x99012,x99012),f332(f332(f18(x99011,x99012,f875(x99012,x99012)),f332(f332(f8(a862,f875(x99012,f875(x99012,x99012)),x99011),f99(x99012)),f332(a329,x99013))),x99014)),f79(x99012))),x99015),f79(x99012))+P24(f332(f332(f334(x99011),x99013),x99015)) % 165.30/165.05 [9902]~P74(x99022)+~P24(f332(f62(x99021),x99025))+E(f332(f332(f6(x99021,x99022),f332(f332(f7(x99021,x99022,x99022),f332(f332(f18(x99021,x99022,f875(x99022,x99022)),f332(f332(f8(a862,f875(x99022,f875(x99022,x99022)),x99021),f99(x99022)),f332(a329,x99023))),x99024)),f2(x99022))),x99025),f332(x99024,x99023))+~P24(f332(f332(f334(x99021),x99023),x99025)) % 165.30/165.05 [9903]~P73(x99032)+~P24(f332(f62(x99031),x99035))+E(f332(f332(f9(x99031,x99032),f332(f332(f7(x99031,x99032,x99032),f332(f332(f18(x99031,x99032,f875(x99032,x99032)),f332(f332(f8(a862,f875(x99032,f875(x99032,x99032)),x99031),f99(x99032)),f332(a329,x99033))),x99034)),f79(x99032))),x99035),f332(x99034,x99033))+~P24(f332(f332(f334(x99031),x99033),x99035)) % 165.30/165.05 [9958]~P74(x99582)+~P24(f332(f62(x99581),x99585))+E(f332(f332(f6(x99581,x99582),f332(f332(f7(x99581,x99582,x99582),f332(f332(f18(x99581,x99582,f875(x99582,x99582)),f332(f332(f8(a862,f875(x99582,f875(x99582,x99582)),x99581),f99(x99582)),f332(f332(f7(x99581,x99581,a862),a329),x99583))),x99584)),f2(x99582))),x99585),f2(x99582))+P24(f332(f332(f334(x99581),x99583),x99585)) % 165.30/165.05 [9959]~P73(x99592)+~P24(f332(f62(x99591),x99595))+E(f332(f332(f9(x99591,x99592),f332(f332(f7(x99591,x99592,x99592),f332(f332(f18(x99591,x99592,f875(x99592,x99592)),f332(f332(f8(a862,f875(x99592,f875(x99592,x99592)),x99591),f99(x99592)),f332(f332(f7(x99591,x99591,a862),a329),x99593))),x99594)),f79(x99592))),x99595),f79(x99592))+P24(f332(f332(f334(x99591),x99593),x99595)) % 165.30/165.05 [9961]~P74(x99612)+~P24(f332(f62(x99611),x99615))+E(f332(f332(f6(x99611,x99612),f332(f332(f7(x99611,x99612,x99612),f332(f332(f18(x99611,x99612,f875(x99612,x99612)),f332(f332(f8(a862,f875(x99612,f875(x99612,x99612)),x99611),f99(x99612)),f332(f332(f7(x99611,x99611,a862),a329),x99613))),x99614)),f2(x99612))),x99615),f332(x99614,x99613))+~P24(f332(f332(f334(x99611),x99613),x99615)) % 165.30/165.05 [9962]~P73(x99622)+~P24(f332(f62(x99621),x99625))+E(f332(f332(f9(x99621,x99622),f332(f332(f7(x99621,x99622,x99622),f332(f332(f18(x99621,x99622,f875(x99622,x99622)),f332(f332(f8(a862,f875(x99622,f875(x99622,x99622)),x99621),f99(x99622)),f332(f332(f7(x99621,x99621,a862),a329),x99623))),x99624)),f79(x99622))),x99625),f332(x99624,x99623))+~P24(f332(f332(f334(x99621),x99623),x99625)) % 165.30/165.05 [7799]~P66(x77992)+~P24(f332(f62(x77991),x77994))+E(f332(f332(f6(x77991,x77992),x77993),f332(f332(f22(f875(x77991,a862)),x77994),f332(f332(f310(x77991),x77995),f196(f875(x77991,a862))))),f332(f332(f6(x77991,x77992),x77993),x77994))+P24(f332(f332(f334(x77991),x77995),x77994)) % 165.30/165.05 [8295]~P125(x82952)+~P24(f332(f62(x82951),x82954))+E(f332(f332(f6(x82951,x82952),x82953),f332(f332(f22(f875(x82951,a862)),x82954),f332(f332(f310(x82951),x82955),f196(f875(x82951,a862))))),f332(f332(f22(x82952),f332(f332(f6(x82951,x82952),x82953),x82954)),f332(x82953,x82955)))+~P24(f332(f332(f334(x82951),x82955),x82954)) % 165.30/165.05 [8296]~P66(x82962)+~P24(f332(f62(x82961),x82964))+E(f332(f332(f6(x82961,x82962),x82963),f332(f332(f22(f875(x82961,a862)),x82964),f332(f332(f310(x82961),x82965),f196(f875(x82961,a862))))),f332(f332(f22(x82962),f332(f332(f6(x82961,x82962),x82963),x82964)),f332(x82963,x82965)))+~P24(f332(f332(f334(x82961),x82965),x82964)) % 165.30/165.05 [8327]~P66(x83271)+~P24(f332(f62(x83272),x83274))+E(f332(f332(f22(x83271),f332(f332(f6(x83272,x83271),x83273),x83274)),f332(f332(f6(x83272,x83271),x83273),x83275)),f332(f332(f6(x83272,x83271),x83273),f332(f332(f22(f875(x83272,a862)),x83274),x83275)))+~P24(f332(f332(f246(f875(x83272,a862)),x83275),x83274)) % 165.30/165.05 [8347]P24(f332(f62(x83471),f332(x83472,x83473)))+~P24(f332(f62(x83474),x83475))+~P24(f332(f332(f334(x83474),x83473),x83475))+~P24(f332(f62(x83471),f332(f332(f42(x83474,f875(x83471,a862)),x83475),x83472))) % 165.30/165.05 [8773]~P6(x87731,x87735,x87734)+~E(f332(f286(x87731,x87731,x87734),f332(f332(f310(x87731),x87732),f196(f875(x87731,a862)))),f332(f286(x87731,x87731,x87734),f332(f332(f310(x87731),x87733),f196(f875(x87731,a862)))))+~P24(f332(f332(f334(x87731),x87733),x87735))+P24(f332(f332(f334(f874(x87731,x87731)),f332(f332(f267(x87731,x87731),x87732),x87733)),x87734)) % 165.30/165.05 [9064]~P24(f332(x90641,x90645))+P24(f332(x90641,f852(x90641,x90642,x90643,x90644)))+P24(f332(x90641,f844(x90641,x90642,x90643,x90644)))+~P24(f332(f332(f334(x90644),x90645),f332(f332(f113(f875(x90644,a862)),x90643),x90642))) % 165.30/165.05 [9237]~P24(f332(x92371,x92375))+P24(f332(x92371,f844(x92371,x92372,x92373,x92374)))+P24(f332(f332(f334(x92374),f852(x92371,x92372,x92373,x92374)),x92372))+~P24(f332(f332(f334(x92374),x92375),f332(f332(f113(f875(x92374,a862)),x92373),x92372))) % 165.30/165.05 [9238]~P24(f332(x92381,x92385))+P24(f332(x92381,f852(x92381,x92382,x92383,x92384)))+P24(f332(f332(f334(x92384),f844(x92381,x92382,x92383,x92384)),x92383))+~P24(f332(f332(f334(x92384),x92385),f332(f332(f113(f875(x92384,a862)),x92383),x92382))) % 165.30/165.05 [9242]P24(f332(x92421,x92422))+~P24(f332(x92421,f373(x92421,x92423,x92424,x92425)))+~P24(f332(x92421,f362(x92421,x92423,x92424,x92425)))+~P24(f332(f332(f334(x92425),x92422),f332(f332(f113(f875(x92425,a862)),x92424),x92423))) % 165.30/165.05 [9284]E(x92841,x92842)+~P24(f332(f332(f334(f874(x92843,x92843)),f332(f332(f267(x92843,x92843),x92841),x92842)),f308(x92843,x92845)))+P24(f332(f332(f334(x92843),x92841),x92844))+~P24(f332(f332(f246(f875(f874(x92843,x92843),a862)),x92845),f332(f332(f269(x92843,x92843),x92844),f332(f16(f875(x92843,a862),x92843),x92844)))) % 165.30/165.05 [9302]P24(f332(x93021,x93022))+~P24(f332(x93021,f362(x93021,x93024,x93025,x93023)))+P24(f332(f332(f334(x93023),f373(x93021,x93024,x93025,x93023)),x93024))+~P24(f332(f332(f334(x93023),x93022),f332(f332(f113(f875(x93023,a862)),x93025),x93024))) % 165.30/165.05 [9303]P24(f332(x93031,x93032))+~P24(f332(x93031,f373(x93031,x93034,x93035,x93033)))+P24(f332(f332(f334(x93033),f362(x93031,x93034,x93035,x93033)),x93035))+~P24(f332(f332(f334(x93033),x93032),f332(f332(f113(f875(x93033,a862)),x93035),x93034))) % 165.30/165.05 [9362]P24(f332(x93621,x93622))+P24(f332(f332(f334(x93623),f373(x93621,x93624,x93625,x93623)),x93624))+P24(f332(f332(f334(x93623),f362(x93621,x93624,x93625,x93623)),x93625))+~P24(f332(f332(f334(x93623),x93622),f332(f332(f113(f875(x93623,a862)),x93625),x93624))) % 165.30/165.05 [9364]~P24(f332(x93642,x93645))+P24(f332(f332(f334(x93641),f852(x93642,x93643,x93644,x93641)),x93643))+P24(f332(f332(f334(x93641),f844(x93642,x93643,x93644,x93641)),x93644))+~P24(f332(f332(f334(x93641),x93645),f332(f332(f113(f875(x93641,a862)),x93644),x93643))) % 165.30/165.05 [9507]~P6(x95071,x95075,x95074)+~P24(f332(f332(f334(x95071),x95073),x95075))+P24(f332(f332(f334(f874(x95071,x95071)),f332(f332(f267(x95071,x95071),x95072),x95073)),x95074))+~P24(f332(f332(f246(f875(x95071,a862)),f332(f286(x95071,x95071,x95074),f332(f332(f310(x95071),x95073),f196(f875(x95071,a862))))),f332(f286(x95071,x95071,x95074),f332(f332(f310(x95071),x95072),f196(f875(x95071,a862)))))) % 165.30/165.05 [9631]~P106(x96315)+~P30(x96315)+P24(f332(f332(f334(x96311),f602(x96312,x96313,x96314,x96311,x96315)),x96314))+~P24(f332(f332(f247(x96315),f332(f332(f43(x96311,x96315),x96314),x96313)),x96312)) % 165.30/165.05 [9663]~P84(x96635)+~P80(x96635)+P24(f332(f332(f334(x96631),f539(x96632,x96633,x96634,x96631,x96635)),f332(f174(x96631),x96634)))+P24(f332(f332(f246(x96635),f332(f167(x96635),f332(f332(f155(x96631,x96635),x96633),x96634))),f332(f167(x96635),f332(f332(f155(x96631,x96635),x96632),x96634)))) % 165.30/165.05 [9780]~P106(x97801)+~P30(x97801)+P24(f332(f332(f247(x97801),f332(x97802,f602(x97803,x97802,x97804,x97805,x97801))),x97803))+~P24(f332(f332(f247(x97801),f332(f332(f43(x97805,x97801),x97804),x97802)),x97803)) % 165.30/165.05 [9918]~P84(x99181)+~P80(x99181)+~P24(f332(f332(f246(x99181),f332(x99183,f539(x99185,x99183,x99184,x99182,x99181))),f332(x99185,f539(x99185,x99183,x99184,x99182,x99181))))+P24(f332(f332(f246(x99181),f332(f167(x99181),f332(f332(f155(x99182,x99181),x99183),x99184))),f332(f167(x99181),f332(f332(f155(x99182,x99181),x99185),x99184)))) % 165.30/165.05 [8624]~P74(x86241)+~P24(f332(f62(x86244),x86245))+~P24(f332(f332(f334(x86244),x86243),x86245))+E(f332(f332(f81(x86241),f332(x86242,x86243)),f332(f332(f6(x86244,x86241),x86242),f332(f332(f22(f875(x86244,a862)),x86245),f332(f332(f310(x86244),x86243),f196(f875(x86244,a862)))))),f332(f332(f6(x86244,x86241),x86242),x86245)) % 165.30/165.05 [8625]~P73(x86251)+~P24(f332(f62(x86254),x86255))+~P24(f332(f332(f334(x86254),x86253),x86255))+E(f332(f332(f82(x86251),f332(x86252,x86253)),f332(f332(f9(x86254,x86251),x86252),f332(f332(f22(f875(x86254,a862)),x86255),f332(f332(f310(x86254),x86253),f196(f875(x86254,a862)))))),f332(f332(f9(x86254,x86251),x86252),x86255)) % 165.30/165.05 [8680]~P14(x86801,x86804,x86805)+~P24(f332(f62(x86801),x86802))+E(f332(f332(f22(f875(x86801,a862)),x86802),f332(f332(f310(x86801),x86803),f196(f875(x86801,a862)))),f196(f875(x86801,a862)))+E(f332(f332(x86804,x86803),f332(x86805,f332(f332(f22(f875(x86801,a862)),x86802),f332(f332(f310(x86801),x86803),f196(f875(x86801,a862)))))),f332(x86805,f332(f332(f310(x86801),x86803),x86802))) % 165.30/165.05 [9043]~P74(x90431)+~P24(f332(f62(x90432),x90435))+~P24(f332(f62(x90432),x90434))+E(f332(f332(f81(x90431),f332(f332(f6(x90432,x90431),x90433),f332(f332(f113(f875(x90432,a862)),x90434),x90435))),f332(f332(f6(x90432,x90431),x90433),f332(f332(f104(f875(x90432,a862)),x90434),x90435))),f332(f332(f81(x90431),f332(f332(f6(x90432,x90431),x90433),x90434)),f332(f332(f6(x90432,x90431),x90433),x90435))) % 165.30/165.05 [9045]~P73(x90451)+~P24(f332(f62(x90452),x90455))+~P24(f332(f62(x90452),x90454))+E(f332(f332(f82(x90451),f332(f332(f9(x90452,x90451),x90453),f332(f332(f113(f875(x90452,a862)),x90454),x90455))),f332(f332(f9(x90452,x90451),x90453),f332(f332(f104(f875(x90452,a862)),x90454),x90455))),f332(f332(f82(x90451),f332(f332(f9(x90452,x90451),x90453),x90454)),f332(f332(f9(x90452,x90451),x90453),x90455))) % 165.30/165.05 [9178]~P66(x91781)+~P24(f332(f62(x91782),x91785))+~P24(f332(f62(x91782),x91784))+E(f332(f332(f22(x91781),f332(f332(f81(x91781),f332(f332(f6(x91782,x91781),x91783),x91784)),f332(f332(f6(x91782,x91781),x91783),x91785))),f332(f332(f6(x91782,x91781),x91783),f332(f332(f104(f875(x91782,a862)),x91784),x91785))),f332(f332(f6(x91782,x91781),x91783),f332(f332(f113(f875(x91782,a862)),x91784),x91785))) % 165.30/165.05 [9373]~P21(x93731,x93732,x93733,x93735)+~P21(x93731,x93732,x93733,x93734)+P21(x93731,x93732,x93733,f332(f332(f113(f875(x93731,a862)),x93734),x93735))+~E(f332(f332(f104(f875(x93732,a862)),f332(f311(x93731,x93732,x93733),f332(f332(f22(f875(x93731,a862)),x93734),x93735))),f332(f311(x93731,x93732,x93733),f332(f332(f22(f875(x93731,a862)),x93735),x93734))),f196(f875(x93732,a862))) % 165.30/165.05 [9482]E(x94821,f2(a1))+~P24(f332(f332(f247(a1),f2(a1)),x94823))+~P24(f332(f49(x94822,x94821),f332(f332(f267(a1,a1),x94824),x94825)))+P24(f332(f49(x94822,f332(f332(f82(a1),x94821),x94823)),f332(f332(f267(a1,a1),f332(f332(f39(a1),x94824),x94823)),f332(f332(f81(a1),f332(f332(f82(a1),x94821),f45(a1,x94824,x94823))),x94825)))) % 165.30/165.05 [9490]~P24(f332(f332(f247(a868),f2(a868)),x94903))+~P24(f332(f332(f247(a868),f2(a868)),x94902))+~P24(f332(f48(x94901,x94902),f332(f332(f267(a868,a868),x94904),x94905)))+P24(f332(f48(x94901,f332(f332(f82(a868),x94902),x94903)),f332(f332(f267(a868,a868),f332(f332(f39(a868),x94904),x94903)),f332(f332(f81(a868),f332(f332(f82(a868),x94902),f45(a868,x94904,x94903))),x94905)))) % 165.30/165.05 [9539]~P73(x95391)+~P24(f332(f62(x95392),x95395))+~P24(f332(f62(x95392),x95394))+E(f332(f332(f82(x95391),f332(f332(f332(f66(x95391,x95392,f82(x95391)),x95393),f79(x95391)),f332(f332(f113(f875(x95392,a862)),x95394),x95395))),f332(f332(f332(f66(x95391,x95392,f82(x95391)),x95393),f79(x95391)),f332(f332(f104(f875(x95392,a862)),x95394),x95395))),f332(f332(f82(x95391),f332(f332(f332(f66(x95391,x95392,f82(x95391)),x95393),f79(x95391)),x95394)),f332(f332(f332(f66(x95391,x95392,f82(x95391)),x95393),f79(x95391)),x95395))) % 165.30/165.05 [9541]~E(f332(f332(f177(x95411),x95415),x95412),f332(f332(f177(x95411),x95415),x95413))+P24(f332(f332(f334(f874(f869(x95411),f869(x95411))),f332(f332(f267(f869(x95411),f869(x95411)),x95412),x95413)),f148(x95411,x95414)))+~P24(f332(f332(f247(a868),x95415),f332(f332(f244(a868),f332(f197(f869(x95411)),x95412)),f332(f197(f869(x95411)),x95413))))+~P24(f332(f332(f334(f874(x95411,x95411)),f332(f332(f267(x95411,x95411),f332(f332(f166(x95411),x95412),x95415)),f332(f332(f166(x95411),x95413),x95415))),x95414)) % 165.30/165.05 [9651]~P84(x96515)+~P142(x96515)+P24(f332(f332(f334(x96511),f350(x96512,x96513,x96514,x96511,x96515)),x96514))+P24(f332(f332(f246(x96515),f332(f332(f6(x96511,x96515),x96513),x96514)),f332(f332(f82(x96515),f332(f103(x96515),f332(f38(x96511),x96514))),x96512))) % 165.30/165.05 [9846]~P84(x98461)+~P142(x98461)+~P24(f332(f332(f246(x98461),f332(x98463,f350(x98465,x98463,x98464,x98462,x98461))),x98465))+P24(f332(f332(f246(x98461),f332(f332(f6(x98462,x98461),x98463),x98464)),f332(f332(f82(x98461),f332(f103(x98461),f332(f38(x98462),x98464))),x98465))) % 165.30/165.05 [8652]E(f332(f332(f135(x86521),x86522),x86523),f332(f332(f135(x86521),x86524),x86525))+~E(f332(f332(f177(x86521),f332(f197(f869(x86521)),x86522)),x86524),x86522)+~E(f332(f332(f135(x86521),f332(f332(f139(x86521),f332(f197(f869(x86521)),x86522)),x86524)),x86525),x86523)+P24(f332(f332(f246(a868),f332(f197(f869(x86521)),x86524)),f332(f197(f869(x86521)),x86522))) % 165.30/165.05 [8772]E(f332(f332(f135(x87721),x87722),x87723),f332(f332(f135(x87721),x87724),x87725))+~E(f332(f332(f177(x87721),f332(f197(f869(x87721)),x87722)),x87724),x87722)+~E(x87723,f332(f332(f135(x87721),f332(f332(f139(x87721),f332(f197(f869(x87721)),x87722)),x87724)),x87725))+~P24(f332(f332(f246(a868),f332(f197(f869(x87721)),x87722)),f332(f197(f869(x87721)),x87724))) % 165.30/165.05 [9980]~P24(f332(x99805,x99804))+~P24(f332(f62(x99802),f332(f252(x99802),x99805)))+P24(f332(f62(x99801),f332(f252(x99801),f332(f332(f7(x99801,x99802,a862),x99803),x99804))))+~P24(f332(f62(x99801),f332(f252(x99801),f332(f332(f8(f875(x99802,a862),a862,x99801),f88(x99802)),f332(f332(f8(f875(x99802,a862),f875(x99802,a862),x99801),f332(f18(x99802,a862,a862),f332(f332(f8(a862,f875(a862,a862),x99802),a330),x99805))),x99803))))) % 165.30/165.05 [8451]~P15(x84515,x84511,x84516,x84512)+E(f332(f74(x84511,x84511,x84511,f332(x84512,x84513)),f332(x84512,x84514)),f332(f74(x84511,x84511,x84511,f332(x84512,x84514)),f332(x84512,x84513)))+~P24(f332(f62(x84515),x84514))+~P24(f332(f62(x84515),x84513)) % 165.30/165.05 [7855]~P21(x78551,x78552,x78554,x78553)+~E(f332(x78554,x78556),x78555)+E(f332(f78(x78551,x78552,x78553,x78554),x78555),x78556)+~P24(f332(f332(f334(x78551),x78556),x78553)) % 165.30/165.05 [8046]~P16(x80466,x80461,x80464,x80462)+E(f332(f74(x80461,x80461,x80461,f332(x80462,x80463)),f332(x80464,x80465)),f332(x80462,x80463))+~P24(f332(f62(x80466),x80463))+~P24(f332(f332(f334(x80466),x80465),x80463)) % 165.30/165.05 [9223]~P15(x92233,x92231,x92236,x92232)+E(f332(f74(x92231,x92231,x92231,f332(x92232,f332(f332(f22(f875(x92233,a862)),x92234),f332(f332(f310(x92233),x92235),f196(f875(x92233,a862)))))),f332(x92236,x92235)),f332(x92232,x92234))+~P24(f332(f62(x92233),x92234))+~P24(f332(f332(f334(x92233),x92235),x92234)) % 165.30/165.05 [6941]~P29(x69411)+~E(f45(x69411,x69413,x69414),f45(x69411,x69416,x69414))+~E(f45(x69411,x69412,x69414),f45(x69411,x69415,x69414))+E(f45(x69411,f332(f332(f22(x69411),x69412),x69413),x69414),f45(x69411,f332(f332(f22(x69411),x69415),x69416),x69414)) % 165.30/165.05 [6942]~P28(x69421)+~E(f45(x69421,x69423,x69424),f45(x69421,x69426,x69424))+~E(f45(x69421,x69422,x69424),f45(x69421,x69425,x69424))+E(f45(x69421,f332(f332(f81(x69421),x69422),x69423),x69424),f45(x69421,f332(f332(f81(x69421),x69425),x69426),x69424)) % 165.30/165.05 [6943]~P28(x69431)+~E(f45(x69431,x69433,x69434),f45(x69431,x69436,x69434))+~E(f45(x69431,x69432,x69434),f45(x69431,x69435,x69434))+E(f45(x69431,f332(f332(f82(x69431),x69432),x69433),x69434),f45(x69431,f332(f332(f82(x69431),x69435),x69436),x69434)) % 165.30/165.05 [7751]~P12(x77511,x77512,x77513)+~P24(f332(f62(x77511),x77516))+E(f332(f332(f65(x77511,x77512,x77513),x77514),f332(f332(f310(x77511),x77515),x77516)),f332(f332(f65(x77511,x77512,x77513),f332(f332(x77513,x77515),x77514)),x77516))+P24(f332(f332(f334(x77511),x77515),x77516)) % 165.30/165.05 [7813]~P30(x78131)+P24(f332(f332(f246(x78131),x78132),f332(x78133,x78134)))+~P24(f332(f332(f334(x78135),x78134),x78136))+~P24(f332(f332(f246(x78131),x78132),f332(f332(f43(x78135,x78131),x78136),x78133))) % 165.30/165.05 [7970]~P12(x79701,x79702,x79703)+~P24(f332(f62(x79701),x79706))+E(f332(f332(f65(x79701,x79702,x79703),x79704),f332(f332(f310(x79701),x79705),x79706)),f332(f332(x79703,x79705),f332(f332(f65(x79701,x79702,x79703),x79704),x79706)))+P24(f332(f332(f334(x79701),x79705),x79706)) % 165.30/165.05 [8062]~P106(x80623)+~P24(f332(x80622,x80625))+~P32(x80623,f332(f332(f155(x80621,x80623),x80624),x80626))+E(f332(f137(x80621,x80622),f332(f332(f149(x80621,x80623,x80624),x80625),x80626)),f332(f332(f149(x80621,x80623,x80624),x80625),f332(f137(x80621,x80622),x80626))) % 165.30/165.05 [8084]E(x80841,x80842)+E(x80843,f2(a1))+~P24(f332(f49(x80844,x80843),f332(f332(f267(a1,a1),x80845),x80842)))+~P24(f332(f49(x80844,x80843),f332(f332(f267(a1,a1),x80846),x80841))) % 165.30/165.05 [8085]E(x80851,x80852)+E(x80853,f2(a1))+~P24(f332(f49(x80854,x80853),f332(f332(f267(a1,a1),x80852),x80855)))+~P24(f332(f49(x80854,x80853),f332(f332(f267(a1,a1),x80851),x80856))) % 165.30/165.05 [8105]~P15(x81052,x81055,x81056,x81051)+~P24(f332(f62(x81052),x81054))+E(f332(x81051,f332(f332(f310(x81052),x81053),x81054)),f332(f74(x81055,x81055,x81055,f332(x81051,x81054)),f332(x81056,x81053)))+P24(f332(f332(f334(x81052),x81053),x81054)) % 165.30/165.05 [8330]~P16(x83305,x83301,x83306,x83302)+E(f332(f74(x83301,x83301,x83301,f332(x83302,x83303)),f332(x83302,x83304)),f332(x83302,x83303))+~P24(f332(f62(x83305),x83303))+~P24(f332(f332(f246(f875(x83305,a862)),x83304),x83303)) % 165.30/165.05 [9418]~P21(x94181,x94182,x94184,x94183)+~P24(f332(f332(f334(x94182),x94185),f332(f311(x94181,x94182,x94184),x94183)))+P24(f332(f332(f334(x94181),f332(f78(x94181,x94182,x94183,x94184),x94185)),x94186))+~P24(f332(f332(f246(f875(x94181,a862)),x94183),x94186)) % 165.30/165.05 [9791]~P74(x97912)+~E(f526(x97911,x97913,x97915,x97916,x97914,x97912),f527(x97911,x97913,x97915,x97916,x97914,x97912))+~P24(f332(f62(x97914),x97916))+E(f332(f332(f6(x97911,x97912),x97913),f332(f311(x97914,x97911,x97915),x97916)),f332(f332(f6(x97914,x97912),f332(f74(x97911,x97912,x97914,x97913),x97915)),x97916)) % 165.30/165.05 [9828]~P74(x98286)+E(f332(x98281,f526(x98282,x98283,x98281,x98284,x98285,x98286)),f332(x98281,f527(x98282,x98283,x98281,x98284,x98285,x98286)))+E(f332(f332(f6(x98282,x98286),x98283),f332(f311(x98285,x98282,x98281),x98284)),f332(f332(f6(x98285,x98286),f332(f74(x98282,x98286,x98285,x98283),x98281)),x98284))+~P24(f332(f62(x98285),x98284)) % 165.30/165.05 [9868]~P74(x98682)+~E(f332(x98683,f332(x98685,f527(x98681,x98683,x98685,x98686,x98684,x98682))),f2(x98682))+~P24(f332(f62(x98684),x98686))+E(f332(f332(f6(x98681,x98682),x98683),f332(f311(x98684,x98681,x98685),x98686)),f332(f332(f6(x98684,x98682),f332(f74(x98681,x98682,x98684,x98683),x98685)),x98686)) % 165.30/165.05 [9926]~P74(x99262)+~P24(f332(f62(x99264),x99266))+E(f332(f332(f6(x99261,x99262),x99263),f332(f311(x99264,x99261,x99265),x99266)),f332(f332(f6(x99264,x99262),f332(f74(x99261,x99262,x99264,x99263),x99265)),x99266))+P24(f332(f332(f334(x99264),f527(x99261,x99263,x99265,x99266,x99264,x99262)),x99266)) % 165.30/165.05 [9927]~P74(x99272)+~P24(f332(f62(x99274),x99276))+E(f332(f332(f6(x99271,x99272),x99273),f332(f311(x99274,x99271,x99275),x99276)),f332(f332(f6(x99274,x99272),f332(f74(x99271,x99272,x99274,x99273),x99275)),x99276))+P24(f332(f332(f334(x99274),f526(x99271,x99273,x99275,x99276,x99274,x99272)),x99276)) % 165.30/165.05 [10038]~P73(x100381)+~P24(f332(f62(x100382),x100386))+E(f332(f332(f332(f66(x100381,x100382,f82(x100381)),f332(f332(f18(x100382,f875(x100383,a862),x100381),f332(f332(f7(x100382,x100381,f875(f875(x100383,a862),x100381)),f332(f332(f8(f875(x100383,x100381),f875(x100381,f875(f875(x100383,a862),x100381)),x100382),f66(x100381,x100383,f82(x100381))),x100384)),f79(x100381))),x100385)),f79(x100381)),x100386),f332(f332(f332(f66(x100381,f874(x100382,x100383),f82(x100381)),f332(f271(x100382,x100383,x100381),x100384)),f79(x100381)),f332(f332(f269(x100382,x100383),x100386),x100385)))+P24(f332(f332(f334(x100382),f579(x100384,x100385,x100383,x100386,x100382,x100381)),x100386)) % 165.30/165.05 [10056]~P73(x100561)+~P24(f332(f62(x100562),x100566))+E(f332(f332(f332(f66(x100561,x100562,f82(x100561)),f332(f332(f18(x100562,f875(x100563,a862),x100561),f332(f332(f7(x100562,x100561,f875(f875(x100563,a862),x100561)),f332(f332(f8(f875(x100563,x100561),f875(x100561,f875(f875(x100563,a862),x100561)),x100562),f66(x100561,x100563,f82(x100561))),x100564)),f79(x100561))),x100565)),f79(x100561)),x100566),f332(f332(f332(f66(x100561,f874(x100562,x100563),f82(x100561)),f332(f271(x100562,x100563,x100561),x100564)),f79(x100561)),f332(f332(f269(x100562,x100563),x100566),x100565)))+~P24(f332(f62(x100563),f332(x100565,f579(x100564,x100565,x100563,x100566,x100562,x100561)))) % 165.30/165.05 [8244]~P16(x82442,x82445,x82446,x82441)+~P24(f332(f62(x82442),x82444))+~P24(f332(f62(x82442),x82443))+E(f332(x82441,f332(f332(f113(f875(x82442,a862)),x82443),x82444)),f332(f74(x82445,x82445,x82445,f332(x82441,x82443)),f332(x82441,x82444))) % 165.30/165.05 [8452]~P30(x84521)+P24(f332(f332(f246(x84521),f332(x84522,x84523)),x84524))+~P24(f332(f332(f334(x84525),x84523),x84526))+~P24(f332(f332(f246(x84521),f332(f332(f42(x84525,x84521),x84526),x84522)),x84524)) % 165.30/165.05 [8851]~P21(x88512,x88511,x88513,x88516)+E(f332(f332(f22(f875(x88511,a862)),f332(f311(x88512,x88511,x88513),x88514)),f332(f311(x88512,x88511,x88513),x88515)),f332(f311(x88512,x88511,x88513),f332(f332(f22(f875(x88512,a862)),x88514),x88515)))+~P24(f332(f332(f246(f875(x88512,a862)),x88515),x88516))+~P24(f332(f332(f246(f875(x88512,a862)),x88514),x88516)) % 165.30/165.05 [8852]~P21(x88522,x88521,x88523,x88526)+E(f332(f332(f104(f875(x88521,a862)),f332(f311(x88522,x88521,x88523),x88524)),f332(f311(x88522,x88521,x88523),x88525)),f332(f311(x88522,x88521,x88523),f332(f332(f104(f875(x88522,a862)),x88524),x88525)))+~P24(f332(f332(f246(f875(x88522,a862)),x88525),x88526))+~P24(f332(f332(f246(f875(x88522,a862)),x88524),x88526)) % 165.30/165.05 [9108]E(x91081,x91082)+~P53(x91083,x91084,x91085)+~P24(f332(f332(f334(f874(x91083,x91084)),f332(f332(f267(x91083,x91084),x91086),x91082)),x91085))+~P24(f332(f332(f334(f874(x91083,x91084)),f332(f332(f267(x91083,x91084),x91086),x91081)),x91085)) % 165.30/165.05 [9863]~P71(x98631)+~E(f332(x98633,f488(x98634,x98636,x98633,x98635,x98632,x98631)),f332(x98636,f488(x98634,x98636,x98633,x98635,x98632,x98631)))+~P24(f332(f62(x98632),x98635))+E(f332(f332(f332(f66(x98631,x98632,f82(x98631)),x98633),x98634),x98635),f332(f332(f332(f66(x98631,x98632,f82(x98631)),x98636),x98634),x98635)) % 165.30/165.05 [9924]~P71(x99241)+~P24(f332(f62(x99242),x99245))+E(f332(f332(f332(f66(x99241,x99242,f82(x99241)),x99243),x99244),x99245),f332(f332(f332(f66(x99241,x99242,f82(x99241)),x99246),x99244),x99245))+P24(f332(f332(f334(x99242),f488(x99244,x99243,x99246,x99245,x99242,x99241)),x99245)) % 165.30/165.05 [8665]~P71(x86651)+~P24(f332(f62(x86652),x86656))+P24(f332(f332(f334(x86652),x86655),x86656))+E(f332(f332(f332(f66(x86651,x86652,f82(x86651)),x86653),x86654),f332(f332(f310(x86652),x86655),x86656)),f332(f332(f82(x86651),f332(x86653,x86655)),f332(f332(f332(f66(x86651,x86652,f82(x86651)),x86653),x86654),x86656))) % 165.30/165.05 [8711]~P6(x87111,x87116,x87113)+~P9(x87111,f875(x87112,a862),x87113,x87115)+~P24(f332(f332(f334(x87111),x87114),x87116))+E(f332(f332(f42(x87111,f875(x87112,a862)),f332(f286(x87111,x87111,x87113),f332(f332(f310(x87111),x87114),f196(f875(x87111,a862))))),x87115),f332(x87115,x87114)) % 165.30/165.05 [8828]~P12(x88283,x88284,x88281)+~P24(f332(f62(x88283),x88286))+~P24(f332(f332(f334(x88283),x88282),x88286))+E(f332(f332(x88281,x88282),f332(f332(f65(x88283,x88284,x88281),x88285),f332(f332(f22(f875(x88283,a862)),x88286),f332(f332(f310(x88283),x88282),f196(f875(x88283,a862)))))),f332(f332(f65(x88283,x88284,x88281),x88285),x88286)) % 165.30/165.05 [9119]~P15(x91193,x91191,x91196,x91192)+~P24(f332(f62(x91193),x91195))+~P24(f332(f62(x91193),x91194))+E(f332(f74(x91191,x91191,x91191,f332(x91192,f332(f332(f113(f875(x91193,a862)),x91194),x91195))),f332(x91192,f332(f332(f104(f875(x91193,a862)),x91194),x91195))),f332(f74(x91191,x91191,x91191,f332(x91192,x91194)),f332(x91192,x91195))) % 165.30/165.05 [9437]~E(x94373,f332(f332(f160(x94371,x94372),x94375),x94376))+P24(f332(f332(f334(f874(f869(x94371),f869(x94371))),f332(f332(f267(f869(x94371),f869(x94371)),x94372),x94373)),f158(x94371,x94374)))+~P24(f332(f332(f247(a868),x94375),f332(f197(f869(x94371)),x94372)))+~P24(f332(f332(f334(f874(x94371,x94371)),f332(f332(f267(x94371,x94371),f332(f332(f166(x94371),x94372),x94375)),x94376)),x94374)) % 165.30/165.05 [9937]~P74(x99372)+~P24(f332(f62(x99371),x99376))+P24(f332(f332(f334(x99371),f578(x99374,x99375,x99373,x99376,x99371,x99372)),x99376))+E(f332(f332(f6(x99371,x99372),f332(f332(f18(x99371,f875(x99373,a862),x99372),f332(f332(f8(f875(x99373,x99372),f875(f875(x99373,a862),x99372),x99371),f6(x99373,x99372)),x99374)),x99375)),x99376),f332(f332(f6(f874(x99371,x99373),x99372),f332(f271(x99371,x99373,x99372),x99374)),f332(f332(f269(x99371,x99373),x99376),x99375))) % 165.30/165.05 [9938]~P73(x99382)+~P24(f332(f62(x99381),x99386))+P24(f332(f332(f334(x99381),f576(x99384,x99385,x99383,x99386,x99381,x99382)),x99386))+E(f332(f332(f9(x99381,x99382),f332(f332(f18(x99381,f875(x99383,a862),x99382),f332(f332(f8(f875(x99383,x99382),f875(f875(x99383,a862),x99382),x99381),f9(x99383,x99382)),x99384)),x99385)),x99386),f332(f332(f9(f874(x99381,x99383),x99382),f332(f271(x99381,x99383,x99382),x99384)),f332(f332(f269(x99381,x99383),x99386),x99385))) % 165.30/165.05 [9978]~P74(x99782)+~P24(f332(f62(x99781),x99786))+~P24(f332(f62(x99783),f332(x99785,f578(x99784,x99785,x99783,x99786,x99781,x99782))))+E(f332(f332(f6(x99781,x99782),f332(f332(f18(x99781,f875(x99783,a862),x99782),f332(f332(f8(f875(x99783,x99782),f875(f875(x99783,a862),x99782),x99781),f6(x99783,x99782)),x99784)),x99785)),x99786),f332(f332(f6(f874(x99781,x99783),x99782),f332(f271(x99781,x99783,x99782),x99784)),f332(f332(f269(x99781,x99783),x99786),x99785))) % 165.30/165.05 [9979]~P73(x99792)+~P24(f332(f62(x99791),x99796))+~P24(f332(f62(x99793),f332(x99795,f576(x99794,x99795,x99793,x99796,x99791,x99792))))+E(f332(f332(f9(x99791,x99792),f332(f332(f18(x99791,f875(x99793,a862),x99792),f332(f332(f8(f875(x99793,x99792),f875(f875(x99793,a862),x99792),x99791),f9(x99793,x99792)),x99794)),x99795)),x99796),f332(f332(f9(f874(x99791,x99793),x99792),f332(f271(x99791,x99793,x99792),x99794)),f332(f332(f269(x99791,x99793),x99796),x99795))) % 165.30/165.05 [9960]~P73(x99602)+~P24(f332(f62(x99601),x99606))+P24(f332(f332(f334(x99601),x99603),x99606))+E(f332(f332(f9(x99601,x99602),f332(f332(f7(x99601,x99602,x99602),f332(f332(f18(x99601,x99602,f875(x99602,x99602)),f332(f332(f8(a862,f875(x99602,f875(x99602,x99602)),x99601),f99(x99602)),f332(f332(f7(x99601,x99601,a862),a329),x99603))),x99604)),x99605)),x99606),f332(f332(f257(x99602),x99605),f332(f38(x99601),x99606))) % 165.30/165.05 [9965]~P73(x99652)+~P24(f332(f62(x99651),x99656))+~P24(f332(f332(f334(x99651),x99653),x99656))+E(f332(f332(f9(x99651,x99652),f332(f332(f7(x99651,x99652,x99652),f332(f332(f18(x99651,x99652,f875(x99652,x99652)),f332(f332(f8(a862,f875(x99652,f875(x99652,x99652)),x99651),f99(x99652)),f332(f332(f7(x99651,x99651,a862),a329),x99653))),x99654)),x99655)),x99656),f332(f332(f82(x99652),f332(x99654,x99653)),f332(f332(f257(x99652),x99655),f332(f332(f22(a868),f332(f38(x99651),x99656)),f79(a868))))) % 165.30/165.05 [10031]~P24(f332(f62(x100311),x100315))+~P24(f332(f62(x100312),x100313))+P24(f332(f332(f334(x100312),f434(x100316,x100314,x100313,x100312,x100315,x100311)),x100313))+E(f332(f332(f6(x100311,a868),f332(f332(f8(f875(x100312,a862),a868,x100311),f38(x100312)),f332(f332(f8(f875(x100312,a862),f875(x100312,a862),x100311),f252(x100312)),f332(f332(f8(f875(x100312,a862),f875(x100312,a862),x100311),f332(f18(x100312,a862,a862),f332(f332(f8(a862,f875(a862,a862),x100312),a330),f332(f332(f7(x100312,f875(x100312,a862),a862),f334(x100312)),x100313)))),x100314)))),x100315),f332(f332(f82(a868),x100316),f332(f38(x100312),x100313))) % 165.30/165.05 [10032]~P24(f332(f62(x100321),x100325))+~P24(f332(f62(x100322),x100323))+P24(f332(f332(f334(x100322),f435(x100326,x100324,x100323,x100322,x100325,x100321)),x100323))+E(f332(f332(f6(x100321,a868),f332(f332(f8(f875(x100322,a862),a868,x100321),f38(x100322)),f332(f332(f8(f875(x100322,a862),f875(x100322,a862),x100321),f252(x100322)),f332(f332(f8(f875(x100322,a862),f875(x100322,a862),x100321),f332(f18(x100322,a862,a862),f332(f332(f8(a862,f875(a862,a862),x100322),a330),f332(f332(f7(x100322,f875(x100322,a862),a862),f334(x100322)),x100323)))),x100324)))),x100325),f332(f332(f6(x100322,a868),x100326),x100323)) % 165.30/165.05 [10062]~P24(f332(f62(x100622),x100623))+~P24(f332(f62(x100621),x100625))+~E(f332(f38(x100621),f332(f252(x100621),f332(f332(f18(x100621,a862,a862),f332(f332(f8(a862,f875(a862,a862),x100621),a330),f332(f332(f7(x100621,f875(x100621,a862),a862),f334(x100621)),x100625))),f332(f332(f7(x100621,x100622,a862),x100624),f434(x100626,x100624,x100623,x100622,x100625,x100621))))),x100626)+E(f332(f332(f6(x100621,a868),f332(f332(f8(f875(x100622,a862),a868,x100621),f38(x100622)),f332(f332(f8(f875(x100622,a862),f875(x100622,a862),x100621),f252(x100622)),f332(f332(f8(f875(x100622,a862),f875(x100622,a862),x100621),f332(f18(x100622,a862,a862),f332(f332(f8(a862,f875(a862,a862),x100622),a330),f332(f332(f7(x100622,f875(x100622,a862),a862),f334(x100622)),x100623)))),x100624)))),x100625),f332(f332(f82(a868),x100626),f332(f38(x100622),x100623))) % 165.30/165.05 [10064]~P24(f332(f62(x100642),x100643))+~P24(f332(f62(x100641),x100645))+~E(f332(f38(x100641),f332(f252(x100641),f332(f332(f18(x100641,a862,a862),f332(f332(f8(a862,f875(a862,a862),x100641),a330),f332(f332(f7(x100641,f875(x100641,a862),a862),f334(x100641)),x100645))),f332(f332(f7(x100641,x100642,a862),x100644),f435(x100646,x100644,x100643,x100642,x100645,x100641))))),f332(x100646,f435(x100646,x100644,x100643,x100642,x100645,x100641)))+E(f332(f332(f6(x100641,a868),f332(f332(f8(f875(x100642,a862),a868,x100641),f38(x100642)),f332(f332(f8(f875(x100642,a862),f875(x100642,a862),x100641),f252(x100642)),f332(f332(f8(f875(x100642,a862),f875(x100642,a862),x100641),f332(f18(x100642,a862,a862),f332(f332(f8(a862,f875(a862,a862),x100642),a330),f332(f332(f7(x100642,f875(x100642,a862),a862),f334(x100642)),x100643)))),x100644)))),x100645),f332(f332(f6(x100642,a868),x100646),x100643)) % 165.30/165.05 [9718]E(x97181,x97182)+~P12(x97183,x97184,x97185)+~P24(f332(f67(x97183,x97184,x97185,x97186,x97187),x97182))+~P24(f332(f67(x97183,x97184,x97185,x97186,x97187),x97181)) % 165.30/165.05 [9510]P24(f332(x95101,x95102))+~P24(f332(f332(f334(x95107),x95102),f332(x95106,x95104)))+~P24(f332(x95101,f467(x95101,x95106,x95105,x95103,x95107)))+~P24(f332(f332(f334(x95103),x95104),x95105)) % 165.30/165.05 [9952]~P12(x99527,x99526,x99521)+E(f332(f332(x99521,x99522),f768(x99522,x99523,x99524,x99525,x99521,x99526,x99527)),x99523)+~P24(f332(f67(x99527,x99526,x99521,x99525,x99524),x99523))+~P24(f332(f332(f334(x99527),x99522),x99524)) % 165.30/165.05 [10017]~P12(x100171,x100172,x100173)+~P24(f332(f67(x100171,x100172,x100173,x100174,x100175),x100177))+P24(f332(f67(x100171,x100172,x100173,x100174,f332(f332(f22(f875(x100171,a862)),x100175),f332(f332(f310(x100171),x100176),f196(f875(x100171,a862))))),f768(x100176,x100177,x100175,x100174,x100173,x100172,x100171)))+~P24(f332(f332(f334(x100171),x100176),x100175)) % 165.30/165.05 [9414]~P71(x94141)+~P21(x94145,x94142,x94146,x94147)+~P24(f332(f62(x94145),x94147))+E(f332(f332(f332(f66(x94141,x94142,f82(x94141)),x94143),x94144),f332(f311(x94145,x94142,x94146),x94147)),f332(f332(f332(f66(x94141,x94145,f82(x94141)),f332(f74(x94142,x94141,x94145,x94143),x94146)),x94144),x94147)) % 165.30/165.05 [9534]~E(f332(f332(f310(x95341),x95345),x95346),f332(f332(f310(x95341),x95342),x95343))+~P24(f332(f67(x95341,x95341,x95344,x95342,x95343),x95347))+P24(f332(f332(f334(x95341),x95342),x95343))+P24(f332(f63(x95341,x95344,f332(f332(f310(x95341),x95345),x95346)),x95347)) % 165.30/165.05 [9617]P24(f332(x96171,x96172))+~P24(f332(f332(f334(x96173),x96172),f332(x96174,x96177)))+~P24(f332(f332(f334(x96176),x96177),x96175))+P24(f332(f332(f334(x96173),f467(x96171,x96174,x96175,x96176,x96173)),f332(f332(f42(x96176,f875(x96173,a862)),x96175),x96174))) % 165.30/165.05 [9632]~P21(x96322,x96321,x96325,x96324)+~P21(x96321,x96323,x96326,f332(f311(x96322,x96321,x96325),x96324))+E(f332(f332(f74(x96321,x96322,x96323,f78(x96322,x96321,x96324,x96325)),f78(x96321,x96323,f332(f311(x96322,x96321,x96325),x96324),x96326)),x96327),f332(f78(x96322,x96323,x96324,f332(f74(x96321,x96323,x96322,x96326),x96325)),x96327))+~P24(f332(f332(f334(x96323),x96327),f332(f311(x96321,x96323,x96326),f332(f311(x96322,x96321,x96325),x96324)))) % 165.30/165.05 [9953]~P12(x99537,x99536,x99531)+E(f332(f332(x99531,x99532),f769(x99533,x99534,x99532,x99535,x99531,x99536,x99537)),x99533)+P24(f332(f332(f334(x99537),x99532),x99534))+~P24(f332(f67(x99537,x99536,x99531,x99535,f332(f332(f310(x99537),x99532),x99534)),x99533)) % 165.30/165.05 [10016]~P12(x100161,x100164,x100165)+P24(f332(f67(x100161,x100164,x100165,x100166,x100163),f769(x100167,x100163,x100162,x100166,x100165,x100164,x100161)))+P24(f332(f332(f334(x100161),x100162),x100163))+~P24(f332(f67(x100161,x100164,x100165,x100166,f332(f332(f310(x100161),x100162),x100163)),x100167)) % 165.30/165.05 [9700]E(x97001,f2(a1))+~P24(f332(f49(x97003,x97001),f332(f332(f267(a1,a1),x97005),x97007)))+~P24(f332(f49(x97002,x97001),f332(f332(f267(a1,a1),x97004),x97006)))+P24(f332(f49(f332(f332(f81(a1),x97002),x97003),x97001),f332(f332(f267(a1,a1),f332(f332(f81(a1),f332(f332(f81(a1),x97004),x97005)),f332(f332(f39(a1),f332(f332(f81(a1),x97006),x97007)),x97001))),f45(a1,f332(f332(f81(a1),x97006),x97007),x97001)))) % 165.30/165.05 [9702]~P24(f332(f332(f247(a868),f2(a868)),x97023))+~P24(f332(f48(x97022,x97023),f332(f332(f267(a868,a868),x97025),x97027)))+~P24(f332(f48(x97021,x97023),f332(f332(f267(a868,a868),x97024),x97026)))+P24(f332(f48(f332(f332(f81(a868),x97021),x97022),x97023),f332(f332(f267(a868,a868),f332(f332(f81(a868),f332(f332(f81(a868),x97024),x97025)),f332(f332(f39(a868),f332(f332(f81(a868),x97026),x97027)),x97023))),f45(a868,f332(f332(f81(a868),x97026),x97027),x97023)))) % 165.30/165.05 [10061]~P74(x100612)+~P24(f332(f62(x100613),x100615))+~P24(f332(f62(x100611),x100617))+E(f332(f332(f6(x100611,x100612),f332(f332(f18(x100611,f875(x100613,a862),x100612),f332(f332(f8(f875(x100613,x100612),f875(f875(x100613,a862),x100612),x100611),f6(x100613,x100612)),x100614)),f332(f332(f8(f875(x100613,a862),f875(x100613,a862),x100611),f252(x100613)),f332(f332(f8(f875(x100613,a862),f875(x100613,a862),x100611),f332(f18(x100613,a862,a862),f332(f332(f8(a862,f875(a862,a862),x100613),a330),f332(f332(f7(x100613,f875(x100613,a862),a862),f334(x100613)),x100615)))),x100616)))),x100617),f332(f332(f6(x100613,x100612),f332(f332(f18(x100613,f875(x100611,a862),x100612),f332(f332(f8(f875(x100611,x100612),f875(f875(x100611,a862),x100612),x100613),f6(x100611,x100612)),f332(f7(x100611,x100613,x100612),x100614))),f332(f332(f8(f875(x100611,a862),f875(x100611,a862),x100613),f252(x100611)),f332(f332(f8(f875(x100611,a862),f875(x100611,a862),x100613),f332(f18(x100611,a862,a862),f332(f332(f8(a862,f875(a862,a862),x100611),a330),f332(f332(f7(x100611,f875(x100611,a862),a862),f334(x100611)),x100617)))),f332(f7(x100611,x100613,a862),x100616))))),x100615)) % 165.30/165.05 [9570]~P18(x95707,x95706,x95701,x95708,x95702,x95704)+E(f332(f332(x95701,f332(x95702,x95703)),f332(x95704,x95705)),f332(x95704,x95705))+~P24(f332(f62(x95706),x95705))+~P24(f332(f332(f334(x95706),x95703),x95705)) % 165.30/165.05 [9574]~P10(x95746,x95741,x95742,x95748,x95743,x95744)+~P6(x95746,x95747,x95748)+P9(x95741,x95742,x95743,f332(x95744,x95745))+~P24(f332(f332(f334(x95746),x95745),x95747)) % 165.30/165.05 [9208]~P15(x92087,x92081,x92088,x92083)+~P24(f332(f62(x92087),x92085))+~P24(f332(f62(x92087),x92084))+E(f332(f74(x92081,x92081,x92082,f332(x92083,x92084)),f332(f74(x92081,x92081,x92082,f332(x92083,x92085)),x92086)),f332(f74(x92081,x92081,x92082,f332(x92083,x92085)),f332(f74(x92081,x92081,x92082,f332(x92083,x92084)),x92086))) % 165.30/165.05 [9216]~P38(x92161,x92162,x92163,x92164,x92167)+P38(x92161,x92162,x92163,f332(f332(f160(x92161,x92164),x92165),x92166),f332(f332(f160(x92162,x92167),x92165),x92168))+~P24(f332(f332(x92163,x92166),x92168))+~P24(f332(f332(f247(a868),x92165),f332(f197(f869(x92161)),x92164))) % 165.30/165.05 [9217]~P38(x92171,x92172,x92173,x92174,x92177)+P38(x92171,x92172,x92173,f332(f332(f160(x92171,x92174),x92175),x92176),f332(f332(f160(x92172,x92177),x92175),x92178))+~P24(f332(f332(x92173,x92176),x92178))+~P24(f332(f332(f247(a868),x92175),f332(f197(f869(x92172)),x92177))) % 165.30/165.05 [9291]~P21(x92912,x92912,x92915,x92916)+~P17(x92913,x92912,x92917,x92918,x92911)+~P24(f332(f62(x92912),x92916))+E(f332(f332(x92911,f332(f74(x92912,x92913,x92912,x92914),x92915)),x92916),f332(f332(x92911,x92914),f332(f311(x92912,x92912,x92915),x92916))) % 165.30/165.05 [9572]~P19(x95727,x95722,x95725,x95728,x95726,x95721)+~P24(f332(f62(x95722),x95724))+E(f332(x95721,f332(f332(f310(x95722),x95723),x95724)),f332(f332(x95725,f332(x95726,x95723)),f332(x95721,x95724)))+P24(f332(f332(f334(x95722),x95723),x95724)) % 165.30/165.05 [9583]~P18(x95836,x95835,x95831,x95837,x95838,x95832)+E(f332(f332(x95831,f332(x95832,x95833)),f332(x95832,x95834)),f332(x95832,x95834))+~P24(f332(f62(x95835),x95834))+~P24(f332(f332(f246(f875(x95835,a862)),x95833),x95834)) % 165.30/165.05 [9193]P24(f332(f332(f334(f874(f869(x91931),f869(x91931))),f332(f332(f267(f869(x91931),f869(x91931)),x91932),x91933)),f158(x91931,x91934)))+~E(x91933,f332(f332(f135(x91931),x91935),f332(f332(f152(x91931),x91936),x91937)))+~E(x91932,f332(f332(f135(x91931),x91935),f332(f332(f152(x91931),x91938),x91937)))+~P24(f332(f332(f334(f874(x91931,x91931)),f332(f332(f267(x91931,x91931),x91938),x91936)),x91934)) % 165.30/165.05 [9577]~P18(x95776,x95772,x95775,x95777,x95778,x95771)+~P24(f332(f62(x95772),x95774))+~P24(f332(f62(x95772),x95773))+E(f332(x95771,f332(f332(f113(f875(x95772,a862)),x95773),x95774)),f332(f332(x95775,f332(x95771,x95773)),f332(x95771,x95774))) % 165.30/165.05 [10099]~P21(x100994,x100992,x100995,x100998)+E(f332(f332(f43(x100991,f875(x100992,a862)),x100993),f332(f332(f8(f875(x100994,a862),f875(x100992,a862),x100991),f311(x100994,x100992,x100995)),x100996)),f332(f311(x100994,x100992,x100995),f332(f332(f43(x100991,f875(x100994,a862)),x100993),x100996)))+~P24(f332(f332(f334(x100991),x100997),x100993))+P24(f332(f332(f334(x100991),f634(x100997,x100996,x100993,x100991,x100998,x100995,x100992,x100994)),x100993)) % 165.30/165.05 [10123]~P21(x101234,x101232,x101235,x101237)+E(f332(f332(f43(x101231,f875(x101232,a862)),x101233),f332(f332(f8(f875(x101234,a862),f875(x101232,a862),x101231),f311(x101234,x101232,x101235)),x101236)),f332(f311(x101234,x101232,x101235),f332(f332(f43(x101231,f875(x101234,a862)),x101233),x101236)))+~P24(f332(f332(f334(x101231),x101238),x101233))+~P24(f332(f332(f246(f875(x101234,a862)),f332(x101236,f634(x101238,x101236,x101233,x101231,x101237,x101235,x101232,x101234))),x101237)) % 165.30/165.05 [9641]~P19(x96417,x96415,x96411,x96418,x96412,x96414)+~P24(f332(f62(x96415),x96416))+~P24(f332(f332(f334(x96415),x96413),x96416))+E(f332(f332(x96411,f332(x96412,x96413)),f332(x96414,f332(f332(f22(f875(x96415,a862)),x96416),f332(f332(f310(x96415),x96413),f196(f875(x96415,a862)))))),f332(x96414,x96416)) % 165.30/165.05 [9649]~P19(x96496,x96493,x96491,x96497,x96498,x96492)+~P24(f332(f62(x96493),x96495))+~P24(f332(f62(x96493),x96494))+E(f332(f332(x96491,f332(x96492,f332(f332(f113(f875(x96493,a862)),x96494),x96495))),f332(x96492,f332(f332(f104(f875(x96493,a862)),x96494),x96495))),f332(f332(x96491,f332(x96492,x96494)),f332(x96492,x96495))) % 165.30/165.05 [9742]P46(x97421,x97422,x97423,x97424,x97425,f332(f332(x97423,x97426),x97427))+~P46(x97421,x97422,x97423,x97424,f332(f332(f22(f875(x97421,a862)),x97425),f332(f332(f310(x97421),x97428),f196(f875(x97421,a862)))),x97429)+~E(f332(f332(x97423,x97426),x97427),f332(f332(x97423,x97428),x97429))+~P24(f332(f332(f334(x97421),x97428),x97425)) % 165.30/165.05 [10134]P20(x101341,x101342,f332(f332(f310(f867(x101341)),f332(f332(f332(f93(x101341),f332(x101343,f439(x101344,x101345,x101346,x101347,x101343,x101342,x101341,x101348,x101349))),f332(x101347,f439(x101344,x101345,x101346,x101347,x101343,x101342,x101341,x101348,x101349))),f332(x101346,f439(x101344,x101345,x101346,x101347,x101343,x101342,x101341,x101348,x101349)))),f196(f875(f867(x101341),a862))))+~P24(f332(f62(x101349),x101348))+~P20(x101341,x101342,f332(f311(x101349,f867(x101341),f332(f332(f18(x101349,f875(x101341,f875(a864,a862)),f867(x101341)),f332(f332(f18(x101349,a863,f875(f875(x101341,f875(a864,a862)),f867(x101341))),f332(f332(f8(f875(x101341,f875(a864,a862)),f875(a863,f875(f875(x101341,f875(a864,a862)),f867(x101341))),x101349),f93(x101341)),x101343)),x101347)),x101346)),x101348))+P20(x101341,x101342,f332(f311(x101349,f867(x101341),f332(f332(f18(x101349,f875(x101341,f875(a864,a862)),f867(x101341)),f332(f332(f18(x101349,a863,f875(f875(x101341,f875(a864,a862)),f867(x101341))),f332(f332(f8(f875(x101341,f875(a864,a862)),f875(a863,f875(f875(x101341,f875(a864,a862)),f867(x101341))),x101349),f93(x101341)),x101345)),x101347)),x101344)),x101348)) % 165.30/165.05 [10135]~P20(x101351,x101352,f332(f332(f310(f867(x101351)),f332(f332(f332(f93(x101351),f332(x101354,f439(x101356,x101354,x101358,x101355,x101359,x101352,x101351,x101357,x101353))),f332(x101355,f439(x101356,x101354,x101358,x101355,x101359,x101352,x101351,x101357,x101353))),f332(x101356,f439(x101356,x101354,x101358,x101355,x101359,x101352,x101351,x101357,x101353)))),f196(f875(f867(x101351),a862))))+~P24(f332(f62(x101353),x101357))+~P20(x101351,x101352,f332(f311(x101353,f867(x101351),f332(f332(f18(x101353,f875(x101351,f875(a864,a862)),f867(x101351)),f332(f332(f18(x101353,a863,f875(f875(x101351,f875(a864,a862)),f867(x101351))),f332(f332(f8(f875(x101351,f875(a864,a862)),f875(a863,f875(f875(x101351,f875(a864,a862)),f867(x101351))),x101353),f93(x101351)),x101359)),x101355)),x101358)),x101357))+P20(x101351,x101352,f332(f311(x101353,f867(x101351),f332(f332(f18(x101353,f875(x101351,f875(a864,a862)),f867(x101351)),f332(f332(f18(x101353,a863,f875(f875(x101351,f875(a864,a862)),f867(x101351))),f332(f332(f8(f875(x101351,f875(a864,a862)),f875(a863,f875(f875(x101351,f875(a864,a862)),f867(x101351))),x101353),f93(x101351)),x101354)),x101355)),x101356)),x101357)) % 165.30/165.05 [9675]~P10(x96756,x96757,x96758,x96759,x967510,x96751)+E(f332(f332(x96751,x96752),x96753),f332(f332(x96751,x96754),x96755))+~P24(f332(f332(f334(f874(x96757,x96757)),f332(f332(f267(x96757,x96757),x96753),x96755)),x967510))+~P24(f332(f332(f334(f874(x96756,x96756)),f332(f332(f267(x96756,x96756),x96752),x96754)),x96759)) % 165.30/165.05 [9293]~P26(x92932)+E(x92931,f196(f875(x92932,a862)))+~P24(f332(f62(x92932),x92931))+P24(f332(f332(f334(x92932),f10(x92932,x92931)),x92931))+~P24(f332(f332(f334(x92932),f332(f332(f113(x92932),f748(x92931,x92932)),f762(x92931,x92932))),f332(f332(f310(x92932),f748(x92931,x92932)),f332(f332(f310(x92932),f762(x92931,x92932)),f196(f875(x92932,a862)))))) % 165.30/165.05 [9294]~P26(x92942)+E(x92941,f196(f875(x92942,a862)))+~P24(f332(f62(x92942),x92941))+P24(f332(f332(f334(x92942),f11(x92942,x92941)),x92941))+~P24(f332(f332(f334(x92942),f332(f332(f104(x92942),f818(x92941,x92942)),f819(x92941,x92942))),f332(f332(f310(x92942),f818(x92941,x92942)),f332(f332(f310(x92942),f819(x92941,x92942)),f196(f875(x92942,a862)))))) % 165.30/165.05 [9324]~P71(x93242)+E(x93241,f196(f875(x93242,a862)))+~P24(f332(f62(x93242),x93241))+P24(f332(f332(f334(x93242),f332(f64(x93242,f82(x93242)),x93241)),x93241))+~P24(f332(f332(f334(x93242),f332(f332(f82(x93242),f838(x93241,x93242)),f839(x93241,x93242))),f332(f332(f310(x93242),f838(x93241,x93242)),f332(f332(f310(x93242),f839(x93241,x93242)),f196(f875(x93242,a862)))))) % 165.30/165.05 [9329]~P106(x93292)+E(x93291,f196(f875(x93292,a862)))+~P24(f332(f62(x93292),x93291))+P24(f332(f332(f334(x93292),f12(x93292,f244(x93292),x93291)),x93291))+~P24(f332(f332(f334(x93292),f332(f332(f244(x93292),f442(x93291,x93292)),f445(x93291,x93292))),f332(f332(f310(x93292),f442(x93291,x93292)),f332(f332(f310(x93292),f445(x93291,x93292)),f196(f875(x93292,a862)))))) % 165.30/165.05 [9330]~P106(x93302)+E(x93301,f196(f875(x93302,a862)))+~P24(f332(f62(x93302),x93301))+P24(f332(f332(f334(x93302),f13(x93302,f245(x93302),x93301)),x93301))+~P24(f332(f332(f334(x93302),f332(f332(f245(x93302),f443(x93301,x93302)),f444(x93301,x93302))),f332(f332(f310(x93302),f443(x93301,x93302)),f332(f332(f310(x93302),f444(x93301,x93302)),f196(f875(x93302,a862)))))) % 165.30/165.05 [6513]~P87(x65132)+E(x65131,f2(x65132))+~E(f332(f332(f81(x65132),x65133),x65131),f2(x65132))+~P24(f332(f332(f246(x65132),f2(x65132)),x65133))+~P24(f332(f332(f246(x65132),f2(x65132)),x65131)) % 165.30/165.05 [6514]~P87(x65142)+E(x65141,f2(x65142))+~E(f332(f332(f81(x65142),x65141),x65143),f2(x65142))+~P24(f332(f332(f246(x65142),f2(x65142)),x65143))+~P24(f332(f332(f246(x65142),f2(x65142)),x65141)) % 165.30/165.05 [7041]~P106(x70412)+~P32(x70412,x70411)+E(x70411,f116(x70412))+~P24(f332(f332(f334(x70412),x70413),f332(f174(x70412),f607(x70411,x70412))))+P24(f332(f332(f246(x70412),f648(x70411,x70412)),x70413)) % 165.30/165.05 [7207]~P106(x72071)+E(f15(x72071,x72072),x72073)+~P24(f332(f62(x72071),x72072))+~P24(f332(f332(f246(x72071),x72073),f487(x72073,x72072,x72071)))+~P24(f332(f332(f334(x72071),x72073),x72072)) % 165.30/165.05 [7238]~P106(x72381)+~P32(x72381,x72382)+~P32(x72381,x72383)+P32(x72381,f332(f332(f135(x72381),x72382),x72383))+P24(f332(f332(f334(x72381),f613(x72383,x72382,x72381)),f332(f174(x72381),x72382))) % 165.30/165.05 [7239]~P106(x72391)+~P32(x72391,x72392)+~P32(x72391,x72393)+P32(x72391,f332(f332(f135(x72391),x72392),x72393))+P24(f332(f332(f334(x72391),f614(x72393,x72392,x72391)),f332(f174(x72391),x72393))) % 165.30/165.05 [7295]~P106(x72951)+E(f14(x72951,x72952),x72953)+~P24(f332(f62(x72951),x72952))+P24(f332(f332(f334(x72951),f490(x72953,x72952,x72951)),x72952))+~P24(f332(f332(f334(x72951),x72953),x72952)) % 165.30/165.05 [7296]~P106(x72961)+E(f15(x72961,x72962),x72963)+~P24(f332(f62(x72961),x72962))+P24(f332(f332(f334(x72961),f487(x72963,x72962,x72961)),x72962))+~P24(f332(f332(f334(x72961),x72963),x72962)) % 165.30/165.05 [7873]~P106(x78731)+E(f14(x78731,x78732),x78733)+~P24(f332(f62(x78731),x78732))+~P24(f332(f332(f334(x78731),x78733),x78732))+~P24(f332(f332(f246(x78731),f490(x78733,x78732,x78731)),x78733)) % 165.30/165.05 [8192]~P106(x81921)+~P32(x81921,x81922)+~P32(x81921,x81923)+P32(x81921,f332(f332(f135(x81921),x81922),x81923))+~P24(f332(f332(f246(x81921),f613(x81923,x81922,x81921)),f614(x81923,x81922,x81921))) % 165.30/165.05 [8947]~P26(x89472)+E(x89471,f196(f875(x89472,a862)))+~E(f332(f332(f113(x89472),f332(x89473,f795(x89471,x89473,x89472))),f332(x89473,f807(x89471,x89473,x89472))),f332(x89473,f332(f332(f113(x89472),f795(x89471,x89473,x89472)),f807(x89471,x89473,x89472))))+E(f10(x89472,f332(f311(x89472,x89472,x89473),x89471)),f332(x89473,f10(x89472,x89471)))+~P24(f332(f62(x89472),x89471)) % 165.30/165.05 [8948]~P26(x89482)+E(x89481,f196(f875(x89482,a862)))+~E(f332(f332(f104(x89482),f332(x89483,f817(x89481,x89483,x89482))),f332(x89483,f820(x89481,x89483,x89482))),f332(x89483,f332(f332(f104(x89482),f817(x89481,x89483,x89482)),f820(x89481,x89483,x89482))))+E(f11(x89482,f332(f311(x89482,x89482,x89483),x89481)),f332(x89483,f11(x89482,x89481)))+~P24(f332(f62(x89482),x89481)) % 165.30/165.05 [8949]~P106(x89492)+E(x89491,f196(f875(x89492,a862)))+~E(f332(f332(f245(x89492),f332(x89493,f456(x89491,x89493,x89492))),f332(x89493,f461(x89491,x89493,x89492))),f332(x89493,f332(f332(f245(x89492),f456(x89491,x89493,x89492)),f461(x89491,x89493,x89492))))+E(f14(x89492,f332(f311(x89492,x89492,x89493),x89491)),f332(x89493,f14(x89492,x89491)))+~P24(f332(f62(x89492),x89491)) % 165.30/165.05 [8950]~P106(x89502)+E(x89501,f196(f875(x89502,a862)))+~E(f332(f332(f244(x89502),f332(x89503,f462(x89501,x89503,x89502))),f332(x89503,f463(x89501,x89503,x89502))),f332(x89503,f332(f332(f244(x89502),f462(x89501,x89503,x89502)),f463(x89501,x89503,x89502))))+E(f15(x89502,f332(f311(x89502,x89502,x89503),x89501)),f332(x89503,f15(x89502,x89501)))+~P24(f332(f62(x89502),x89501)) % 165.30/165.05 [9019]~P106(x90192)+E(x90191,f196(f875(x90192,a862)))+~E(f332(f332(f244(x90192),f332(x90193,f457(x90191,x90193,x90192))),f332(x90193,f460(x90191,x90193,x90192))),f332(x90193,f332(f332(f244(x90192),f457(x90191,x90193,x90192)),f460(x90191,x90193,x90192))))+E(f12(x90192,f244(x90192),f332(f311(x90192,x90192,x90193),x90191)),f332(x90193,f12(x90192,f244(x90192),x90191)))+~P24(f332(f62(x90192),x90191)) % 165.30/165.05 [9020]~P106(x90202)+E(x90201,f196(f875(x90202,a862)))+~E(f332(f332(f245(x90202),f332(x90203,f458(x90201,x90203,x90202))),f332(x90203,f459(x90201,x90203,x90202))),f332(x90203,f332(f332(f245(x90202),f458(x90201,x90203,x90202)),f459(x90201,x90203,x90202))))+E(f13(x90202,f245(x90202),f332(f311(x90202,x90202,x90203),x90201)),f332(x90203,f13(x90202,f245(x90202),x90201)))+~P24(f332(f62(x90202),x90201)) % 165.30/165.05 [6529]~P71(x65292)+E(x65291,f196(f875(x65292,a862)))+~P24(f332(f62(x65292),x65291))+E(f332(f64(x65292,f82(x65292)),f332(f332(f310(x65292),x65293),x65291)),f332(f332(f82(x65292),x65293),f332(f64(x65292,f82(x65292)),x65291)))+P24(f332(f332(f334(x65292),x65293),x65291)) % 165.30/165.05 [7047]~P26(x70472)+E(f332(f332(f113(x70472),f10(x70472,x70471)),f10(x70472,x70473)),f10(x70472,x70473))+E(x70471,f196(f875(x70472,a862)))+~P24(f332(f62(x70472),x70473))+~P24(f332(f332(f246(f875(x70472,a862)),x70471),x70473)) % 165.30/165.05 [7048]~P26(x70482)+E(f332(f332(f104(x70482),f11(x70482,x70481)),f11(x70482,x70483)),f11(x70482,x70483))+E(x70481,f196(f875(x70482,a862)))+~P24(f332(f62(x70482),x70483))+~P24(f332(f332(f246(f875(x70482,a862)),x70481),x70483)) % 165.30/165.05 [7049]~P106(x70492)+E(f332(f332(f244(x70492),f15(x70492,x70491)),f15(x70492,x70493)),f15(x70492,x70493))+E(x70491,f196(f875(x70492,a862)))+~P24(f332(f62(x70492),x70493))+~P24(f332(f332(f246(f875(x70492,a862)),x70491),x70493)) % 165.30/165.05 [7050]~P106(x70502)+E(f332(f332(f245(x70502),f14(x70502,x70501)),f14(x70502,x70503)),f14(x70502,x70503))+E(x70501,f196(f875(x70502,a862)))+~P24(f332(f62(x70502),x70503))+~P24(f332(f332(f246(f875(x70502,a862)),x70501),x70503)) % 165.30/165.05 [7344]~P106(x73442)+E(x73441,f196(f875(x73442,a862)))+~P24(f332(f62(x73442),x73443))+P24(f332(f332(f246(x73442),f14(x73442,x73441)),f14(x73442,x73443)))+~P24(f332(f332(f246(f875(x73442,a862)),x73441),x73443)) % 165.30/165.05 [7345]~P106(x73452)+E(x73451,f196(f875(x73452,a862)))+~P24(f332(f62(x73452),x73453))+P24(f332(f332(f246(x73452),f15(x73452,x73453)),f15(x73452,x73451)))+~P24(f332(f332(f246(f875(x73452,a862)),x73451),x73453)) % 165.30/165.05 [7404]~P26(x74041)+E(f10(x74041,x74042),x74043)+~P24(f332(f62(x74041),x74042))+~E(f332(f332(f22(f875(x74041,a862)),x74042),f332(f332(f310(x74041),x74043),f196(f875(x74041,a862)))),f196(f875(x74041,a862)))+~P24(f332(f332(f334(x74041),x74043),x74042)) % 165.30/165.05 [7405]~P26(x74051)+E(f11(x74051,x74052),x74053)+~P24(f332(f62(x74051),x74052))+~E(f332(f332(f22(f875(x74051,a862)),x74052),f332(f332(f310(x74051),x74053),f196(f875(x74051,a862)))),f196(f875(x74051,a862)))+~P24(f332(f332(f334(x74051),x74053),x74052)) % 165.30/165.05 [7406]~P106(x74061)+E(f14(x74061,x74062),x74063)+~P24(f332(f62(x74061),x74062))+~E(f332(f332(f22(f875(x74061,a862)),x74062),f332(f332(f310(x74061),x74063),f196(f875(x74061,a862)))),f196(f875(x74061,a862)))+~P24(f332(f332(f334(x74061),x74063),x74062)) % 165.30/165.05 [7407]~P106(x74071)+E(f15(x74071,x74072),x74073)+~P24(f332(f62(x74071),x74072))+~E(f332(f332(f22(f875(x74071,a862)),x74072),f332(f332(f310(x74071),x74073),f196(f875(x74071,a862)))),f196(f875(x74071,a862)))+~P24(f332(f332(f334(x74071),x74073),x74072)) % 165.30/165.05 [7505]~P106(x75051)+E(f12(x75051,f244(x75051),x75052),x75053)+~P24(f332(f62(x75051),x75052))+~E(f332(f332(f22(f875(x75051,a862)),x75052),f332(f332(f310(x75051),x75053),f196(f875(x75051,a862)))),f196(f875(x75051,a862)))+~P24(f332(f332(f334(x75051),x75053),x75052)) % 165.30/165.05 [7506]~P106(x75061)+E(f13(x75061,f245(x75061),x75062),x75063)+~P24(f332(f62(x75061),x75062))+~E(f332(f332(f22(f875(x75061,a862)),x75062),f332(f332(f310(x75061),x75063),f196(f875(x75061,a862)))),f196(f875(x75061,a862)))+~P24(f332(f332(f334(x75061),x75063),x75062)) % 165.30/165.05 [7543]~P100(x75432)+E(x75431,f196(f875(x75432,a862)))+~P24(f332(f62(x75432),x75431))+~P24(f332(f332(f246(x75432),x75433),f825(x75433,x75431,x75432)))+P24(f332(f332(f246(x75432),x75433),f332(f64(x75432,f104(x75432)),x75431))) % 165.30/165.05 [7544]~P106(x75442)+E(x75441,f196(f875(x75442,a862)))+~P24(f332(f62(x75442),x75441))+~P24(f332(f332(f246(x75442),x75443),f428(x75443,x75441,x75442)))+P24(f332(f332(f246(x75442),x75443),f332(f64(x75442,f244(x75442)),x75441))) % 165.30/165.05 [7545]~P106(x75452)+E(x75451,f196(f875(x75452,a862)))+~P24(f332(f62(x75452),x75451))+~P24(f332(f332(f247(x75452),x75453),f437(x75453,x75451,x75452)))+P24(f332(f332(f247(x75452),x75453),f332(f64(x75452,f244(x75452)),x75451))) % 165.30/165.05 [7630]~P100(x76302)+E(x76301,f196(f875(x76302,a862)))+~P24(f332(f62(x76302),x76301))+P24(f332(f332(f334(x76302),f825(x76303,x76301,x76302)),x76301))+P24(f332(f332(f246(x76302),x76303),f332(f64(x76302,f104(x76302)),x76301))) % 165.30/165.05 [7631]~P106(x76312)+E(x76311,f196(f875(x76312,a862)))+~P24(f332(f62(x76312),x76311))+P24(f332(f332(f334(x76312),f428(x76313,x76311,x76312)),x76311))+P24(f332(f332(f246(x76312),x76313),f332(f64(x76312,f244(x76312)),x76311))) % 165.30/165.05 [7632]~P106(x76322)+E(x76321,f196(f875(x76322,a862)))+~P24(f332(f62(x76322),x76321))+P24(f332(f332(f334(x76322),f437(x76323,x76321,x76322)),x76321))+P24(f332(f332(f247(x76322),x76323),f332(f64(x76322,f244(x76322)),x76321))) % 165.30/165.05 [7753]~P106(x77532)+E(x77531,f196(f875(x77532,a862)))+E(f332(f332(f244(x77532),f12(x77532,f244(x77532),x77531)),f12(x77532,f244(x77532),x77533)),f12(x77532,f244(x77532),x77533))+~P24(f332(f62(x77532),x77533))+~P24(f332(f332(f246(f875(x77532,a862)),x77531),x77533)) % 165.30/165.05 [7754]~P106(x77542)+E(x77541,f196(f875(x77542,a862)))+E(f332(f332(f245(x77542),f13(x77542,f245(x77542),x77541)),f13(x77542,f245(x77542),x77543)),f13(x77542,f245(x77542),x77543))+~P24(f332(f62(x77542),x77543))+~P24(f332(f332(f246(f875(x77542,a862)),x77541),x77543)) % 165.30/165.05 [7951]~E(f661(x79511,x79513,x79512),f653(x79511,x79513,x79512))+~E(f332(f38(x79512),f654(x79511,x79513,x79512)),x79511)+E(f332(f332(f82(a868),x79511),f332(f38(f875(x79512,a862)),x79513)),f332(f38(x79512),f40(f875(x79512,a862),x79513)))+~P24(f332(f62(x79512),f40(f875(x79512,a862),x79513)))+~P24(f332(f62(f875(x79512,a862)),x79513)) % 165.30/165.05 [8126]~P106(x81262)+E(x81261,f196(f875(x81262,a862)))+~P24(f332(f62(x81262),x81263))+P24(f332(f332(f246(x81262),f332(f64(x81262,f244(x81262)),x81263)),f332(f64(x81262,f244(x81262)),x81261)))+~P24(f332(f332(f246(f875(x81262,a862)),x81261),x81263)) % 165.30/165.05 [8425]~E(f661(x84251,x84253,x84252),f653(x84251,x84253,x84252))+E(f332(f332(f82(a868),x84251),f332(f38(f875(x84252,a862)),x84253)),f332(f38(x84252),f40(f875(x84252,a862),x84253)))+P24(f332(f332(f334(f875(x84252,a862)),f654(x84251,x84253,x84252)),x84253))+~P24(f332(f62(x84252),f40(f875(x84252,a862),x84253)))+~P24(f332(f62(f875(x84252,a862)),x84253)) % 165.30/165.05 [8448]~E(f332(f38(x84482),f654(x84481,x84483,x84482)),x84481)+E(f332(f332(f82(a868),x84481),f332(f38(f875(x84482,a862)),x84483)),f332(f38(x84482),f40(f875(x84482,a862),x84483)))+P24(f332(f332(f334(f875(x84482,a862)),f653(x84481,x84483,x84482)),x84483))+~P24(f332(f62(x84482),f40(f875(x84482,a862),x84483)))+~P24(f332(f62(f875(x84482,a862)),x84483)) % 165.30/165.05 [8449]~E(f332(f38(x84492),f654(x84491,x84493,x84492)),x84491)+E(f332(f332(f82(a868),x84491),f332(f38(f875(x84492,a862)),x84493)),f332(f38(x84492),f40(f875(x84492,a862),x84493)))+P24(f332(f332(f334(f875(x84492,a862)),f661(x84491,x84493,x84492)),x84493))+~P24(f332(f62(x84492),f40(f875(x84492,a862),x84493)))+~P24(f332(f62(f875(x84492,a862)),x84493)) % 165.30/165.05 [8474]~E(f332(f38(x84742),f654(x84741,x84743,x84742)),x84741)+~E(f332(f332(f104(f875(x84742,a862)),f653(x84741,x84743,x84742)),f661(x84741,x84743,x84742)),f196(f875(x84742,a862)))+E(f332(f332(f82(a868),x84741),f332(f38(f875(x84742,a862)),x84743)),f332(f38(x84742),f40(f875(x84742,a862),x84743)))+~P24(f332(f62(f875(x84742,a862)),x84743))+~P24(f332(f62(x84742),f40(f875(x84742,a862),x84743))) % 165.30/165.05 [8716]E(f332(f332(f82(a868),x87161),f332(f38(f875(x87162,a862)),x87163)),f332(f38(x87162),f40(f875(x87162,a862),x87163)))+P24(f332(f332(f334(f875(x87162,a862)),f654(x87161,x87163,x87162)),x87163))+P24(f332(f332(f334(f875(x87162,a862)),f653(x87161,x87163,x87162)),x87163))+~P24(f332(f62(f875(x87162,a862)),x87163))+~P24(f332(f62(x87162),f40(f875(x87162,a862),x87163))) % 165.30/165.05 [8717]E(f332(f332(f82(a868),x87171),f332(f38(f875(x87172,a862)),x87173)),f332(f38(x87172),f40(f875(x87172,a862),x87173)))+P24(f332(f332(f334(f875(x87172,a862)),f654(x87171,x87173,x87172)),x87173))+P24(f332(f332(f334(f875(x87172,a862)),f661(x87171,x87173,x87172)),x87173))+~P24(f332(f62(f875(x87172,a862)),x87173))+~P24(f332(f62(x87172),f40(f875(x87172,a862),x87173))) % 165.30/165.05 [8742]~E(f332(f332(f104(f875(x87422,a862)),f653(x87421,x87423,x87422)),f661(x87421,x87423,x87422)),f196(f875(x87422,a862)))+E(f332(f332(f82(a868),x87421),f332(f38(f875(x87422,a862)),x87423)),f332(f38(x87422),f40(f875(x87422,a862),x87423)))+~P24(f332(f62(f875(x87422,a862)),x87423))+P24(f332(f332(f334(f875(x87422,a862)),f654(x87421,x87423,x87422)),x87423))+~P24(f332(f62(x87422),f40(f875(x87422,a862),x87423))) % 165.30/165.05 [8994]~P95(x89942)+E(x89941,f196(f875(x89942,a862)))+~E(f332(f332(f82(x89942),f332(x89943,f837(x89941,x89943,x89942))),f332(x89943,f840(x89941,x89943,x89942))),f332(x89943,f332(f332(f82(x89942),f837(x89941,x89943,x89942)),f840(x89941,x89943,x89942))))+~P24(f332(f62(x89942),x89941))+E(f332(f64(x89942,f82(x89942)),f332(f311(x89942,x89942,x89943),x89941)),f332(x89943,f332(f64(x89942,f82(x89942)),x89941))) % 165.30/165.05 [9898]P24(f332(f332(x98981,x98982),x98983))+P24(f332(f332(f247(a1),f505(x98981,x98983,x98982)),f507(x98981,x98983,x98982)))+P24(f332(f332(f246(a1),f507(x98981,x98983,x98982)),f2(a1)))+P24(f332(f332(x98981,f505(x98981,x98983,x98982)),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f507(x98981,x98983,x98982))))+~P24(f332(f320(f874(a1,a1),a57),f332(f332(f267(a1,a1),x98982),x98983))) % 165.30/165.05 [9904]P24(f332(f332(x99041,x99042),x99043))+P24(f332(f332(f246(a1),f504(x99041,x99043,x99042)),f2(a1)))+P24(f332(f332(x99041,f503(x99041,x99043,x99042)),f332(f332(f82(a1),f332(f106(a1),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f504(x99041,x99043,x99042))))+P24(f332(f332(f246(a1),f2(a1)),f332(f332(f81(a1),f503(x99041,x99043,x99042)),f504(x99041,x99043,x99042))))+~P24(f332(f320(f874(a1,a1),a52),f332(f332(f267(a1,a1),x99042),x99043))) % 165.30/165.05 [7922]~P118(x79221)+~P24(f332(f332(f246(x79221),x79222),f79(x79221)))+~P24(f332(f332(f246(x79221),f2(x79221)),x79222))+~P24(f332(f332(f246(x79221),f2(x79221)),x79223))+P24(f332(f332(f246(x79221),f332(f332(f82(x79221),x79222),x79223)),x79223)) % 165.30/165.05 [7923]~P118(x79231)+~P24(f332(f332(f246(x79231),x79233),f79(x79231)))+~P24(f332(f332(f246(x79231),f2(x79231)),x79233))+~P24(f332(f332(f246(x79231),f2(x79231)),x79232))+P24(f332(f332(f246(x79231),f332(f332(f82(x79231),x79232),x79233)),x79232)) % 165.30/165.05 [8274]~P106(x82742)+E(x82741,f196(f875(x82742,a862)))+~P24(f332(f62(x82742),x82741))+P24(f332(f332(f246(x82742),f436(x82743,x82741,x82742)),x82743))+~P24(f332(f332(f246(x82742),f332(f64(x82742,f244(x82742)),x82741)),x82743)) % 165.30/165.05 [8275]~P106(x82752)+E(x82751,f196(f875(x82752,a862)))+~P24(f332(f62(x82752),x82751))+P24(f332(f332(f334(x82752),f436(x82753,x82751,x82752)),x82751))+~P24(f332(f332(f246(x82752),f332(f64(x82752,f244(x82752)),x82751)),x82753)) % 165.30/165.05 [8276]~P106(x82762)+E(x82761,f196(f875(x82762,a862)))+~P24(f332(f62(x82762),x82761))+P24(f332(f332(f334(x82762),f438(x82763,x82761,x82762)),x82761))+~P24(f332(f332(f247(x82762),f332(f64(x82762,f244(x82762)),x82761)),x82763)) % 165.30/165.05 [8277]~P106(x82772)+E(x82771,f196(f875(x82772,a862)))+~P24(f332(f62(x82772),x82771))+P24(f332(f332(f247(x82772),f438(x82773,x82771,x82772)),x82773))+~P24(f332(f332(f247(x82772),f332(f64(x82772,f244(x82772)),x82771)),x82773)) % 165.30/165.05 [8361]~P24(f332(x83611,x83613))+P24(f332(x83611,f402(x83611,x83612)))+P24(f332(x83611,f398(x83611,x83612)))+~P24(f332(f332(f247(a1),f2(a1)),x83612))+P24(f332(x83611,f332(f332(f22(a1),f398(x83611,x83612)),f332(f332(f82(a1),f403(x83611,x83612)),x83612)))) % 165.30/165.05 [8569]~P24(f332(x85691,x85693))+P24(f332(x85691,f398(x85691,x85692)))+~P24(f332(f332(f247(a1),f2(a1)),x85692))+P24(f332(f332(f334(a1),f402(x85691,x85692)),f303(a1,f79(a1),x85692)))+P24(f332(x85691,f332(f332(f22(a1),f398(x85691,x85692)),f332(f332(f82(a1),f403(x85691,x85692)),x85692)))) % 165.30/165.05 [8764]~P24(f332(x87641,x87643))+~P24(f332(x87641,f398(x87641,x87642)))+P24(f332(x87641,f402(x87641,x87642)))+~P24(f332(f332(f247(a1),f2(a1)),x87642))+~P24(f332(x87641,f332(f332(f22(a1),f398(x87641,x87642)),f332(f332(f82(a1),f403(x87641,x87642)),x87642)))) % 165.30/165.05 [8887]~P24(f332(x88871,x88873))+~P24(f332(x88871,f398(x88871,x88872)))+~P24(f332(f332(f247(a1),f2(a1)),x88872))+P24(f332(f332(f334(a1),f402(x88871,x88872)),f303(a1,f79(a1),x88872)))+~P24(f332(x88871,f332(f332(f22(a1),f398(x88871,x88872)),f332(f332(f82(a1),f403(x88871,x88872)),x88872)))) % 165.30/165.05 [8676]~P26(x86761)+~P24(f332(f62(x86761),x86762))+E(f332(f332(f22(f875(x86761,a862)),x86762),f332(f332(f310(x86761),x86763),f196(f875(x86761,a862)))),f196(f875(x86761,a862)))+~P24(f332(f332(f334(x86761),x86763),x86762))+E(f332(f332(f113(x86761),x86763),f10(x86761,f332(f332(f22(f875(x86761,a862)),x86762),f332(f332(f310(x86761),x86763),f196(f875(x86761,a862)))))),f10(x86761,x86762)) % 165.30/165.05 [8677]~P26(x86771)+~P24(f332(f62(x86771),x86772))+E(f332(f332(f22(f875(x86771,a862)),x86772),f332(f332(f310(x86771),x86773),f196(f875(x86771,a862)))),f196(f875(x86771,a862)))+~P24(f332(f332(f334(x86771),x86773),x86772))+E(f332(f332(f104(x86771),x86773),f11(x86771,f332(f332(f22(f875(x86771,a862)),x86772),f332(f332(f310(x86771),x86773),f196(f875(x86771,a862)))))),f11(x86771,x86772)) % 165.30/165.05 [8678]~P106(x86781)+~P24(f332(f62(x86781),x86782))+E(f332(f332(f22(f875(x86781,a862)),x86782),f332(f332(f310(x86781),x86783),f196(f875(x86781,a862)))),f196(f875(x86781,a862)))+~P24(f332(f332(f334(x86781),x86783),x86782))+E(f332(f332(f245(x86781),x86783),f14(x86781,f332(f332(f22(f875(x86781,a862)),x86782),f332(f332(f310(x86781),x86783),f196(f875(x86781,a862)))))),f14(x86781,x86782)) % 165.30/165.05 [8679]~P106(x86791)+~P24(f332(f62(x86791),x86792))+E(f332(f332(f22(f875(x86791,a862)),x86792),f332(f332(f310(x86791),x86793),f196(f875(x86791,a862)))),f196(f875(x86791,a862)))+~P24(f332(f332(f334(x86791),x86793),x86792))+E(f332(f332(f244(x86791),x86793),f15(x86791,f332(f332(f22(f875(x86791,a862)),x86792),f332(f332(f310(x86791),x86793),f196(f875(x86791,a862)))))),f15(x86791,x86792)) % 165.30/165.05 [8736]~P106(x87361)+~P24(f332(f62(x87361),x87362))+E(f332(f332(f22(f875(x87361,a862)),x87362),f332(f332(f310(x87361),x87363),f196(f875(x87361,a862)))),f196(f875(x87361,a862)))+~P24(f332(f332(f334(x87361),x87363),x87362))+E(f332(f332(f244(x87361),x87363),f12(x87361,f244(x87361),f332(f332(f22(f875(x87361,a862)),x87362),f332(f332(f310(x87361),x87363),f196(f875(x87361,a862)))))),f12(x87361,f244(x87361),x87362)) % 165.30/165.05 [8737]~P106(x87371)+~P24(f332(f62(x87371),x87372))+E(f332(f332(f22(f875(x87371,a862)),x87372),f332(f332(f310(x87371),x87373),f196(f875(x87371,a862)))),f196(f875(x87371,a862)))+~P24(f332(f332(f334(x87371),x87373),x87372))+E(f332(f332(f245(x87371),x87373),f13(x87371,f245(x87371),f332(f332(f22(f875(x87371,a862)),x87372),f332(f332(f310(x87371),x87373),f196(f875(x87371,a862)))))),f13(x87371,f245(x87371),x87372)) % 165.30/165.05 [8751]~P26(x87511)+~P24(f332(f62(x87511),x87513))+~P24(f332(f62(x87511),x87512))+E(f332(f332(f104(f875(x87511,a862)),x87512),x87513),f196(f875(x87511,a862)))+E(f332(f332(f113(x87511),f10(x87511,f332(f332(f113(f875(x87511,a862)),x87512),x87513))),f10(x87511,f332(f332(f104(f875(x87511,a862)),x87512),x87513))),f332(f332(f113(x87511),f10(x87511,x87512)),f10(x87511,x87513))) % 165.30/165.05 [8752]~P26(x87521)+~P24(f332(f62(x87521),x87523))+~P24(f332(f62(x87521),x87522))+E(f332(f332(f104(f875(x87521,a862)),x87522),x87523),f196(f875(x87521,a862)))+E(f332(f332(f104(x87521),f11(x87521,f332(f332(f113(f875(x87521,a862)),x87522),x87523))),f11(x87521,f332(f332(f104(f875(x87521,a862)),x87522),x87523))),f332(f332(f104(x87521),f11(x87521,x87522)),f11(x87521,x87523))) % 165.30/165.05 [8753]~P106(x87531)+~P24(f332(f62(x87531),x87533))+~P24(f332(f62(x87531),x87532))+E(f332(f332(f104(f875(x87531,a862)),x87532),x87533),f196(f875(x87531,a862)))+E(f332(f332(f244(x87531),f15(x87531,f332(f332(f113(f875(x87531,a862)),x87532),x87533))),f15(x87531,f332(f332(f104(f875(x87531,a862)),x87532),x87533))),f332(f332(f244(x87531),f15(x87531,x87532)),f15(x87531,x87533))) % 165.30/165.05 [8754]~P106(x87541)+~P24(f332(f62(x87541),x87543))+~P24(f332(f62(x87541),x87542))+E(f332(f332(f104(f875(x87541,a862)),x87542),x87543),f196(f875(x87541,a862)))+E(f332(f332(f245(x87541),f14(x87541,f332(f332(f113(f875(x87541,a862)),x87542),x87543))),f14(x87541,f332(f332(f104(f875(x87541,a862)),x87542),x87543))),f332(f332(f245(x87541),f14(x87541,x87542)),f14(x87541,x87543))) % 165.30/165.05 [8966]~P106(x89661)+~P24(f332(f62(x89661),x89663))+~P24(f332(f62(x89661),x89662))+E(f332(f332(f104(f875(x89661,a862)),x89662),x89663),f196(f875(x89661,a862)))+E(f332(f332(f244(x89661),f12(x89661,f244(x89661),f332(f332(f113(f875(x89661,a862)),x89662),x89663))),f12(x89661,f244(x89661),f332(f332(f104(f875(x89661,a862)),x89662),x89663))),f332(f332(f244(x89661),f12(x89661,f244(x89661),x89662)),f12(x89661,f244(x89661),x89663))) % 165.30/165.05 [8967]~P106(x89671)+~P24(f332(f62(x89671),x89673))+~P24(f332(f62(x89671),x89672))+E(f332(f332(f104(f875(x89671,a862)),x89672),x89673),f196(f875(x89671,a862)))+E(f332(f332(f245(x89671),f13(x89671,f245(x89671),f332(f332(f113(f875(x89671,a862)),x89672),x89673))),f13(x89671,f245(x89671),f332(f332(f104(f875(x89671,a862)),x89672),x89673))),f332(f332(f245(x89671),f13(x89671,f245(x89671),x89672)),f13(x89671,f245(x89671),x89673))) % 165.30/165.05 [9739]~P112(x97393)+E(x97391,x97392)+~P24(f332(f332(f246(x97393),f2(x97393)),x97392))+~P24(f332(f332(f246(x97393),f2(x97393)),x97391))+~E(f332(f332(f257(x97393),x97391),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)))),f332(f332(f257(x97393),x97392),f332(f106(a868),f332(f332(f81(a1),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100)),f332(f332(f22(a1),f332(f332(f81(a1),a84),a84)),a100))))) % 165.30/165.05 [6327]E(f848(x63271,x63272,x63273),x63274)+E(f332(x63271,x63274),f2(a868))+~E(f332(f332(f6(x63273,a868),x63271),x63272),f79(a868))+~P24(f332(f62(x63273),x63272))+~P24(f332(f332(f334(x63273),x63274),x63272)) % 165.30/165.05 [6391]E(f846(x63911,x63912,x63913),x63914)+E(f332(x63911,x63914),f2(a868))+~E(f332(f332(f6(x63913,a868),x63911),x63912),f332(a115,f2(a868)))+~P24(f332(f62(x63913),x63912))+~P24(f332(f332(f334(x63913),x63914),x63912)) % 165.30/165.05 [6497]~P106(x64971)+~P30(x64971)+P24(f332(f332(f247(x64971),x64972),f40(x64971,x64973)))+~P24(f332(f332(f247(x64971),x64972),x64974))+~P24(f332(f332(f334(x64971),x64974),x64973)) % 165.30/165.05 [6669]~P106(x66691)+~P30(x66691)+~P24(f332(f332(f247(x66691),x66694),x66693))+P24(f332(f332(f247(x66691),f41(x66691,x66692)),x66693))+~P24(f332(f332(f334(x66691),x66694),x66692)) % 165.30/165.05 [6927]~P112(x69273)+E(x69271,x69272)+~E(f332(f332(f257(x69273),x69271),f332(a115,x69274)),f332(f332(f257(x69273),x69272),f332(a115,x69274)))+~P24(f332(f332(f246(x69273),f2(x69273)),x69272))+~P24(f332(f332(f246(x69273),f2(x69273)),x69271)) % 165.30/165.05 [7136]~E(f850(x71362,x71363,x71361,x71364),x71364)+~E(f332(x71362,x71364),f79(a868))+E(f332(f332(f6(x71361,a868),x71362),x71363),f79(a868))+~P24(f332(f62(x71361),x71363))+~P24(f332(f332(f334(x71361),x71364),x71363)) % 165.30/165.05 [7143]~P113(x71434)+~P127(x71434)+E(f332(x71431,f842(x71431,x71432,x71433,x71434)),f2(x71434))+~E(f332(f332(f9(x71433,x71434),x71431),x71432),f2(x71434))+~P24(f332(f62(x71433),x71432)) % 165.30/165.05 [7229]~E(f847(x72292,x72293,x72291,x72294),x72294)+~E(f332(x72292,x72294),f332(a115,f2(a868)))+E(f332(f332(f6(x72291,a868),x72292),x72293),f332(a115,f2(a868)))+~P24(f332(f62(x72291),x72293))+~P24(f332(f332(f334(x72291),x72294),x72293)) % 165.30/165.05 [7963]~E(f332(x79632,x79634),f79(a868))+~E(f332(x79632,f850(x79632,x79633,x79631,x79634)),f2(a868))+E(f332(f332(f6(x79631,a868),x79632),x79633),f79(a868))+~P24(f332(f62(x79631),x79633))+~P24(f332(f332(f334(x79631),x79634),x79633)) % 165.30/165.05 [8001]~E(f332(x80012,x80014),f332(a115,f2(a868)))+~E(f332(x80012,f847(x80012,x80013,x80011,x80014)),f2(a868))+E(f332(f332(f6(x80011,a868),x80012),x80013),f332(a115,f2(a868)))+~P24(f332(f62(x80011),x80013))+~P24(f332(f332(f334(x80011),x80014),x80013)) % 165.30/165.05 [8539]~P106(x85391)+~P32(x85391,x85394)+P32(x85391,x85392)+~E(x85392,f332(f332(f152(x85391),x85393),x85394))+~P24(f332(f332(f246(x85391),x85393),f655(x85392,x85391,x85394,x85393))) % 165.30/165.05 [8573]E(x85731,x85732)+E(f332(f332(f22(a1),f384(x85733,x85732,x85734,x85731)),f385(x85733,x85732,x85734,x85731)),x85731)+~E(f332(f332(f81(a1),x85731),x85734),x85732)+~P24(f332(f332(f247(a1),f2(a1)),x85734))+~P24(f332(f332(f334(a1),x85732),x85733)) % 165.30/165.05 [8574]E(x85741,x85742)+E(f332(f332(f81(a1),f388(x85743,x85742,x85744,x85741)),f389(x85743,x85742,x85744,x85741)),x85741)+~E(f332(f332(f22(a1),x85741),x85744),x85742)+~P24(f332(f332(f247(a1),f2(a1)),x85744))+~P24(f332(f332(f334(a1),x85742),x85743)) % 165.30/165.05 [8749]E(f332(x87491,f758(x87492,x87491,x87493,x87494)),x87492)+P24(f332(f332(f246(a868),x87494),f759(x87492,x87491,x87493,x87494)))+~P24(f332(f332(f246(a1),x87492),f332(x87491,x87493)))+~P24(f332(f332(f247(a868),x87494),x87493))+~P24(f332(f332(f246(a1),f332(x87491,x87494)),x87492)) % 165.30/165.05 [8750]~P106(x87501)+~P32(x87501,x87503)+P32(x87501,x87502)+~E(x87502,f332(f332(f152(x87501),x87504),x87503))+P24(f332(f332(f334(x87501),f655(x87502,x87501,x87503,x87504)),f332(f174(x87501),x87503))) % 165.30/165.05 [8768]~P113(x87684)+~P127(x87684)+~E(f332(f332(f9(x87681,x87684),x87682),x87683),f2(x87684))+~P24(f332(f62(x87681),x87683))+P24(f332(f332(f334(x87681),f842(x87682,x87683,x87681,x87684)),x87683)) % 165.30/165.05 [8802]~E(f332(x88022,x88024),f79(a868))+E(f332(f332(f6(x88021,a868),x88022),x88023),f79(a868))+~P24(f332(f62(x88021),x88023))+~P24(f332(f332(f334(x88021),x88024),x88023))+P24(f332(f332(f334(x88021),f850(x88022,x88023,x88021,x88024)),x88023)) % 165.30/165.05 [8811]E(x88111,x88112)+~E(f332(f332(f81(a1),x88112),x88114),x88111)+~P24(f332(f332(f247(a1),f2(a1)),x88114))+~P24(f332(f332(f334(a1),x88111),x88113))+P24(f332(f332(f334(a1),f384(x88113,x88111,x88114,x88112)),x88113)) % 165.30/165.05 [8812]E(x88121,x88122)+~E(f332(f332(f22(a1),x88122),x88124),x88121)+~P24(f332(f332(f247(a1),f2(a1)),x88124))+~P24(f332(f332(f334(a1),x88121),x88123))+P24(f332(f332(f334(a1),f388(x88123,x88121,x88124,x88122)),x88123)) % 165.30/165.05 [8814]~E(f332(x88142,x88144),f332(a115,f2(a868)))+E(f332(f332(f6(x88141,a868),x88142),x88143),f332(a115,f2(a868)))+~P24(f332(f62(x88141),x88143))+~P24(f332(f332(f334(x88141),x88144),x88143))+P24(f332(f332(f334(x88141),f847(x88142,x88143,x88141,x88144)),x88143)) % 165.30/165.05 [8819]P57(x88192,x88193,x88194,x88191)+E(x88191,f196(f875(x88192,a862)))+~P24(f332(f62(x88192),x88194))+~P24(f332(f62(x88192),x88191))+P24(f332(f332(f334(x88192),f665(x88191,x88194,x88193,x88192)),x88194)) % 165.30/165.05 [8899]E(x88991,x88992)+~E(f332(f332(f81(a1),x88992),x88994),x88991)+~P24(f332(f332(f247(a1),f2(a1)),x88994))+~P24(f332(f332(f334(a1),x88991),x88993))+P24(f332(f332(f334(a1),f385(x88993,x88991,x88994,x88992)),f303(a1,f79(a1),x88994))) % 165.30/165.05 [8900]E(x89001,x89002)+~E(f332(f332(f22(a1),x89002),x89004),x89001)+~P24(f332(f332(f247(a1),f2(a1)),x89004))+~P24(f332(f332(f334(a1),x89001),x89003))+P24(f332(f332(f334(a1),f389(x89003,x89001,x89004,x89002)),f303(a1,f79(a1),x89004))) % 165.30/165.05 [8972]P24(f332(f332(f246(a868),x89721),f758(x89722,x89723,x89724,x89721)))+~P24(f332(f332(f246(a1),x89722),f332(x89723,x89724)))+P24(f332(f332(f246(a868),x89721),f759(x89722,x89723,x89724,x89721)))+~P24(f332(f332(f247(a868),x89721),x89724))+~P24(f332(f332(f246(a1),f332(x89723,x89721)),x89722)) % 165.30/165.05 [9082]E(f332(x90821,f758(x90822,x90821,x90823,x90824)),x90822)+~P24(f332(f332(f246(a1),x90822),f332(x90821,x90823)))+P24(f332(f332(f247(a868),f759(x90822,x90821,x90823,x90824)),x90823))+~P24(f332(f332(f247(a868),x90824),x90823))+~P24(f332(f332(f246(a1),f332(x90821,x90824)),x90822)) % 165.30/165.05 [9205]~P24(f332(f332(f246(a1),x92052),f332(x92053,x92054)))+P24(f332(f332(f246(a868),x92051),f759(x92052,x92053,x92054,x92051)))+P24(f332(f332(f246(a868),f758(x92052,x92053,x92054,x92051)),x92054))+~P24(f332(f332(f247(a868),x92051),x92054))+~P24(f332(f332(f246(a1),f332(x92053,x92051)),x92052)) % 165.30/165.05 [9206]~P24(f332(f332(f246(a1),x92062),f332(x92063,x92064)))+P24(f332(f332(f246(a868),x92061),f758(x92062,x92063,x92064,x92061)))+P24(f332(f332(f247(a868),f759(x92062,x92063,x92064,x92061)),x92064))+~P24(f332(f332(f247(a868),x92061),x92064))+~P24(f332(f332(f246(a1),f332(x92063,x92061)),x92062)) % 165.30/165.05 [9307]~P24(f332(f332(f246(a1),x93071),f332(x93072,x93073)))+P24(f332(f332(f247(a868),f759(x93071,x93072,x93073,x93074)),x93073))+~P24(f332(f332(f247(a868),x93074),x93073))+~P24(f332(f332(f246(a1),f332(x93072,x93074)),x93071))+P24(f332(f332(f246(a868),f758(x93071,x93072,x93073,x93074)),x93073)) % 165.30/165.05 [9383]E(x93831,f196(f875(x93832,a862)))+~P24(f332(f62(x93832),x93834))+~P24(f332(f62(x93832),x93831))+P24(f332(f332(f334(f874(f875(x93832,a862),f875(x93832,a862))),f332(f332(f267(f875(x93832,a862),f875(x93832,a862)),x93834),x93831)),f323(x93832,x93833)))+P24(f332(f332(f334(x93832),f674(x93833,x93831,x93834,x93832)),x93834)) % 165.30/165.05 [9384]E(x93841,f196(f875(x93842,a862)))+~P24(f332(f62(x93842),x93844))+~P24(f332(f62(x93842),x93841))+P24(f332(f332(f334(f874(f875(x93842,a862),f875(x93842,a862))),f332(f332(f267(f875(x93842,a862),f875(x93842,a862)),x93844),x93841)),f323(x93842,x93843)))+P24(f332(f332(f334(x93842),f721(x93843,x93841,x93844,x93842)),x93844)) % 165.30/165.05 [10039]E(f332(x100391,f758(x100392,x100391,x100393,x100394)),x100392)+~P24(f332(f332(f246(a1),x100392),f332(x100391,x100393)))+~P24(f332(f332(f246(a1),f332(f76(a1),f332(f332(f22(a1),f332(x100391,f332(f332(f81(a868),f759(x100392,x100391,x100393,x100394)),f79(a868)))),f332(x100391,f759(x100392,x100391,x100393,x100394))))),f79(a1)))+~P24(f332(f332(f247(a868),x100394),x100393))+~P24(f332(f332(f246(a1),f332(x100391,x100394)),x100392)) % 165.30/165.05 [10040]~P24(f332(f332(f246(a1),x100402),f332(x100403,x100404)))+P24(f332(f332(f246(a868),x100401),f758(x100402,x100403,x100404,x100401)))+~P24(f332(f332(f246(a1),f332(f76(a1),f332(f332(f22(a1),f332(x100403,f332(f332(f81(a868),f759(x100402,x100403,x100404,x100401)),f79(a868)))),f332(x100403,f759(x100402,x100403,x100404,x100401))))),f79(a1)))+~P24(f332(f332(f247(a868),x100401),x100404))+~P24(f332(f332(f246(a1),f332(x100403,x100401)),x100402)) % 165.30/165.05 [10041]~P24(f332(f332(f246(a1),x100411),f332(x100412,x100413)))+~P24(f332(f332(f246(a1),f332(f76(a1),f332(f332(f22(a1),f332(x100412,f332(f332(f81(a868),f759(x100411,x100412,x100413,x100414)),f79(a868)))),f332(x100412,f759(x100411,x100412,x100413,x100414))))),f79(a1)))+~P24(f332(f332(f247(a868),x100414),x100413))+~P24(f332(f332(f246(a1),f332(x100412,x100414)),x100411))+P24(f332(f332(f246(a868),f758(x100411,x100412,x100413,x100414)),x100413)) % 165.30/165.05 [7196]~P62(x71961)+P24(f332(f332(f247(x71961),x71962),f2(x71961)))+~P24(f332(f332(f246(x71961),x71963),f2(x71961)))+P24(f332(f332(f247(x71961),f2(x71961)),x71962))+P24(f332(f332(f246(x71961),x71963),f332(f332(f290(x71961),x71964),x71962))) % 165.30/165.05 [7197]~P62(x71971)+P24(f332(f332(f247(x71971),x71972),f2(x71971)))+~P24(f332(f332(f247(x71971),x71973),f2(x71971)))+P24(f332(f332(f247(x71971),f2(x71971)),x71972))+P24(f332(f332(f247(x71971),x71973),f332(f332(f290(x71971),x71974),x71972))) % 165.30/165.05 [7443]~P62(x74431)+P24(f332(f332(f246(x74431),x74432),f2(x74431)))+P24(f332(f332(f247(x74431),x74433),f2(x74431)))+P24(f332(f332(f247(x74431),f2(x74431)),x74433))+~P24(f332(f332(f246(x74431),x74432),f332(f332(f290(x74431),x74434),x74433))) % 165.30/165.05 [7444]~P62(x74441)+P24(f332(f332(f247(x74441),x74442),f2(x74441)))+P24(f332(f332(f247(x74441),x74443),f2(x74441)))+P24(f332(f332(f247(x74441),f2(x74441)),x74443))+~P24(f332(f332(f247(x74441),x74442),f332(f332(f290(x74441),x74444),x74443))) % 165.30/165.05 [7563]E(x75631,x75632)+~E(f332(f332(f166(x75633),x75634),x75631),f332(f332(f166(x75633),x75634),x75632))+~P24(f332(f138(x75633),x75634))+~P24(f332(f332(f247(a868),x75632),f332(f197(f869(x75633)),x75634)))+~P24(f332(f332(f247(a868),x75631),f332(f197(f869(x75633)),x75634))) % 165.30/165.05 [7924]~P62(x79241)+~P24(f332(f332(f246(x79241),x79243),f2(x79241)))+P24(f332(f332(f247(x79241),f2(x79241)),x79242))+~P24(f332(f332(f246(x79241),x79244),f332(f332(f82(x79241),x79243),x79242)))+P24(f332(f332(f246(x79241),x79243),f332(f332(f290(x79241),x79244),x79242))) % 165.30/165.05 [7925]~P62(x79251)+~P24(f332(f332(f247(x79251),x79253),f2(x79251)))+P24(f332(f332(f247(x79251),f2(x79251)),x79252))+~P24(f332(f332(f247(x79251),x79254),f332(f332(f82(x79251),x79253),x79252)))+P24(f332(f332(f247(x79251),x79253),f332(f332(f290(x79251),x79254),x79252))) % 165.30/165.05 [7926]~P62(x79261)+~P24(f332(f332(f247(x79261),x79262),f2(x79261)))+P24(f332(f332(f247(x79261),f2(x79261)),x79262))+~P24(f332(f332(f246(x79261),x79264),f332(f332(f82(x79261),x79263),x79262)))+P24(f332(f332(f246(x79261),x79263),f332(f332(f290(x79261),x79264),x79262))) % 165.30/165.05 [7927]~P62(x79271)+~P24(f332(f332(f247(x79271),x79272),f2(x79271)))+P24(f332(f332(f247(x79271),f2(x79271)),x79272))+~P24(f332(f332(f246(x79271),x79274),f332(f332(f290(x79271),x79273),x79272)))+P24(f332(f332(f246(x79271),x79273),f332(f332(f82(x79271),x79274),x79272))) % 165.30/165.05 [7928]~P62(x79281)+~P24(f332(f332(f247(x79281),x79282),f2(x79281)))+P24(f332(f332(f247(x79281),f2(x79281)),x79282))+~P24(f332(f332(f247(x79281),x79284),f332(f332(f82(x79281),x79283),x79282)))+P24(f332(f332(f247(x79281),x79283),f332(f332(f290(x79281),x79284),x79282))) % 165.30/165.05 [7929]~P62(x79291)+~P24(f332(f332(f247(x79291),x79292),f2(x79291)))+P24(f332(f332(f247(x79291),f2(x79291)),x79292))+~P24(f332(f332(f247(x79291),x79294),f332(f332(f290(x79291),x79293),x79292)))+P24(f332(f332(f247(x79291),x79293),f332(f332(f82(x79291),x79294),x79292))) % 165.30/165.05 [8066]~P106(x80661)+~P32(x80661,x80662)+~P24(f332(f332(f246(a868),x80663),x80664))+P24(f332(f332(f246(x80661),f332(f332(f166(x80661),x80662),x80663)),f332(f332(f166(x80661),x80662),x80664)))+~P24(f332(f332(f247(a868),x80664),f332(f197(f869(x80661)),x80662))) % 165.30/165.05 [8116]~P112(x81161)+~P24(f332(f332(f246(x81161),x81162),f79(x81161)))+~P24(f332(f332(f246(x81161),f2(x81161)),x81162))+~P24(f332(f332(f246(a868),x81164),x81163))+P24(f332(f332(f246(x81161),f332(f332(f257(x81161),x81162),x81163)),f332(f332(f257(x81161),x81162),x81164))) % 165.30/165.05 [8117]~P112(x81171)+~P24(f332(f332(f247(x81171),x81172),f79(x81171)))+~P24(f332(f332(f247(x81171),f2(x81171)),x81172))+~P24(f332(f332(f247(a868),x81174),x81173))+P24(f332(f332(f247(x81171),f332(f332(f257(x81171),x81172),x81173)),f332(f332(f257(x81171),x81172),x81174))) % 165.30/165.05 [8118]~P112(x81181)+~P24(f332(f332(f246(x81181),f2(x81181)),x81182))+~P24(f332(f332(f247(a868),f2(a868)),x81183))+~P24(f332(f332(f247(x81181),x81182),x81184))+P24(f332(f332(f247(x81181),f332(f332(f257(x81181),x81182),x81183)),f332(f332(f257(x81181),x81184),x81183))) % 165.30/165.05 [8138]~P106(x81381)+~P32(x81381,f332(f170(x81381),x81382))+~P24(f332(f332(f246(a868),x81384),x81383))+P24(f332(f332(f246(x81381),f332(f332(f166(x81381),x81382),x81383)),f332(f332(f166(x81381),x81382),x81384)))+~P24(f332(f332(f247(a868),x81383),f332(f197(f869(x81381)),x81382))) % 165.30/165.05 [8381]~P62(x83811)+~P24(f332(f332(f246(x83811),x83812),f2(x83811)))+~P24(f332(f332(f246(x83811),x83813),x83814))+~P24(f332(f332(f247(x83811),f2(x83811)),f332(f332(f82(x83811),x83813),x83814)))+P24(f332(f332(f246(x83811),f332(f332(f290(x83811),x83812),x83813)),f332(f332(f290(x83811),x83812),x83814))) % 165.30/165.05 [8382]~P63(x83821)+~P24(f332(f332(f247(x83821),x83822),f2(x83821)))+~P24(f332(f332(f247(x83821),x83823),x83824))+~P24(f332(f332(f247(x83821),f2(x83821)),f332(f332(f82(x83821),x83823),x83824)))+P24(f332(f332(f247(x83821),f332(f332(f290(x83821),x83822),x83823)),f332(f332(f290(x83821),x83822),x83824))) % 165.30/165.05 [8391]~P63(x83911)+~P24(f332(f332(f246(x83911),x83914),x83913))+~P24(f332(f332(f246(x83911),f2(x83911)),x83912))+~P24(f332(f332(f247(x83911),f2(x83911)),f332(f332(f82(x83911),x83913),x83914)))+P24(f332(f332(f246(x83911),f332(f332(f290(x83911),x83912),x83913)),f332(f332(f290(x83911),x83912),x83914))) % 165.30/165.05 [8392]~P63(x83921)+~P24(f332(f332(f247(x83921),x83924),x83923))+~P24(f332(f332(f247(x83921),f2(x83921)),x83922))+~P24(f332(f332(f247(x83921),f2(x83921)),f332(f332(f82(x83921),x83923),x83924)))+P24(f332(f332(f247(x83921),f332(f332(f290(x83921),x83922),x83923)),f332(f332(f290(x83921),x83922),x83924))) % 165.30/165.05 [8489]P24(f332(x84891,x84892))+~P24(f332(f62(x84894),x84892))+P24(f332(x84891,f464(x84891,x84893,x84892,x84894)))+~P24(f332(x84891,f196(f875(x84894,a862))))+~P24(f332(f332(f246(f875(x84894,a862)),x84892),x84893)) % 165.30/165.05 [8497]P24(f332(x84971,x84972))+P24(f332(f62(x84973),f464(x84971,x84974,x84972,x84973)))+~P24(f332(f62(x84973),x84972))+~P24(f332(x84971,f196(f875(x84973,a862))))+~P24(f332(f332(f246(f875(x84973,a862)),x84972),x84974)) % 165.30/165.05 [8744]E(f332(f332(f81(a1),f391(x87441,x87442,x87443,x87444)),f392(x87441,x87442,x87443,x87444)),x87444)+~P24(f332(f332(f247(a1),f2(a1)),x87443))+~P24(f332(f332(f247(a1),x87442),x87444))+~P24(f332(f332(f334(a1),x87442),x87441))+P24(f332(f332(f247(a1),x87442),f332(f332(f22(a1),x87444),x87443))) % 165.30/165.05 [8953]~P24(f332(f332(f247(a1),f2(a1)),x89533))+~P24(f332(f332(f247(a1),x89532),x89534))+~P24(f332(f332(f334(a1),x89532),x89531))+P24(f332(f332(f334(a1),f391(x89531,x89532,x89533,x89534)),x89531))+P24(f332(f332(f247(a1),x89532),f332(f332(f22(a1),x89534),x89533))) % 165.30/165.05 [8965]P24(f332(x89651,x89652))+~P24(f332(f62(x89653),x89652))+P24(f332(f332(f334(x89653),f440(x89651,x89654,x89652,x89653)),x89654))+~P24(f332(x89651,f196(f875(x89653,a862))))+~P24(f332(f332(f246(f875(x89653,a862)),x89652),x89654)) % 165.30/165.05 [8982]E(f332(f332(f81(a1),f377(x89821,x89822,x89823,x89824)),f378(x89821,x89822,x89823,x89824)),x89824)+~P24(f332(f332(f247(a1),f2(a1)),x89823))+~P24(f332(f332(f246(a1),x89822),x89824))+P24(f332(f332(f246(a1),x89822),f332(f332(f22(a1),x89824),x89823)))+~P24(f332(f332(f334(a1),f332(f332(f22(a1),x89822),f79(a1))),x89821)) % 165.30/165.05 [9033]~P24(f332(f332(f247(a1),f2(a1)),x90333))+~P24(f332(f332(f247(a1),x90331),x90332))+~P24(f332(f332(f334(a1),x90331),x90334))+P24(f332(f332(f334(a1),f392(x90334,x90331,x90333,x90332)),f303(a1,f79(a1),x90333)))+P24(f332(f332(f247(a1),x90331),f332(f332(f22(a1),x90332),x90333))) % 165.30/165.05 [9126]~P24(f332(f332(f247(a1),f2(a1)),x91263))+~P24(f332(f332(f246(a1),x91262),x91264))+P24(f332(f332(f334(a1),f377(x91261,x91262,x91263,x91264)),x91261))+P24(f332(f332(f246(a1),x91262),f332(f332(f22(a1),x91264),x91263)))+~P24(f332(f332(f334(a1),f332(f332(f22(a1),x91262),f79(a1))),x91261)) % 165.30/165.05 [9166]~P24(f332(f332(f247(a1),f2(a1)),x91663))+~P24(f332(f332(f246(a1),x91661),x91662))+P24(f332(f332(f334(a1),f378(x91664,x91661,x91663,x91662)),f303(a1,f79(a1),x91663)))+P24(f332(f332(f246(a1),x91661),f332(f332(f22(a1),x91662),x91663)))+~P24(f332(f332(f334(a1),f332(f332(f22(a1),x91661),f79(a1))),x91664)) % 165.30/165.05 [9386]P24(f332(x93861,x93862))+~P24(f332(f332(f334(x93863),f440(x93861,x93864,x93862,x93863)),f464(x93861,x93864,x93862,x93863)))+~P24(f332(f62(x93863),x93862))+~P24(f332(x93861,f196(f875(x93863,a862))))+~P24(f332(f332(f246(f875(x93863,a862)),x93862),x93864)) % 165.30/165.05 [9597]P24(f332(x95971,x95972))+~P24(f332(f62(x95973),x95972))+~P24(f332(x95971,f332(f332(f310(x95973),f440(x95971,x95974,x95972,x95973)),f464(x95971,x95974,x95972,x95973))))+~P24(f332(x95971,f196(f875(x95973,a862))))+~P24(f332(f332(f246(f875(x95973,a862)),x95972),x95974)) % 165.30/165.05 [7699]~P62(x76991)+P24(f332(f332(f247(x76991),x76992),f2(x76991)))+~P24(f332(f332(f246(x76991),f2(x76991)),x76994))+P24(f332(f332(f247(x76991),f2(x76991)),x76992))+P24(f332(f332(f246(x76991),f332(f332(f290(x76991),x76993),x76992)),x76994)) % 165.30/165.05 [7700]~P62(x77001)+P24(f332(f332(f247(x77001),x77002),f2(x77001)))+P24(f332(f332(f247(x77001),f2(x77001)),x77002))+~P24(f332(f332(f247(x77001),f2(x77001)),x77004))+P24(f332(f332(f247(x77001),f332(f332(f290(x77001),x77003),x77002)),x77004)) % 165.30/165.05 [7976]~P24(f332(f332(f246(a1),x79764),f2(a1)))+~E(x79762,f332(f332(f81(a1),f332(f332(f82(a1),x79761),x79763)),x79764))+P24(f332(f332(f247(a1),f2(a1)),x79761))+~P24(f332(f332(f247(a1),x79761),x79764))+P24(f332(f49(x79762,x79761),f332(f332(f267(a1,a1),x79763),x79764))) % 165.30/165.05 [8010]~P24(f332(x80101,x80104))+P24(f332(x80101,f370(x80102,x80101,x80103)))+~P24(f332(f332(f246(a1),f2(a1)),x80102))+~P24(f332(f332(f247(a1),f2(a1)),x80103))+P24(f332(x80101,f332(f332(f22(a1),x80104),f332(f332(f82(a1),x80102),x80103)))) % 165.30/165.05 [8011]~P24(f332(x80111,x80114))+P24(f332(x80111,f374(x80112,x80111,x80113)))+~P24(f332(f332(f246(a1),f2(a1)),x80112))+~P24(f332(f332(f247(a1),f2(a1)),x80113))+P24(f332(x80111,f332(f332(f81(a1),x80114),f332(f332(f82(a1),x80112),x80113)))) % 165.30/165.05 [8012]~P62(x80121)+P24(f332(f332(f247(x80121),x80122),f2(x80121)))+P24(f332(f332(f247(x80121),f2(x80121)),x80122))+P24(f332(f332(f246(x80121),f2(x80121)),x80123))+~P24(f332(f332(f246(x80121),f332(f332(f290(x80121),x80124),x80122)),x80123)) % 165.30/165.05 [8013]~P62(x80131)+P24(f332(f332(f247(x80131),x80132),f2(x80131)))+P24(f332(f332(f247(x80131),f2(x80131)),x80132))+P24(f332(f332(f247(x80131),f2(x80131)),x80133))+~P24(f332(f332(f247(x80131),f332(f332(f290(x80131),x80134),x80132)),x80133)) % 165.30/165.05 [8061]~E(x80611,f332(f332(f81(a1),f332(f332(f82(a1),x80612),x80613)),x80614))+~P24(f332(f332(f246(a1),f2(a1)),x80614))+~P24(f332(f332(f247(a1),f2(a1)),x80612))+~P24(f332(f332(f247(a1),x80614),x80612))+P24(f332(f49(x80611,x80612),f332(f332(f267(a1,a1),x80613),x80614))) % 165.30/165.05 [8182]~P62(x81821)+P24(f332(f332(f247(x81821),x81822),f2(x81821)))+~P24(f332(f332(f246(x81821),f2(x81821)),x81824))+~P24(f332(f332(f246(x81821),x81823),f332(f332(f82(x81821),x81824),x81822)))+P24(f332(f332(f246(x81821),f332(f332(f290(x81821),x81823),x81822)),x81824)) % 165.30/165.05 [8183]~P62(x81831)+P24(f332(f332(f247(x81831),x81832),f2(x81831)))+~P24(f332(f332(f247(x81831),f2(x81831)),x81834))+~P24(f332(f332(f247(x81831),x81833),f332(f332(f82(x81831),x81834),x81832)))+P24(f332(f332(f247(x81831),f332(f332(f290(x81831),x81833),x81832)),x81834)) % 165.30/165.05 [8264]~P62(x82641)+P24(f332(f332(f247(x82641),x82642),f2(x82641)))+~P24(f332(f332(f246(x82641),x82643),f2(x82641)))+P24(f332(f332(f246(x82641),x82643),f332(f332(f290(x82641),x82644),x82642)))+~P24(f332(f332(f246(x82641),f332(f332(f82(x82641),x82643),x82642)),x82644)) % 165.30/165.05 [8265]~P62(x82651)+P24(f332(f332(f247(x82651),x82652),f2(x82651)))+~P24(f332(f332(f247(x82651),x82653),f2(x82651)))+P24(f332(f332(f247(x82651),x82653),f332(f332(f290(x82651),x82654),x82652)))+~P24(f332(f332(f247(x82651),f332(f332(f82(x82651),x82653),x82652)),x82654)) % 165.30/165.05 [8414]~P62(x84141)+~P24(f332(f332(f247(x84141),x84142),f2(x84141)))+P24(f332(f332(f247(x84141),f2(x84141)),x84142))+~P24(f332(f332(f246(x84141),f332(f332(f290(x84141),x84144),x84142)),x84143))+P24(f332(f332(f246(x84141),f332(f332(f82(x84141),x84143),x84142)),x84144)) % 165.30/165.05 [8415]~P62(x84151)+~P24(f332(f332(f247(x84151),x84152),f2(x84151)))+P24(f332(f332(f247(x84151),f2(x84151)),x84152))+~P24(f332(f332(f246(x84151),f332(f332(f82(x84151),x84154),x84152)),x84153))+P24(f332(f332(f246(x84151),f332(f332(f290(x84151),x84153),x84152)),x84154)) % 165.30/165.05 [8416]~P62(x84161)+~P24(f332(f332(f247(x84161),x84162),f2(x84161)))+P24(f332(f332(f247(x84161),f2(x84161)),x84162))+~P24(f332(f332(f247(x84161),f332(f332(f290(x84161),x84164),x84162)),x84163))+P24(f332(f332(f247(x84161),f332(f332(f82(x84161),x84163),x84162)),x84164)) % 165.30/165.05 [8417]~P62(x84171)+~P24(f332(f332(f247(x84171),x84172),f2(x84171)))+P24(f332(f332(f247(x84171),f2(x84171)),x84172))+~P24(f332(f332(f247(x84171),f332(f332(f82(x84171),x84174),x84172)),x84173))+P24(f332(f332(f247(x84171),f332(f332(f290(x84171),x84173),x84172)),x84174)) % 165.30/165.05 [8435]~P62(x84351)+~P24(f332(f332(f246(x84351),f2(x84351)),x84354))+P24(f332(f332(f247(x84351),f2(x84351)),x84352))+~P24(f332(f332(f246(x84351),f332(f332(f82(x84351),x84354),x84352)),x84353))+P24(f332(f332(f246(x84351),f332(f332(f290(x84351),x84353),x84352)),x84354)) % 165.30/165.05 [8436]~P62(x84361)+~P24(f332(f332(f247(x84361),f2(x84361)),x84364))+P24(f332(f332(f247(x84361),f2(x84361)),x84362))+~P24(f332(f332(f247(x84361),f332(f332(f82(x84361),x84364),x84362)),x84363))+P24(f332(f332(f247(x84361),f332(f332(f290(x84361),x84363),x84362)),x84364)) % 165.30/165.05 [8505]~P62(x85051)+~P24(f332(f332(f247(x85051),x85054),f2(x85051)))+~P24(f332(f332(f246(x85051),x85053),f332(f332(f82(x85051),x85052),x85054)))+P24(f332(f332(f246(x85051),x85052),f332(f332(f290(x85051),x85053),x85054)))+~P24(f332(f332(f246(x85051),f332(f332(f82(x85051),x85052),x85054)),x85053)) % 165.30/165.05 [8506]~P62(x85061)+~P24(f332(f332(f246(x85061),x85062),f2(x85061)))+~P24(f332(f332(f246(x85061),x85063),f332(f332(f82(x85061),x85062),x85064)))+P24(f332(f332(f246(x85061),x85062),f332(f332(f290(x85061),x85063),x85064)))+~P24(f332(f332(f246(x85061),f332(f332(f82(x85061),x85062),x85064)),x85063)) % 165.30/165.05 [8507]~P62(x85071)+~P24(f332(f332(f247(x85071),x85074),f2(x85071)))+~P24(f332(f332(f247(x85071),x85073),f332(f332(f82(x85071),x85072),x85074)))+P24(f332(f332(f247(x85071),x85072),f332(f332(f290(x85071),x85073),x85074)))+~P24(f332(f332(f247(x85071),f332(f332(f82(x85071),x85072),x85074)),x85073)) % 165.30/165.05 [8508]~P62(x85081)+~P24(f332(f332(f247(x85081),x85082),f2(x85081)))+~P24(f332(f332(f247(x85081),x85083),f332(f332(f82(x85081),x85082),x85084)))+P24(f332(f332(f247(x85081),x85082),f332(f332(f290(x85081),x85083),x85084)))+~P24(f332(f332(f247(x85081),f332(f332(f82(x85081),x85082),x85084)),x85083)) % 165.30/165.05 [8620]~P62(x86201)+~P24(f332(f332(f247(x86201),x86203),f2(x86201)))+~P24(f332(f332(f246(x86201),x86202),f332(f332(f82(x86201),x86204),x86203)))+~P24(f332(f332(f246(x86201),f332(f332(f82(x86201),x86204),x86203)),x86202))+P24(f332(f332(f246(x86201),f332(f332(f290(x86201),x86202),x86203)),x86204)) % 165.30/165.05 [8621]~P62(x86211)+~P24(f332(f332(f247(x86211),x86213),f2(x86211)))+~P24(f332(f332(f247(x86211),x86212),f332(f332(f82(x86211),x86214),x86213)))+~P24(f332(f332(f247(x86211),f332(f332(f82(x86211),x86214),x86213)),x86212))+P24(f332(f332(f247(x86211),f332(f332(f290(x86211),x86212),x86213)),x86214)) % 165.30/165.05 [8637]~P62(x86371)+~P24(f332(f332(f246(x86371),f2(x86371)),x86374))+~P24(f332(f332(f246(x86371),x86372),f332(f332(f82(x86371),x86374),x86373)))+~P24(f332(f332(f246(x86371),f332(f332(f82(x86371),x86374),x86373)),x86372))+P24(f332(f332(f246(x86371),f332(f332(f290(x86371),x86372),x86373)),x86374)) % 165.30/165.05 [8638]~P62(x86381)+~P24(f332(f332(f247(x86381),f2(x86381)),x86384))+~P24(f332(f332(f247(x86381),x86382),f332(f332(f82(x86381),x86384),x86383)))+~P24(f332(f332(f247(x86381),f332(f332(f82(x86381),x86384),x86383)),x86382))+P24(f332(f332(f247(x86381),f332(f332(f290(x86381),x86382),x86383)),x86384)) % 165.30/165.05 [8804]E(f332(f332(f22(a1),f386(x88041,x88042,x88043,x88044)),f387(x88041,x88042,x88043,x88044)),x88044)+~P24(f332(f332(f247(a1),f2(a1)),x88043))+~P24(f332(f332(f334(a1),x88042),x88041))+~P24(f332(f332(f247(a1),x88044),x88042))+P24(f332(f332(f247(a1),f332(f332(f81(a1),x88044),x88043)),x88042)) % 165.30/165.05 [8883]~P24(f332(x88831,x88832))+~P24(f332(f332(f246(a1),f2(a1)),x88833))+~P24(f332(f332(f247(a1),f2(a1)),x88834))+~P24(f332(x88831,f332(f332(f22(a1),f370(x88833,x88831,x88834)),x88834)))+P24(f332(x88831,f332(f332(f22(a1),x88832),f332(f332(f82(a1),x88833),x88834)))) % 165.30/165.05 [8884]~P24(f332(x88841,x88842))+~P24(f332(f332(f246(a1),f2(a1)),x88843))+~P24(f332(f332(f247(a1),f2(a1)),x88844))+~P24(f332(x88841,f332(f332(f81(a1),f374(x88843,x88841,x88844)),x88844)))+P24(f332(x88841,f332(f332(f81(a1),x88842),f332(f332(f82(a1),x88843),x88844)))) % 165.30/165.05 [9027]~P24(f332(f332(f247(a1),f2(a1)),x90273))+~P24(f332(f332(f334(a1),x90272),x90271))+~P24(f332(f332(f247(a1),x90274),x90272))+P24(f332(f332(f334(a1),f386(x90271,x90272,x90273,x90274)),x90271))+P24(f332(f332(f247(a1),f332(f332(f81(a1),x90274),x90273)),x90272)) % 165.30/165.05 [9047]E(f332(f332(f22(a1),f379(x90471,x90472,x90473,x90474)),f380(x90471,x90472,x90473,x90474)),x90474)+~P24(f332(f332(f247(a1),f2(a1)),x90473))+~P24(f332(f332(f246(a1),x90474),x90472))+~P24(f332(f332(f334(a1),f332(f332(f81(a1),x90472),f79(a1))),x90471))+P24(f332(f332(f246(a1),f332(f332(f81(a1),x90474),x90473)),x90472)) % 165.30/165.05 [9074]~P24(f332(f332(f247(a1),f2(a1)),x90742))+~P24(f332(f332(f334(a1),x90743),x90744))+~P24(f332(f332(f247(a1),x90741),x90743))+P24(f332(f332(f334(a1),f387(x90744,x90743,x90742,x90741)),f303(a1,f79(a1),x90742)))+P24(f332(f332(f247(a1),f332(f332(f81(a1),x90741),x90742)),x90743)) % 165.30/165.05 [9161]~P24(f332(f332(f247(a1),f2(a1)),x91613))+~P24(f332(f332(f246(a1),x91614),x91612))+P24(f332(f332(f334(a1),f379(x91611,x91612,x91613,x91614)),x91611))+~P24(f332(f332(f334(a1),f332(f332(f81(a1),x91612),f79(a1))),x91611))+P24(f332(f332(f246(a1),f332(f332(f81(a1),x91614),x91613)),x91612)) % 165.30/165.05 [9201]~P24(f332(f332(f247(a1),f2(a1)),x92012))+~P24(f332(f332(f246(a1),x92011),x92013))+P24(f332(f332(f334(a1),f380(x92014,x92013,x92012,x92011)),f303(a1,f79(a1),x92012)))+~P24(f332(f332(f334(a1),f332(f332(f81(a1),x92013),f79(a1))),x92014))+P24(f332(f332(f246(a1),f332(f332(f81(a1),x92011),x92012)),x92013)) % 165.30/165.05 [9473]~P41(x94731,x94733)+~P22(x94731,x94734)+P41(x94731,f332(f332(f113(f875(f874(x94731,x94731),a862)),x94732),x94733))+~P24(f332(f332(f246(f875(f874(x94731,x94731),a862)),x94732),f332(f266(f875(f874(x94731,x94731),a862),f875(f874(x94731,x94731),a862)),x94734)))+~P24(f332(f332(f246(f875(f874(x94731,x94731),a862)),x94733),f332(f270(f875(f874(x94731,x94731),a862),f875(f874(x94731,x94731),a862)),x94734))) % 165.30/165.05 [9767]~E(f332(f508(x97671,x97674,x97673,x97672),f510(x97671,x97674,x97673,x97672)),f209(f869(a328)))+P24(f332(f332(f247(a1),f509(x97671,x97674,x97673,x97672)),f510(x97671,x97674,x97673,x97672)))+P24(f332(f332(f332(x97671,x97672),x97673),x97674))+P24(f332(f332(f332(x97671,f508(x97671,x97674,x97673,x97672)),f509(x97671,x97674,x97673,x97672)),f332(f332(f81(a1),f510(x97671,x97674,x97673,x97672)),f79(a1))))+~P24(f332(f320(f874(f875(a1,f872(f869(a328))),f874(a1,a1)),a318),f332(f332(f267(f875(a1,f872(f869(a328))),f874(a1,a1)),x97672),f332(f332(f267(a1,a1),x97673),x97674)))) % 165.30/165.05 [9867]~P14(x98672,x98674,x98673)+E(x98671,f196(f875(x98672,a862)))+~P24(f332(f62(x98672),x98671))+P24(f332(f332(f334(x98672),f332(x98673,x98671)),x98671))+~P24(f332(f332(f334(x98672),f332(f332(x98674,f495(x98671,x98673,x98674,x98672)),f506(x98671,x98673,x98674,x98672))),f332(f332(f310(x98672),f495(x98671,x98673,x98674,x98672)),f332(f332(f310(x98672),f506(x98671,x98673,x98674,x98672)),f196(f875(x98672,a862)))))) % 165.30/165.05 [9797]~P107(x97972)+~P59(x97971)+~P24(f332(f332(f246(f875(x97971,x97972)),x97973),x97974))+P24(f332(f332(f247(f875(x97971,x97972)),x97973),x97974))+~P24(f332(f58(x97971),f332(f332(f8(a862,a862,x97971),a327),f332(f332(f18(x97971,x97972,a862),f332(f332(f8(x97972,f875(x97972,a862),x97971),a329),x97973)),x97974)))) % 165.30/165.05 [9393]~P53(x93931,x93931,x93934)+P24(f332(f332(f334(f874(x93931,x93931)),f332(f332(f267(x93931,x93931),x93932),x93933)),f308(x93931,x93934)))+P24(f332(f332(f334(f874(x93931,x93931)),f332(f332(f267(x93931,x93931),x93933),x93932)),f308(x93931,x93934)))+~P24(f332(f332(f334(f874(x93931,x93931)),f332(f332(f267(x93931,x93931),x93935),x93932)),f308(x93931,x93934)))+~P24(f332(f332(f334(f874(x93931,x93931)),f332(f332(f267(x93931,x93931),x93935),x93933)),f308(x93931,x93934))) % 165.30/165.05 [5608]E(x56081,f2(a868))+~E(f332(f38(x56082),x56085),x56081)+E(f332(f38(x56082),x56083),f332(a115,x56081))+~E(x56083,f332(f332(f310(x56082),x56084),x56085))+P24(f332(f332(f334(x56082),x56084),x56085)) % 165.30/165.05 [5734]~P61(x57342)+E(x57341,f2(x57342))+E(x57343,f2(x57342))+~E(f332(f332(f290(x57342),x57344),x57343),f332(f332(f290(x57342),x57345),x57341))+E(f332(f332(f82(x57342),x57344),x57341),f332(f332(f82(x57342),x57345),x57343)) % 165.30/165.05 [5735]~P61(x57352)+E(x57351,f2(x57352))+E(x57353,f2(x57352))+~E(f332(f332(f82(x57352),x57354),x57353),f332(f332(f82(x57352),x57355),x57351))+E(f332(f332(f290(x57352),x57354),x57351),f332(f332(f290(x57352),x57355),x57353)) % 165.30/165.05 [5801]~E(f332(f38(x58011),x58015),x58013)+~E(x58015,f196(f875(x58011,a862)))+E(f332(f38(x58011),x58012),f332(a115,x58013))+~E(x58012,f332(f332(f310(x58011),x58014),x58015))+P24(f332(f332(f334(x58011),x58014),x58015)) % 165.30/165.05 [6028]~P113(x60282)+~E(f332(x60283,x60285),f2(x60282))+E(f332(f332(f9(x60281,x60282),x60283),x60284),f2(x60282))+~P24(f332(f62(x60281),x60284))+~P24(f332(f332(f334(x60281),x60285),x60284)) % 165.30/165.05 [6404]~P106(x64043)+E(x64041,x64042)+~E(f332(f302(x64043,x64044),x64041),f332(f302(x64043,x64045),x64042))+~P24(f332(f332(f247(x64043),x64045),x64042))+~P24(f332(f332(f247(x64043),x64044),x64041)) % 165.30/165.05 [6405]~P106(x64053)+E(x64051,x64052)+~E(f332(f302(x64053,x64051),x64054),f332(f302(x64053,x64052),x64055))+~P24(f332(f332(f247(x64053),x64052),x64055))+~P24(f332(f332(f247(x64053),x64051),x64054)) % 165.30/165.05 [7460]~P106(x74601)+~P32(x74601,f332(f332(f135(x74601),x74604),x74605))+~P24(f332(f332(f334(x74601),x74603),f332(f174(x74601),x74605)))+~P24(f332(f332(f334(x74601),x74602),f332(f174(x74601),x74604)))+P24(f332(f332(f246(x74601),x74602),x74603)) % 165.30/165.05 [8541]~P107(x85411)+~P24(f332(f332(f247(f875(x85411,a862)),f303(x85411,x85415,x85412)),f303(x85411,x85414,x85413)))+~P24(f332(f332(f246(x85411),x85415),x85412))+P24(f332(f332(f247(x85411),x85412),x85413))+P24(f332(f332(f247(x85411),x85414),x85415)) % 165.30/165.05 [9910]~P13(x99102,x99105,x99103)+E(x99101,f196(f875(x99102,a862)))+~E(f332(f332(x99105,f332(x99104,f558(x99101,x99104,x99103,x99105,x99102))),f332(x99104,f575(x99101,x99104,x99103,x99105,x99102))),f332(x99104,f332(f332(x99105,f558(x99101,x99104,x99103,x99105,x99102)),f575(x99101,x99104,x99103,x99105,x99102))))+E(f332(x99103,f332(f311(x99102,x99102,x99104),x99101)),f332(x99104,f332(x99103,x99101)))+~P24(f332(f62(x99102),x99101)) % 165.30/165.05 [6401]~P14(x64012,x64015,x64013)+E(x64011,f196(f875(x64012,a862)))+~P24(f332(f62(x64012),x64011))+E(f332(x64013,f332(f332(f310(x64012),x64014),x64011)),f332(f332(x64015,x64014),f332(x64013,x64011)))+P24(f332(f332(f334(x64012),x64014),x64011)) % 165.30/165.05 [7220]~P13(x72202,x72203,x72204)+E(f332(f332(x72203,f332(x72204,x72201)),f332(x72204,x72205)),f332(x72204,x72205))+E(x72201,f196(f875(x72202,a862)))+~P24(f332(f62(x72202),x72205))+~P24(f332(f332(f246(f875(x72202,a862)),x72201),x72205)) % 165.30/165.05 [7436]~P59(x74364)+~P94(x74365)+E(f332(x74361,x74362),f332(x74363,x74362))+~P24(f332(f332(f334(x74364),x74362),f332(f174(x74364),f56(x74364))))+~P24(f332(f332(f92(f875(x74364,x74365)),x74361),x74363)) % 165.30/165.05 [7596]~P14(x75964,x75965,x75961)+E(f332(x75961,x75962),x75963)+~P24(f332(f62(x75964),x75962))+~E(f332(f332(f22(f875(x75964,a862)),x75962),f332(f332(f310(x75964),x75963),f196(f875(x75964,a862)))),f196(f875(x75964,a862)))+~P24(f332(f332(f334(x75964),x75963),x75962)) % 165.30/165.05 [7682]E(x76821,x76822)+~E(f332(f197(f869(x76823)),x76822),f332(f197(f869(x76824)),x76825))+~E(f332(f197(f869(x76823)),x76821),f332(f197(f869(x76824)),x76825))+~E(f332(f180(x76824,x76823),f332(f332(f184(x76824,x76823),x76825),x76821)),f332(f180(x76824,x76823),f332(f332(f184(x76824,x76823),x76825),x76822)))+~P24(f332(f138(x76824),x76825)) % 165.30/165.05 [8512]E(x85121,x85122)+~P6(x85123,x85124,x85125)+E(f332(f332(f104(f875(x85123,a862)),x85121),x85122),f196(f875(x85123,a862)))+~P24(f332(f332(f334(f875(x85123,a862)),x85122),f332(f332(f61(x85123),x85124),x85125)))+~P24(f332(f332(f334(f875(x85123,a862)),x85121),f332(f332(f61(x85123),x85124),x85125))) % 165.30/165.05 [9278]~P74(x92782)+~E(f332(x92783,f414(x92783,x92784,x92785,x92781,x92782)),f2(x92782))+E(f332(f332(f6(x92781,x92782),x92783),x92784),f332(f332(f6(x92781,x92782),x92783),x92785))+~P24(f332(f62(x92781),x92785))+~P24(f332(f332(f246(f875(x92781,a862)),x92784),x92785)) % 165.30/165.05 [9279]~P74(x92792)+~E(f332(x92793,f415(x92793,x92794,x92795,x92791,x92792)),f2(x92792))+E(f332(f332(f6(x92791,x92792),x92793),x92794),f332(f332(f6(x92791,x92792),x92793),x92795))+~P24(f332(f62(x92791),x92795))+~P24(f332(f332(f246(f875(x92791,a862)),x92794),x92795)) % 165.30/165.05 [9280]~P73(x92802)+~E(f332(x92803,f410(x92803,x92804,x92805,x92801,x92802)),f79(x92802))+E(f332(f332(f9(x92801,x92802),x92803),x92804),f332(f332(f9(x92801,x92802),x92803),x92805))+~P24(f332(f62(x92801),x92805))+~P24(f332(f332(f246(f875(x92801,a862)),x92804),x92805)) % 165.30/165.05 [9281]~P73(x92812)+~E(f332(x92813,f411(x92813,x92814,x92815,x92811,x92812)),f79(x92812))+E(f332(f332(f9(x92811,x92812),x92813),x92814),f332(f332(f9(x92811,x92812),x92813),x92815))+~P24(f332(f62(x92811),x92815))+~P24(f332(f332(f246(f875(x92811,a862)),x92814),x92815)) % 165.30/165.05 [9747]~P87(x97471)+~P24(f332(f62(x97472),x97475))+~P24(f332(f332(f246(x97471),f2(x97471)),f332(x97473,f857(x97473,x97474,x97475,x97472,x97471))))+P24(f332(f332(f246(x97471),f332(f332(f6(x97472,x97471),x97473),x97474)),f332(f332(f6(x97472,x97471),x97473),x97475)))+~P24(f332(f332(f246(f875(x97472,a862)),x97474),x97475)) % 165.30/165.05 [7457]E(x74571,f2(a868))+P24(f332(x74572,x74573))+~E(x74574,f332(f332(f81(a868),f332(f332(f82(a868),x74571),x74573)),x74575))+~P24(f332(f332(f247(a868),x74575),x74571))+~P24(f332(x74572,f332(f332(f39(a868),x74574),x74571))) % 165.30/165.05 [7537]E(x75371,f2(a868))+P24(f332(x75372,x75373))+~P24(f332(x75372,f45(a868,x75374,x75371)))+~E(x75374,f332(f332(f81(a868),f332(f332(f82(a868),x75371),x75375)),x75373))+~P24(f332(f332(f247(a868),x75373),x75371)) % 165.30/165.05 [7826]~P61(x78263)+E(f332(x78261,x78262),f2(x78263))+~P24(f332(f62(x78264),x78265))+E(f332(f332(f9(x78264,x78263),x78261),f332(f332(f22(f875(x78264,a862)),x78265),f332(f332(f310(x78264),x78262),f196(f875(x78264,a862))))),f332(f332(f9(x78264,x78263),x78261),x78265))+P24(f332(f332(f334(x78264),x78262),x78265)) % 165.30/165.05 [8223]~P74(x82231)+~P24(f332(f62(x82232),x82235))+~P24(f332(f62(x82232),x82234))+~E(f332(f332(f104(f875(x82232,a862)),x82234),x82235),f196(f875(x82232,a862)))+E(f332(f332(f81(x82231),f332(f332(f6(x82232,x82231),x82233),x82234)),f332(f332(f6(x82232,x82231),x82233),x82235)),f332(f332(f6(x82232,x82231),x82233),f332(f332(f113(f875(x82232,a862)),x82234),x82235))) % 165.30/165.05 [8225]~P73(x82251)+~P24(f332(f62(x82252),x82255))+~P24(f332(f62(x82252),x82254))+~E(f332(f332(f104(f875(x82252,a862)),x82254),x82255),f196(f875(x82252,a862)))+E(f332(f332(f82(x82251),f332(f332(f9(x82252,x82251),x82253),x82254)),f332(f332(f9(x82252,x82251),x82253),x82255)),f332(f332(f9(x82252,x82251),x82253),f332(f332(f113(f875(x82252,a862)),x82254),x82255))) % 165.30/165.05 [8316]~P61(x83163)+E(f332(x83161,x83162),f2(x83163))+~P24(f332(f62(x83164),x83165))+E(f332(f332(f9(x83164,x83163),x83161),f332(f332(f22(f875(x83164,a862)),x83165),f332(f332(f310(x83164),x83162),f196(f875(x83164,a862))))),f332(f332(f290(x83163),f332(f332(f9(x83164,x83163),x83161),x83165)),f332(x83161,x83162)))+~P24(f332(f332(f334(x83164),x83162),x83165)) % 165.30/165.05 [9006]~P6(x90061,x90065,x90064)+~E(f332(f332(f61(x90061),f332(f332(f310(x90061),x90062),f196(f875(x90061,a862)))),x90064),f332(f332(f61(x90061),f332(f332(f310(x90061),x90063),f196(f875(x90061,a862)))),x90064))+~P24(f332(f332(f334(x90061),x90063),x90065))+~P24(f332(f332(f334(x90061),x90062),x90065))+P24(f332(f332(f334(f874(x90061,x90061)),f332(f332(f267(x90061,x90061),x90062),x90063)),x90064)) % 165.30/165.05 [9026]~P6(x90261,x90265,x90263)+E(f332(f332(f61(x90261),f332(f332(f310(x90261),x90262),f196(f875(x90261,a862)))),x90263),f332(f332(f61(x90261),f332(f332(f310(x90261),x90264),f196(f875(x90261,a862)))),x90263))+~P24(f332(f332(f334(x90261),x90264),x90265))+~P24(f332(f332(f334(x90261),x90262),x90265))+~P24(f332(f332(f334(f874(x90261,x90261)),f332(f332(f267(x90261,x90261),x90262),x90264)),x90263)) % 165.30/165.05 [9306]~P73(x93061)+~P24(f332(f62(x93062),x93065))+~P24(f332(f62(x93062),x93064))+~E(f332(f332(f104(f875(x93062,a862)),x93064),x93065),f196(f875(x93062,a862)))+E(f332(f332(f82(x93061),f332(f332(f332(f66(x93061,x93062,f82(x93061)),x93063),f79(x93061)),x93064)),f332(f332(f332(f66(x93061,x93062,f82(x93061)),x93063),f79(x93061)),x93065)),f332(f332(f332(f66(x93061,x93062,f82(x93061)),x93063),f79(x93061)),f332(f332(f113(f875(x93062,a862)),x93064),x93065))) % 165.30/165.05 [9315]~P74(x93151)+~E(f332(x93153,f855(x93153,x93155,x93154,x93152,x93151)),f2(x93151))+~P24(f332(f62(x93152),x93154))+~P24(f332(f62(x93152),x93155))+E(f332(f332(f81(x93151),f332(f332(f6(x93152,x93151),x93153),x93154)),f332(f332(f6(x93152,x93151),x93153),x93155)),f332(f332(f6(x93152,x93151),x93153),f332(f332(f113(f875(x93152,a862)),x93154),x93155))) % 165.30/165.05 [9316]~P74(x93161)+~E(f332(x93163,f859(x93163,x93165,x93164,x93162,x93161)),f2(x93161))+~P24(f332(f62(x93162),x93164))+~P24(f332(f62(x93162),x93165))+E(f332(f332(f81(x93161),f332(f332(f6(x93162,x93161),x93163),x93164)),f332(f332(f6(x93162,x93161),x93163),x93165)),f332(f332(f6(x93162,x93161),x93163),f332(f332(f113(f875(x93162,a862)),x93164),x93165))) % 165.30/165.05 [9317]~P73(x93171)+~E(f332(x93173,f856(x93173,x93175,x93174,x93172,x93171)),f79(x93171))+~P24(f332(f62(x93172),x93174))+~P24(f332(f62(x93172),x93175))+E(f332(f332(f82(x93171),f332(f332(f9(x93172,x93171),x93173),x93174)),f332(f332(f9(x93172,x93171),x93173),x93175)),f332(f332(f9(x93172,x93171),x93173),f332(f332(f113(f875(x93172,a862)),x93174),x93175))) % 165.30/165.05 [9318]~P73(x93181)+~E(f332(x93183,f858(x93183,x93185,x93184,x93182,x93181)),f79(x93181))+~P24(f332(f62(x93182),x93184))+~P24(f332(f62(x93182),x93185))+E(f332(f332(f82(x93181),f332(f332(f9(x93182,x93181),x93183),x93184)),f332(f332(f9(x93182,x93181),x93183),x93185)),f332(f332(f9(x93182,x93181),x93183),f332(f332(f113(f875(x93182,a862)),x93184),x93185))) % 165.30/165.05 [9517]~P73(x95171)+~E(f332(x95173,f828(x95173,x95175,x95174,x95172,x95171)),f79(x95171))+~P24(f332(f62(x95172),x95174))+~P24(f332(f62(x95172),x95175))+E(f332(f332(f82(x95171),f332(f332(f332(f66(x95171,x95172,f82(x95171)),x95173),f79(x95171)),x95174)),f332(f332(f332(f66(x95171,x95172,f82(x95171)),x95173),f79(x95171)),x95175)),f332(f332(f332(f66(x95171,x95172,f82(x95171)),x95173),f79(x95171)),f332(f332(f113(f875(x95172,a862)),x95174),x95175))) % 165.30/165.05 [9625]~P74(x96252)+E(f332(f332(f6(x96251,x96252),x96253),x96254),f332(f332(f6(x96251,x96252),x96253),x96255))+~P24(f332(f62(x96251),x96255))+~P24(f332(f332(f246(f875(x96251,a862)),x96254),x96255))+P24(f332(f332(f334(x96251),f414(x96253,x96254,x96255,x96251,x96252)),f332(f332(f22(f875(x96251,a862)),x96255),x96254))) % 165.30/165.05 [9626]~P74(x96262)+E(f332(f332(f6(x96261,x96262),x96263),x96264),f332(f332(f6(x96261,x96262),x96263),x96265))+~P24(f332(f62(x96261),x96265))+~P24(f332(f332(f246(f875(x96261,a862)),x96264),x96265))+P24(f332(f332(f334(x96261),f415(x96263,x96264,x96265,x96261,x96262)),f332(f332(f22(f875(x96261,a862)),x96265),x96264))) % 165.30/165.05 [9627]~P73(x96272)+E(f332(f332(f9(x96271,x96272),x96273),x96274),f332(f332(f9(x96271,x96272),x96273),x96275))+~P24(f332(f62(x96271),x96275))+~P24(f332(f332(f246(f875(x96271,a862)),x96274),x96275))+P24(f332(f332(f334(x96271),f410(x96273,x96274,x96275,x96271,x96272)),f332(f332(f22(f875(x96271,a862)),x96275),x96274))) % 165.30/165.05 [9628]~P73(x96282)+E(f332(f332(f9(x96281,x96282),x96283),x96284),f332(f332(f9(x96281,x96282),x96283),x96285))+~P24(f332(f62(x96281),x96285))+~P24(f332(f332(f246(f875(x96281,a862)),x96284),x96285))+P24(f332(f332(f334(x96281),f411(x96283,x96284,x96285,x96281,x96282)),f332(f332(f22(f875(x96281,a862)),x96285),x96284))) % 165.30/165.05 [9645]~P74(x96451)+~P24(f332(f62(x96452),x96454))+~P24(f332(f62(x96452),x96455))+E(f332(f332(f81(x96451),f332(f332(f6(x96452,x96451),x96453),x96454)),f332(f332(f6(x96452,x96451),x96453),x96455)),f332(f332(f6(x96452,x96451),x96453),f332(f332(f113(f875(x96452,a862)),x96454),x96455)))+P24(f332(f332(f334(x96452),f855(x96453,x96455,x96454,x96452,x96451)),f332(f332(f104(f875(x96452,a862)),x96454),x96455))) % 165.30/165.05 [9646]~P74(x96461)+~P24(f332(f62(x96462),x96464))+~P24(f332(f62(x96462),x96465))+E(f332(f332(f81(x96461),f332(f332(f6(x96462,x96461),x96463),x96464)),f332(f332(f6(x96462,x96461),x96463),x96465)),f332(f332(f6(x96462,x96461),x96463),f332(f332(f113(f875(x96462,a862)),x96464),x96465)))+P24(f332(f332(f334(x96462),f859(x96463,x96465,x96464,x96462,x96461)),f332(f332(f104(f875(x96462,a862)),x96464),x96465))) % 165.30/165.05 [9647]~P73(x96471)+~P24(f332(f62(x96472),x96474))+~P24(f332(f62(x96472),x96475))+E(f332(f332(f82(x96471),f332(f332(f9(x96472,x96471),x96473),x96474)),f332(f332(f9(x96472,x96471),x96473),x96475)),f332(f332(f9(x96472,x96471),x96473),f332(f332(f113(f875(x96472,a862)),x96474),x96475)))+P24(f332(f332(f334(x96472),f856(x96473,x96475,x96474,x96472,x96471)),f332(f332(f104(f875(x96472,a862)),x96474),x96475))) % 165.30/165.05 [9648]~P73(x96481)+~P24(f332(f62(x96482),x96484))+~P24(f332(f62(x96482),x96485))+E(f332(f332(f82(x96481),f332(f332(f9(x96482,x96481),x96483),x96484)),f332(f332(f9(x96482,x96481),x96483),x96485)),f332(f332(f9(x96482,x96481),x96483),f332(f332(f113(f875(x96482,a862)),x96484),x96485)))+P24(f332(f332(f334(x96482),f858(x96483,x96485,x96484,x96482,x96481)),f332(f332(f104(f875(x96482,a862)),x96484),x96485))) % 165.30/165.05 [9655]~P87(x96555)+~P24(f332(f62(x96551),x96554))+P24(f332(f332(f246(x96555),f332(f332(f6(x96551,x96555),x96552),x96553)),f332(f332(f6(x96551,x96555),x96552),x96554)))+~P24(f332(f332(f246(f875(x96551,a862)),x96553),x96554))+P24(f332(f332(f334(x96551),f857(x96552,x96553,x96554,x96551,x96555)),f332(f332(f22(f875(x96551,a862)),x96554),x96553))) % 165.30/165.05 [9709]~P73(x97091)+~P24(f332(f62(x97092),x97094))+~P24(f332(f62(x97092),x97095))+E(f332(f332(f82(x97091),f332(f332(f332(f66(x97091,x97092,f82(x97091)),x97093),f79(x97091)),x97094)),f332(f332(f332(f66(x97091,x97092,f82(x97091)),x97093),f79(x97091)),x97095)),f332(f332(f332(f66(x97091,x97092,f82(x97091)),x97093),f79(x97091)),f332(f332(f113(f875(x97092,a862)),x97094),x97095)))+P24(f332(f332(f334(x97092),f828(x97093,x97095,x97094,x97092,x97091)),f332(f332(f104(f875(x97092,a862)),x97094),x97095))) % 165.30/165.05 [8705]~P14(x87051,x87054,x87055)+~P24(f332(f62(x87051),x87052))+E(f332(f332(f22(f875(x87051,a862)),x87052),f332(f332(f310(x87051),x87053),f196(f875(x87051,a862)))),f196(f875(x87051,a862)))+~P24(f332(f332(f334(x87051),x87053),x87052))+E(f332(f332(x87054,x87053),f332(x87055,f332(f332(f22(f875(x87051,a862)),x87052),f332(f332(f310(x87051),x87053),f196(f875(x87051,a862)))))),f332(x87055,x87052)) % 165.30/165.05 [8778]~P14(x87781,x87784,x87785)+~P24(f332(f62(x87781),x87783))+~P24(f332(f62(x87781),x87782))+E(f332(f332(f104(f875(x87781,a862)),x87782),x87783),f196(f875(x87781,a862)))+E(f332(f332(x87784,f332(x87785,f332(f332(f113(f875(x87781,a862)),x87782),x87783))),f332(x87785,f332(f332(f104(f875(x87781,a862)),x87782),x87783))),f332(f332(x87784,f332(x87785,x87782)),f332(x87785,x87783))) % 165.30/165.05 [9320]~P24(f332(f332(f246(a1),x93204),f2(a1)))+~P24(f332(f332(f247(a1),x93203),x93205))+P24(f332(f332(f246(a1),x93201),x93202))+~P24(f332(f332(f247(a1),x93203),x93204))+~P24(f332(f332(f246(a1),f332(f332(f81(a1),f332(f332(f82(a1),x93203),x93202)),x93205)),f332(f332(f81(a1),f332(f332(f82(a1),x93203),x93201)),x93204))) % 165.30/165.05 [9322]~P24(f332(f332(f246(a1),f2(a1)),x93225))+P24(f332(f332(f246(a1),x93221),x93222))+~P24(f332(f332(f247(a1),x93223),x93224))+~P24(f332(f332(f247(a1),x93225),x93224))+~P24(f332(f332(f246(a1),f332(f332(f81(a1),f332(f332(f82(a1),x93224),x93221)),x93225)),f332(f332(f81(a1),f332(f332(f82(a1),x93224),x93222)),x93223))) % 165.30/165.05 [9429]~P61(x94295)+E(f332(x94291,f356(x94291,x94292,x94293,x94294,x94295)),f2(x94295))+~P24(f332(f62(x94294),x94293))+~P24(f332(f62(x94294),x94292))+E(f332(f332(f290(x94295),f332(f332(f82(x94295),f332(f332(f9(x94294,x94295),x94291),x94293)),f332(f332(f9(x94294,x94295),x94291),x94292))),f332(f332(f9(x94294,x94295),x94291),f332(f332(f104(f875(x94294,a862)),x94293),x94292))),f332(f332(f9(x94294,x94295),x94291),f332(f332(f113(f875(x94294,a862)),x94293),x94292))) % 165.30/165.05 [9701]~P61(x97011)+~P24(f332(f62(x97012),x97014))+~P24(f332(f62(x97012),x97015))+E(f332(f332(f290(x97011),f332(f332(f82(x97011),f332(f332(f9(x97012,x97011),x97013),x97014)),f332(f332(f9(x97012,x97011),x97013),x97015))),f332(f332(f9(x97012,x97011),x97013),f332(f332(f104(f875(x97012,a862)),x97014),x97015))),f332(f332(f9(x97012,x97011),x97013),f332(f332(f113(f875(x97012,a862)),x97014),x97015)))+P24(f332(f332(f334(x97012),f356(x97013,x97015,x97014,x97012,x97011)),f332(f332(f104(f875(x97012,a862)),x97014),x97015))) % 165.30/165.05 [9046]E(f332(f332(f135(x90461),x90462),x90463),f332(f332(f135(x90461),x90464),x90465))+~E(f332(f332(f177(x90461),f332(f197(f869(x90461)),x90464)),x90462),x90464)+~E(f332(f332(f177(x90461),f332(f197(f869(x90461)),x90462)),x90464),x90462)+~E(x90465,f332(f332(f135(x90461),f332(f332(f139(x90461),f332(f197(f869(x90461)),x90464)),x90462)),x90463))+~E(f332(f332(f135(x90461),f332(f332(f139(x90461),f332(f197(f869(x90461)),x90462)),x90464)),x90465),x90463) % 165.30/165.05 [9427]~P106(x94272)+E(f332(f332(f149(x94271,x94272,x94273),x94274),f172(x94271,x94274,x94275)),x94275)+~P32(x94272,f332(f332(f155(x94271,x94272),x94273),x94275))+~P24(f332(f332(f334(x94271),x94274),f332(f174(x94271),x94275)))+~E(f332(f142(x94271),f332(f137(x94271,f332(f332(f8(x94272,a862,x94271),f332(a329,f332(x94273,x94274))),x94273)),x94275)),x94274) % 165.30/165.05 [9764]~P71(x97641)+~P24(f332(f67(x97641,x97641,f82(x97641),x97642,x97643),x97645))+~P24(f332(f332(f334(x97641),x97644),x97643))+P24(f332(f332(f334(x97641),x97642),x97643))+P24(f332(f67(x97641,x97641,f82(x97641),x97644,f332(f332(f310(x97641),x97642),f332(f332(f22(f875(x97641,a862)),x97643),f332(f332(f310(x97641),x97644),f196(f875(x97641,a862)))))),x97645)) % 165.30/165.06 [7228]E(x72281,x72282)+~P21(x72284,x72285,x72283,x72286)+~E(f332(x72283,x72281),f332(x72283,x72282))+~P24(f332(f332(f334(x72284),x72282),x72286))+~P24(f332(f332(f334(x72284),x72281),x72286)) % 165.30/165.06 [6492]~P123(x64924)+E(x64921,x64922)+~E(x64925,x64926)+E(x64923,f2(x64924))+~E(f332(f332(f81(x64924),x64925),f332(f332(f82(x64924),x64923),x64921)),f332(f332(f81(x64924),x64926),f332(f332(f82(x64924),x64923),x64922))) % 165.30/165.06 [7517]~P106(x75171)+~P30(x75171)+~P24(f332(f332(f247(x75171),x75172),f332(x75175,x75176)))+~P24(f332(f332(f334(x75173),x75176),x75174))+P24(f332(f332(f247(x75171),x75172),f332(f332(f42(x75173,x75171),x75174),x75175))) % 165.30/165.06 [8193]~P106(x81931)+~P30(x81931)+~P24(f332(f332(f247(x81931),f332(x81934,x81936)),x81935))+~P24(f332(f332(f334(x81932),x81936),x81933))+P24(f332(f332(f247(x81931),f332(f332(f43(x81932,x81931),x81933),x81934)),x81935)) % 165.30/165.06 [8442]~P15(x84422,x84425,x84426,x84421)+~P24(f332(f62(x84422),x84424))+~P24(f332(f62(x84422),x84423))+~E(f332(f332(f104(f875(x84422,a862)),x84423),x84424),f196(f875(x84422,a862)))+E(f332(x84421,f332(f332(f113(f875(x84422,a862)),x84423),x84424)),f332(f74(x84425,x84425,x84425,f332(x84421,x84423)),f332(x84421,x84424))) % 165.30/165.06 [8748]E(x87481,x87482)+~P55(x87484,x87485,x87486,x87483,x87487)+~E(f332(x87483,x87481),f332(x87483,x87482))+~P24(f332(f332(f334(x87485),x87482),x87487))+~P24(f332(f332(f334(x87485),x87481),x87487)) % 165.30/165.06 [10008]~P24(f332(x100082,x100084))+~E(x100085,f332(f137(x100081,x100082),x100087))+E(f332(f137(x100081,x100082),x100083),f332(f332(f152(x100081),x100084),x100085))+~E(x100083,f332(f332(f135(x100081),x100086),f332(f332(f152(x100081),x100084),x100087)))+P24(f332(x100082,f718(x100085,x100084,x100083,x100082,x100081,x100086,x100087))) % 165.30/165.06 [10009]~P24(f332(x100094,x100092))+~E(x100093,f332(f137(x100091,x100094),x100097))+E(f332(f332(f152(x100091),x100092),x100093),f332(f137(x100091,x100094),x100095))+~E(x100095,f332(f332(f135(x100091),x100096),f332(f332(f152(x100091),x100092),x100097)))+P24(f332(x100094,f716(x100095,x100094,x100093,x100092,x100091,x100096,x100097))) % 165.30/165.06 [10042]~P24(f332(x100422,x100424))+~E(x100425,f332(f137(x100421,x100422),x100427))+E(f332(f137(x100421,x100422),x100423),f332(f332(f152(x100421),x100424),x100425))+~E(x100423,f332(f332(f135(x100421),x100426),f332(f332(f152(x100421),x100424),x100427)))+P24(f332(f332(f334(x100421),f718(x100425,x100424,x100423,x100422,x100421,x100426,x100427)),f332(f174(x100421),x100426))) % 165.30/165.06 [10043]~P24(f332(x100434,x100432))+~E(x100433,f332(f137(x100431,x100434),x100437))+E(f332(f332(f152(x100431),x100432),x100433),f332(f137(x100431,x100434),x100435))+~E(x100435,f332(f332(f135(x100431),x100436),f332(f332(f152(x100431),x100432),x100437)))+P24(f332(f332(f334(x100431),f716(x100435,x100434,x100433,x100432,x100431,x100436,x100437)),f332(f174(x100431),x100436))) % 165.30/165.06 [10046]~P6(x100461,x100467,x100466)+~P9(x100461,f875(x100465,a862),x100466,x100464)+P24(f332(f332(f334(x100461),f492(x100462,x100463,x100464,x100465,x100466,x100467,x100461)),x100467))+~P24(f332(f332(f334(f875(x100461,a862)),x100463),f332(f332(f61(x100461),x100467),x100466)))+P24(f332(f332(f334(f875(x100465,a862)),f332(f332(f42(x100461,f875(x100465,a862)),x100463),x100464)),x100462)) % 165.30/165.06 [10091]~P6(x100912,x100916,x100917)+~P9(x100912,f875(x100911,a862),x100917,x100914)+~P24(f332(f332(f334(f875(x100912,a862)),x100913),f332(f332(f61(x100912),x100916),x100917)))+~P24(f332(f332(f334(f875(x100911,a862)),f332(x100914,f492(x100915,x100913,x100914,x100911,x100917,x100916,x100912))),x100915))+P24(f332(f332(f334(f875(x100911,a862)),f332(f332(f42(x100912,f875(x100911,a862)),x100913),x100914)),x100915)) % 165.30/165.06 [8360]~P73(x83602)+~P21(x83601,x83605,x83608,x83604)+~E(x83603,f332(f74(x83605,x83602,x83601,x83606),x83608))+~E(x83607,f332(f311(x83601,x83605,x83608),x83604))+E(f332(f332(f9(x83601,x83602),x83603),x83604),f332(f332(f9(x83605,x83602),x83606),x83607)) % 165.30/165.06 [10095]~P73(x100952)+~P21(x100955,x100951,x100958,x100957)+~E(f332(x100956,f529(x100953,x100956,x100954,x100957,x100958,x100951,x100955,x100952)),f332(f332(f74(x100951,x100952,x100955,x100953),x100958),f529(x100953,x100956,x100954,x100957,x100958,x100951,x100955,x100952)))+~E(x100954,f332(f311(x100955,x100951,x100958),x100957))+E(f332(f332(f9(x100951,x100952),x100953),x100954),f332(f332(f9(x100955,x100952),x100956),x100957)) % 165.30/165.06 [10097]~P74(x100972)+~P21(x100971,x100975,x100978,x100974)+~E(x100977,f332(f311(x100971,x100975,x100978),x100974))+E(f332(f332(f6(x100971,x100972),x100973),x100974),f332(f332(f6(x100975,x100972),x100976),x100977))+P24(f332(f332(f334(x100971),f727(x100976,x100973,x100977,x100974,x100978,x100975,x100971,x100972)),x100974)) % 165.30/165.06 [10098]~P73(x100982)+~P21(x100981,x100985,x100988,x100984)+~E(x100987,f332(f311(x100981,x100985,x100988),x100984))+E(f332(f332(f9(x100981,x100982),x100983),x100984),f332(f332(f9(x100985,x100982),x100986),x100987))+P24(f332(f332(f334(x100981),f529(x100986,x100983,x100987,x100984,x100988,x100985,x100981,x100982)),x100984)) % 165.30/165.06 [10104]~P74(x101042)+~P21(x101045,x101041,x101048,x101047)+~E(x101044,f332(f311(x101045,x101041,x101048),x101047))+~E(f332(x101046,f727(x101043,x101046,x101044,x101047,x101048,x101041,x101045,x101042)),f332(x101043,f332(x101048,f727(x101043,x101046,x101044,x101047,x101048,x101041,x101045,x101042))))+E(f332(f332(f6(x101041,x101042),x101043),x101044),f332(f332(f6(x101045,x101042),x101046),x101047)) % 165.30/165.06 [9479]~E(f332(f197(f869(x94792)),x94795),f332(f197(f869(x94791)),x94793))+~E(f332(f197(f869(x94792)),x94794),f332(f197(f869(x94791)),x94793))+~E(f332(f332(f332(f73(x94791,f872(x94792)),f332(f180(x94791,x94792),f332(f332(f184(x94791,x94792),x94793),x94794))),x94796),f332(f208(x94792),x94797)),f332(f332(f332(f73(x94791,f872(x94792)),f332(f180(x94791,x94792),f332(f332(f184(x94791,x94792),x94793),x94795))),x94796),f332(f208(x94792),x94798)))+E(f332(f180(x94791,x94792),f332(f332(f184(x94791,x94792),x94793),x94794)),f332(f180(x94791,x94792),f332(f332(f184(x94791,x94792),x94793),x94795)))+P24(f332(f332(f334(x94791),x94796),f332(f174(x94791),x94793))) % 165.30/165.06 [9592]~P19(x95926,x95922,x95925,x95927,x95928,x95921)+~P24(f332(f62(x95922),x95924))+~P24(f332(f62(x95922),x95923))+~E(f332(f332(f104(f875(x95922,a862)),x95923),x95924),f196(f875(x95922,a862)))+E(f332(x95921,f332(f332(f113(f875(x95922,a862)),x95923),x95924)),f332(f332(x95925,f332(x95921,x95923)),f332(x95921,x95924))) % 165.30/165.06 [9995]~P19(x99958,x99952,x99955,x99957,x99956,x99951)+~E(f332(x99956,f833(x99954,x99953,x99951,x99956,x99957,x99955,x99952)),x99957)+~P24(f332(f62(x99952),x99953))+~P24(f332(f62(x99952),x99954))+E(f332(x99951,f332(f332(f113(f875(x99952,a862)),x99953),x99954)),f332(f332(x99955,f332(x99951,x99953)),f332(x99951,x99954))) % 165.30/165.06 [10051]~P19(x100518,x100512,x100515,x100517,x100516,x100511)+~P24(f332(f62(x100512),x100513))+~P24(f332(f62(x100512),x100514))+E(f332(x100511,f332(f332(f113(f875(x100512,a862)),x100513),x100514)),f332(f332(x100515,f332(x100511,x100513)),f332(x100511,x100514)))+P24(f332(f332(f334(x100512),f833(x100514,x100513,x100511,x100516,x100517,x100515,x100512)),f332(f332(f104(f875(x100512,a862)),x100513),x100514))) % 165.30/165.06 [9752]~P6(x97524,x97528,x97525)+~P6(x97521,x97529,x97523)+~P10(x97521,x97524,f875(x97522,a862),x97523,x97525,x97527)+P9(x97521,f875(x97522,a862),x97523,f332(f332(f8(f875(x97524,f875(x97522,a862)),f875(x97522,a862),x97521),f332(f42(x97524,f875(x97522,a862)),f332(f286(x97524,x97524,x97525),f332(f332(f310(x97524),x97526),f196(f875(x97524,a862)))))),x97527))+~P24(f332(f332(f334(x97524),x97526),x97528)) % 165.30/165.06 [5413]~P106(x54133)+~P32(x54133,x54131)+E(x54131,f690(x54132,x54133))+~E(f332(f174(x54133),x54131),x54132)+~P24(f332(f62(x54133),x54132))+~P24(f332(f138(x54133),x54131)) % 165.30/165.06 [5030]~P127(x50302)+~P128(x50302)+~P141(x50302)+~P110(x50302)+E(x50301,f2(x50302))+~E(f332(f332(f257(x50302),x50301),x50303),f2(x50302)) % 165.30/165.06 [5031]~P127(x50312)+~P128(x50312)+~P141(x50312)+~P110(x50312)+~E(x50311,f2(a868))+~E(f332(f332(f257(x50312),x50313),x50311),f2(x50312)) % 165.30/165.06 [6474]~P87(x64741)+~E(x64743,f2(x64741))+~E(x64742,f2(x64741))+E(f332(f332(f81(x64741),x64742),x64743),f2(x64741))+~P24(f332(f332(f246(x64741),f2(x64741)),x64743))+~P24(f332(f332(f246(x64741),f2(x64741)),x64742)) % 165.30/165.06 [8809]~E(f332(f266(a868,a868),x88093),f2(a868))+~E(x88091,f332(f332(f81(a868),f332(f332(f82(a868),f332(f266(a868,a868),x88093)),x88092)),f332(f270(a868,a868),x88093)))+P24(f332(f48(x88091,x88092),x88093))+~P24(f332(f332(f246(a868),f332(f270(a868,a868),x88093)),f2(a868)))+P24(f332(f332(f247(a868),f2(a868)),x88092))+~P24(f332(f332(f247(a868),x88092),f332(f270(a868,a868),x88093))) % 165.30/165.06 [8817]E(x88171,f2(a868))+~E(x88172,f332(f332(f81(a868),f332(f332(f82(a868),f332(f266(a868,a868),x88173)),x88171)),f332(f270(a868,a868),x88173)))+P24(f332(f48(x88172,x88171),x88173))+~P24(f332(f332(f247(a868),f2(a868)),x88171))+~P24(f332(f332(f246(a868),f2(a868)),f332(f270(a868,a868),x88173)))+~P24(f332(f332(f247(a868),f332(f270(a868,a868),x88173)),x88171)) % 165.30/165.06 [8835]~E(f332(f266(a868,a868),x88353),f2(a868))+~E(x88351,f332(f332(f81(a868),f332(f332(f82(a868),f332(f266(a868,a868),x88353)),x88352)),f332(f270(a868,a868),x88353)))+P24(f332(f48(x88351,x88352),x88353))+~P24(f332(f332(f247(a868),f2(a868)),x88352))+~P24(f332(f332(f246(a868),f2(a868)),f332(f270(a868,a868),x88353)))+~P24(f332(f332(f247(a868),f332(f270(a868,a868),x88353)),x88352)) % 165.30/165.06 [6855]~P26(x68552)+E(x68551,f196(f875(x68552,a862)))+E(x68553,f196(f875(x68552,a862)))+~P24(f332(f62(x68552),x68551))+~P24(f332(f62(x68552),x68553))+E(f10(x68552,f332(f332(f113(f875(x68552,a862)),x68553),x68551)),f332(f332(f113(x68552),f10(x68552,x68553)),f10(x68552,x68551))) % 165.30/165.06 [6856]~P26(x68562)+E(x68561,f196(f875(x68562,a862)))+E(x68563,f196(f875(x68562,a862)))+~P24(f332(f62(x68562),x68561))+~P24(f332(f62(x68562),x68563))+E(f11(x68562,f332(f332(f113(f875(x68562,a862)),x68563),x68561)),f332(f332(f104(x68562),f11(x68562,x68563)),f11(x68562,x68561))) % 165.30/165.06 [6857]~P106(x68572)+E(x68571,f196(f875(x68572,a862)))+E(x68573,f196(f875(x68572,a862)))+~P24(f332(f62(x68572),x68571))+~P24(f332(f62(x68572),x68573))+E(f14(x68572,f332(f332(f113(f875(x68572,a862)),x68573),x68571)),f332(f332(f245(x68572),f14(x68572,x68573)),f14(x68572,x68571))) % 165.30/165.06 [6858]~P106(x68582)+E(x68581,f196(f875(x68582,a862)))+E(x68583,f196(f875(x68582,a862)))+~P24(f332(f62(x68582),x68581))+~P24(f332(f62(x68582),x68583))+E(f15(x68582,f332(f332(f113(f875(x68582,a862)),x68583),x68581)),f332(f332(f244(x68582),f15(x68582,x68583)),f15(x68582,x68581))) % 165.30/165.06 [7492]~P95(x74922)+E(x74921,f196(f875(x74922,a862)))+E(x74923,f196(f875(x74922,a862)))+~P24(f332(f62(x74922),x74921))+~P24(f332(f62(x74922),x74923))+E(f332(f332(f82(x74922),f332(f64(x74922,f82(x74922)),x74923)),f332(f64(x74922,f82(x74922)),x74921)),f332(f64(x74922,f82(x74922)),f332(f332(f113(f875(x74922,a862)),x74923),x74921))) % 165.30/165.06 [7650]~P106(x76502)+E(x76501,f196(f875(x76502,a862)))+E(x76503,f196(f875(x76502,a862)))+~P24(f332(f62(x76502),x76501))+~P24(f332(f62(x76502),x76503))+E(f332(f332(f244(x76502),f12(x76502,f244(x76502),x76503)),f12(x76502,f244(x76502),x76501)),f12(x76502,f244(x76502),f332(f332(f113(f875(x76502,a862)),x76503),x76501))) % 165.30/165.06 [7651]~P106(x76512)+E(x76511,f196(f875(x76512,a862)))+E(x76513,f196(f875(x76512,a862)))+~P24(f332(f62(x76512),x76511))+~P24(f332(f62(x76512),x76513))+E(f332(f332(f245(x76512),f13(x76512,f245(x76512),x76513)),f13(x76512,f245(x76512),x76511)),f13(x76512,f245(x76512),f332(f332(f113(f875(x76512,a862)),x76513),x76511))) % 165.30/165.06 [8658]~P24(f332(x86581,x86583))+P24(f332(x86581,f404(x86581,x86582)))+P24(f332(x86581,f398(x86581,x86582)))+~P24(f332(f332(f247(a1),f2(a1)),x86582))+~P24(f332(f332(f334(a1),x86583),f303(a1,f79(a1),x86582)))+P24(f332(x86581,f332(f332(f22(a1),f398(x86581,x86582)),f332(f332(f82(a1),f403(x86581,x86582)),x86582)))) % 165.30/165.06 [8946]~P24(f332(x89461,x89463))+~P24(f332(x89461,f398(x89461,x89462)))+P24(f332(x89461,f404(x89461,x89462)))+~P24(f332(f332(f247(a1),f2(a1)),x89462))+~P24(f332(f332(f334(a1),x89463),f303(a1,f79(a1),x89462)))+~P24(f332(x89461,f332(f332(f22(a1),f398(x89461,x89462)),f332(f332(f82(a1),f403(x89461,x89462)),x89462)))) % 165.30/165.06 [10127]~P97(x101272)+E(x101271,f196(f875(x101272,a862)))+E(x101273,f196(f875(x101272,a862)))+~P24(f332(f62(x101272),x101271))+~P24(f332(f62(x101272),x101273))+E(f11(x101272,f332(f252(x101272),f332(f332(f8(f875(x101272,a862),a862,x101272),f88(x101272)),f332(f332(f8(f875(x101272,f875(x101272,a862)),f875(x101272,a862),x101272),f332(f8(f875(x101272,a862),a862,x101272),f88(x101272))),f332(f332(f7(x101272,f875(x101272,f875(x101272,a862)),f875(x101272,f875(x101272,a862))),f332(f332(f8(f875(x101272,f875(f875(x101272,a862),f875(x101272,a862))),f875(f875(x101272,f875(x101272,a862)),f875(x101272,f875(x101272,a862))),x101272),f18(x101272,f875(x101272,a862),f875(x101272,a862))),f332(f332(f8(f875(x101272,f875(x101272,f875(a862,a862))),f875(x101272,f875(f875(x101272,a862),f875(x101272,a862))),x101272),f332(f8(f875(x101272,f875(a862,a862)),f875(f875(x101272,a862),f875(x101272,a862)),x101272),f18(x101272,a862,a862))),f332(f332(f8(f875(x101272,f875(x101272,a862)),f875(x101272,f875(x101272,f875(a862,a862))),x101272),f332(f8(f875(x101272,a862),f875(x101272,f875(a862,a862)),x101272),f332(f8(a862,f875(a862,a862),x101272),a330))),f332(f332(f7(x101272,f875(x101272,f875(x101272,x101272)),f875(x101272,f875(x101272,a862))),f332(f332(f8(f875(f875(x101272,x101272),f875(x101272,a862)),f875(f875(x101272,f875(x101272,x101272)),f875(x101272,f875(x101272,a862))),x101272),f8(f875(x101272,x101272),f875(x101272,a862),x101272)),f332(f332(f8(f875(x101272,a862),f875(f875(x101272,x101272),f875(x101272,a862)),x101272),f8(x101272,a862,x101272)),a329))),f113(x101272)))))),f332(f332(f7(x101272,f875(x101272,a862),f875(x101272,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x101272,a862),f875(x101272,a862)),x101272),f8(a862,a862,x101272)),f332(f332(f8(a862,f875(a862,a862),x101272),a330),f332(f332(f7(x101272,f875(x101272,a862),a862),f334(x101272)),x101273)))),f332(f332(f7(x101272,f875(x101272,a862),a862),f334(x101272)),x101271))))))),f332(f332(f113(x101272),f11(x101272,x101273)),f11(x101272,x101271))) % 165.30/165.06 [10128]~P97(x101282)+E(x101281,f196(f875(x101282,a862)))+E(x101283,f196(f875(x101282,a862)))+~P24(f332(f62(x101282),x101281))+~P24(f332(f62(x101282),x101283))+E(f10(x101282,f332(f252(x101282),f332(f332(f8(f875(x101282,a862),a862,x101282),f88(x101282)),f332(f332(f8(f875(x101282,f875(x101282,a862)),f875(x101282,a862),x101282),f332(f8(f875(x101282,a862),a862,x101282),f88(x101282))),f332(f332(f7(x101282,f875(x101282,f875(x101282,a862)),f875(x101282,f875(x101282,a862))),f332(f332(f8(f875(x101282,f875(f875(x101282,a862),f875(x101282,a862))),f875(f875(x101282,f875(x101282,a862)),f875(x101282,f875(x101282,a862))),x101282),f18(x101282,f875(x101282,a862),f875(x101282,a862))),f332(f332(f8(f875(x101282,f875(x101282,f875(a862,a862))),f875(x101282,f875(f875(x101282,a862),f875(x101282,a862))),x101282),f332(f8(f875(x101282,f875(a862,a862)),f875(f875(x101282,a862),f875(x101282,a862)),x101282),f18(x101282,a862,a862))),f332(f332(f8(f875(x101282,f875(x101282,a862)),f875(x101282,f875(x101282,f875(a862,a862))),x101282),f332(f8(f875(x101282,a862),f875(x101282,f875(a862,a862)),x101282),f332(f8(a862,f875(a862,a862),x101282),a330))),f332(f332(f7(x101282,f875(x101282,f875(x101282,x101282)),f875(x101282,f875(x101282,a862))),f332(f332(f8(f875(f875(x101282,x101282),f875(x101282,a862)),f875(f875(x101282,f875(x101282,x101282)),f875(x101282,f875(x101282,a862))),x101282),f8(f875(x101282,x101282),f875(x101282,a862),x101282)),f332(f332(f8(f875(x101282,a862),f875(f875(x101282,x101282),f875(x101282,a862)),x101282),f8(x101282,a862,x101282)),a329))),f104(x101282)))))),f332(f332(f7(x101282,f875(x101282,a862),f875(x101282,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x101282,a862),f875(x101282,a862)),x101282),f8(a862,a862,x101282)),f332(f332(f8(a862,f875(a862,a862),x101282),a330),f332(f332(f7(x101282,f875(x101282,a862),a862),f334(x101282)),x101283)))),f332(f332(f7(x101282,f875(x101282,a862),a862),f334(x101282)),x101281))))))),f332(f332(f104(x101282),f10(x101282,x101283)),f10(x101282,x101281))) % 165.30/165.06 [10129]~P106(x101292)+E(x101291,f196(f875(x101292,a862)))+E(x101293,f196(f875(x101292,a862)))+~P24(f332(f62(x101292),x101291))+~P24(f332(f62(x101292),x101293))+E(f13(x101292,f245(x101292),f332(f252(x101292),f332(f332(f8(f875(x101292,a862),a862,x101292),f88(x101292)),f332(f332(f8(f875(x101292,f875(x101292,a862)),f875(x101292,a862),x101292),f332(f8(f875(x101292,a862),a862,x101292),f88(x101292))),f332(f332(f7(x101292,f875(x101292,f875(x101292,a862)),f875(x101292,f875(x101292,a862))),f332(f332(f8(f875(x101292,f875(f875(x101292,a862),f875(x101292,a862))),f875(f875(x101292,f875(x101292,a862)),f875(x101292,f875(x101292,a862))),x101292),f18(x101292,f875(x101292,a862),f875(x101292,a862))),f332(f332(f8(f875(x101292,f875(x101292,f875(a862,a862))),f875(x101292,f875(f875(x101292,a862),f875(x101292,a862))),x101292),f332(f8(f875(x101292,f875(a862,a862)),f875(f875(x101292,a862),f875(x101292,a862)),x101292),f18(x101292,a862,a862))),f332(f332(f8(f875(x101292,f875(x101292,a862)),f875(x101292,f875(x101292,f875(a862,a862))),x101292),f332(f8(f875(x101292,a862),f875(x101292,f875(a862,a862)),x101292),f332(f8(a862,f875(a862,a862),x101292),a330))),f332(f332(f7(x101292,f875(x101292,f875(x101292,x101292)),f875(x101292,f875(x101292,a862))),f332(f332(f8(f875(f875(x101292,x101292),f875(x101292,a862)),f875(f875(x101292,f875(x101292,x101292)),f875(x101292,f875(x101292,a862))),x101292),f8(f875(x101292,x101292),f875(x101292,a862),x101292)),f332(f332(f8(f875(x101292,a862),f875(f875(x101292,x101292),f875(x101292,a862)),x101292),f8(x101292,a862,x101292)),a329))),f244(x101292)))))),f332(f332(f7(x101292,f875(x101292,a862),f875(x101292,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x101292,a862),f875(x101292,a862)),x101292),f8(a862,a862,x101292)),f332(f332(f8(a862,f875(a862,a862),x101292),a330),f332(f332(f7(x101292,f875(x101292,a862),a862),f334(x101292)),x101293)))),f332(f332(f7(x101292,f875(x101292,a862),a862),f334(x101292)),x101291))))))),f332(f332(f244(x101292),f13(x101292,f245(x101292),x101293)),f13(x101292,f245(x101292),x101291))) % 165.30/165.06 [10130]~P106(x101302)+E(x101301,f196(f875(x101302,a862)))+E(x101303,f196(f875(x101302,a862)))+~P24(f332(f62(x101302),x101301))+~P24(f332(f62(x101302),x101303))+E(f12(x101302,f244(x101302),f332(f252(x101302),f332(f332(f8(f875(x101302,a862),a862,x101302),f88(x101302)),f332(f332(f8(f875(x101302,f875(x101302,a862)),f875(x101302,a862),x101302),f332(f8(f875(x101302,a862),a862,x101302),f88(x101302))),f332(f332(f7(x101302,f875(x101302,f875(x101302,a862)),f875(x101302,f875(x101302,a862))),f332(f332(f8(f875(x101302,f875(f875(x101302,a862),f875(x101302,a862))),f875(f875(x101302,f875(x101302,a862)),f875(x101302,f875(x101302,a862))),x101302),f18(x101302,f875(x101302,a862),f875(x101302,a862))),f332(f332(f8(f875(x101302,f875(x101302,f875(a862,a862))),f875(x101302,f875(f875(x101302,a862),f875(x101302,a862))),x101302),f332(f8(f875(x101302,f875(a862,a862)),f875(f875(x101302,a862),f875(x101302,a862)),x101302),f18(x101302,a862,a862))),f332(f332(f8(f875(x101302,f875(x101302,a862)),f875(x101302,f875(x101302,f875(a862,a862))),x101302),f332(f8(f875(x101302,a862),f875(x101302,f875(a862,a862)),x101302),f332(f8(a862,f875(a862,a862),x101302),a330))),f332(f332(f7(x101302,f875(x101302,f875(x101302,x101302)),f875(x101302,f875(x101302,a862))),f332(f332(f8(f875(f875(x101302,x101302),f875(x101302,a862)),f875(f875(x101302,f875(x101302,x101302)),f875(x101302,f875(x101302,a862))),x101302),f8(f875(x101302,x101302),f875(x101302,a862),x101302)),f332(f332(f8(f875(x101302,a862),f875(f875(x101302,x101302),f875(x101302,a862)),x101302),f8(x101302,a862,x101302)),a329))),f245(x101302)))))),f332(f332(f7(x101302,f875(x101302,a862),f875(x101302,a862)),f332(f332(f8(f875(a862,a862),f875(f875(x101302,a862),f875(x101302,a862)),x101302),f8(a862,a862,x101302)),f332(f332(f8(a862,f875(a862,a862),x101302),a330),f332(f332(f7(x101302,f875(x101302,a862),a862),f334(x101302)),x101303)))),f332(f332(f7(x101302,f875(x101302,a862),a862),f334(x101302)),x101301))))))),f332(f332(f245(x101302),f12(x101302,f244(x101302),x101303)),f12(x101302,f244(x101302),x101301))) % 165.30/165.06 [7179]~P112(x71793)+E(x71791,x71792)+~E(f332(f332(f257(x71793),x71791),x71794),f332(f332(f257(x71793),x71792),x71794))+~P24(f332(f332(f246(x71793),f2(x71793)),x71792))+~P24(f332(f332(f246(x71793),f2(x71793)),x71791))+~P24(f332(f332(f247(a868),f2(a868)),x71794)) % 165.30/165.06 [7449]~P106(x74492)+E(x74491,f196(f875(x74492,a862)))+~P24(f332(f62(x74492),x74491))+~P24(f332(f332(f334(x74492),x74494),x74491))+P24(f332(f332(f246(x74492),x74493),x74494))+~P24(f332(f332(f246(x74492),x74493),f332(f64(x74492,f244(x74492)),x74491))) % 165.30/165.06 [7450]~P100(x74502)+E(x74501,f196(f875(x74502,a862)))+~P24(f332(f62(x74502),x74501))+~P24(f332(f332(f334(x74502),x74504),x74501))+P24(f332(f332(f246(x74502),x74503),x74504))+~P24(f332(f332(f246(x74502),x74503),f332(f64(x74502,f104(x74502)),x74501))) % 165.30/165.06 [7451]~P106(x74512)+E(x74511,f196(f875(x74512,a862)))+~P24(f332(f62(x74512),x74511))+~P24(f332(f332(f334(x74512),x74514),x74511))+P24(f332(f332(f247(x74512),x74513),x74514))+~P24(f332(f332(f247(x74512),x74513),f332(f64(x74512,f244(x74512)),x74511))) % 165.30/165.06 [7350]E(x73501,f2(a1))+E(f332(f332(f39(a1),x73502),x73501),x73503)+~P24(f332(f332(f246(a1),x73504),f2(a1)))+~E(x73502,f332(f332(f81(a1),f332(f332(f82(a1),x73501),x73503)),x73504))+P24(f332(f332(f247(a1),f2(a1)),x73501))+~P24(f332(f332(f247(a1),x73501),x73504)) % 165.30/165.06 [7365]E(f45(a1,x73652,x73651),x73653)+E(x73651,f2(a1))+~P24(f332(f332(f246(a1),x73653),f2(a1)))+~E(x73652,f332(f332(f81(a1),f332(f332(f82(a1),x73651),x73654)),x73653))+P24(f332(f332(f247(a1),f2(a1)),x73651))+~P24(f332(f332(f247(a1),x73651),x73653)) % 165.30/165.06 [7491]E(x74911,f2(a1))+E(f332(f332(f39(a1),x74912),x74911),x74913)+~E(x74912,f332(f332(f81(a1),f332(f332(f82(a1),x74911),x74913)),x74914))+~P24(f332(f332(f246(a1),f2(a1)),x74914))+~P24(f332(f332(f247(a1),f2(a1)),x74911))+~P24(f332(f332(f247(a1),x74914),x74911)) % 165.30/165.06 [7513]E(f45(a1,x75132,x75131),x75133)+E(x75131,f2(a1))+~E(x75132,f332(f332(f81(a1),f332(f332(f82(a1),x75131),x75134)),x75133))+~P24(f332(f332(f246(a1),f2(a1)),x75133))+~P24(f332(f332(f247(a1),f2(a1)),x75131))+~P24(f332(f332(f247(a1),x75133),x75131)) % 165.30/165.06 [7654]~P106(x76542)+E(x76541,f196(f875(x76542,a862)))+~P24(f332(f62(x76542),x76541))+~P24(f332(f332(f334(x76542),x76544),x76541))+~P24(f332(f332(f246(x76542),x76544),x76543))+P24(f332(f332(f246(x76542),f332(f64(x76542,f244(x76542)),x76541)),x76543)) % 165.30/165.06 [7655]~P106(x76552)+E(x76551,f196(f875(x76552,a862)))+~P24(f332(f62(x76552),x76551))+~P24(f332(f332(f247(x76552),x76554),x76553))+~P24(f332(f332(f334(x76552),x76554),x76551))+P24(f332(f332(f247(x76552),f332(f64(x76552,f244(x76552)),x76551)),x76553)) % 165.30/165.06 [8218]~P24(f332(f332(f246(a1),x82184),f2(a1)))+~E(x82181,f332(f332(f81(a1),f332(f332(f82(a1),x82182),x82183)),x82184))+~P24(f332(f332(f246(a1),f2(a1)),x82184))+~P24(f332(f332(f247(a1),x82184),x82182))+~P24(f332(f332(f247(a1),x82182),x82184))+P24(f332(f49(x82181,x82182),f332(f332(f267(a1,a1),x82183),x82184))) % 165.30/165.06 [9136]~P59(x91363)+~P59(x91364)+E(x91361,x91362)+~E(f332(f197(f869(x91363)),x91362),f332(f197(f869(x91364)),f56(x91364)))+~E(f332(f197(f869(x91363)),x91361),f332(f197(f869(x91364)),f56(x91364)))+~E(f332(f74(f872(x91363),x91363,x91364,f243(x91363)),f332(f180(x91364,x91363),f332(f332(f184(x91364,x91363),f56(x91364)),x91361))),f332(f74(f872(x91363),x91363,x91364,f243(x91363)),f332(f180(x91364,x91363),f332(f332(f184(x91364,x91363),f56(x91364)),x91362)))) % 165.30/165.06 [8378]~P107(x83781)+P24(f332(f332(f247(f875(x83781,a862)),f303(x83781,x83782,x83783)),f303(x83781,x83784,x83785)))+~P24(f332(f332(f246(x83781),x83784),x83782))+~P24(f332(f332(f246(x83781),x83784),x83785))+~P24(f332(f332(f246(x83781),x83783),x83785))+~P24(f332(f332(f247(x83781),x83783),x83785)) % 165.30/165.06 [8379]~P107(x83791)+P24(f332(f332(f247(f875(x83791,a862)),f303(x83791,x83792,x83793)),f303(x83791,x83794,x83795)))+~P24(f332(f332(f246(x83791),x83793),x83795))+~P24(f332(f332(f246(x83791),x83794),x83795))+~P24(f332(f332(f246(x83791),x83794),x83792))+~P24(f332(f332(f247(x83791),x83794),x83792)) % 165.30/165.06 [9196]P57(x91962,x91963,x91964,x91961)+E(x91961,f196(f875(x91962,a862)))+~P24(f332(f62(x91962),x91964))+~P24(f332(f62(x91962),x91961))+~P24(f332(f332(x91963,f665(x91961,x91964,x91963,x91962)),x91965))+~P24(f332(f332(f334(x91962),x91965),x91961)) % 165.30/165.06 [9337]~E(x93373,x93375)+~P73(x93371)+~P74(x93371)+~P42(x93373)+E(f332(f332(f6(a1,x93371),x93372),x93373),f332(f332(f6(a1,x93371),x93374),x93375))+P24(f332(f332(f246(a1),f2(a1)),f424(x93372,x93374,x93373,x93375,x93371))) % 165.30/165.06 [9338]~E(x93383,x93385)+~P73(x93381)+~P74(x93381)+~P42(x93383)+E(f332(f332(f9(a1,x93381),x93382),x93383),f332(f332(f9(a1,x93381),x93384),x93385))+P24(f332(f332(f246(a1),f2(a1)),f417(x93382,x93384,x93383,x93385,x93381))) % 165.30/165.06 [9500]~E(x95005,x95003)+~P73(x95001)+~P74(x95001)+~P42(x95005)+~E(f332(x95002,f424(x95004,x95002,x95005,x95003,x95001)),f332(x95004,f424(x95004,x95002,x95005,x95003,x95001)))+E(f332(f332(f6(a1,x95001),x95002),x95003),f332(f332(f6(a1,x95001),x95004),x95005)) % 165.30/165.06 [9501]~E(x95015,x95013)+~P73(x95011)+~P74(x95011)+~P42(x95015)+~E(f332(x95012,f417(x95014,x95012,x95015,x95013,x95011)),f332(x95014,f417(x95014,x95012,x95015,x95013,x95011)))+E(f332(f332(f9(a1,x95011),x95012),x95013),f332(f332(f9(a1,x95011),x95014),x95015)) % 165.30/165.06 [9589]~P77(x95893)+E(f332(x95891,x95892),f2(x95893))+~E(f332(f332(f6(x95894,x95893),x95891),x95895),f2(x95893))+~P24(f332(f62(x95894),x95895))+P24(f332(f332(f334(x95894),f357(x95892,x95891,x95895,x95894,x95893)),x95895))+~P24(f332(f332(f334(x95894),x95892),x95895)) % 165.30/165.06 [9725]~P77(x97253)+E(f332(x97251,x97252),f2(x97253))+~E(f332(f332(f6(x97254,x97253),x97251),x97255),f2(x97253))+~P24(f332(f62(x97254),x97255))+~P24(f332(f332(f334(x97254),x97252),x97255))+~P24(f332(f332(f246(x97253),f2(x97253)),f332(x97251,f357(x97252,x97251,x97255,x97254,x97253)))) % 165.30/165.06 [8297]~P135(x82971)+~P24(f332(f332(f246(x82971),x82973),x82975))+~P24(f332(f332(f246(x82971),x82972),x82974))+~P24(f332(f332(f246(x82971),f2(x82971)),x82973))+~P24(f332(f332(f246(x82971),f2(x82971)),x82974))+P24(f332(f332(f246(x82971),f332(f332(f82(x82971),x82972),x82973)),f332(f332(f82(x82971),x82974),x82975))) % 165.30/165.06 [8298]~P135(x82981)+~P24(f332(f332(f246(x82981),x82983),x82985))+~P24(f332(f332(f246(x82981),x82982),x82984))+~P24(f332(f332(f246(x82981),f2(x82981)),x82983))+~P24(f332(f332(f246(x82981),f2(x82981)),x82982))+P24(f332(f332(f246(x82981),f332(f332(f82(x82981),x82982),x82983)),f332(f332(f82(x82981),x82984),x82985))) % 165.30/165.06 [8299]~P63(x82991)+~P24(f332(f332(f247(x82991),f2(x82991)),x82995))+~P24(f332(f332(f246(x82991),x82995),x82993))+~P24(f332(f332(f246(x82991),x82992),x82994))+~P24(f332(f332(f246(x82991),f2(x82991)),x82992))+P24(f332(f332(f246(x82991),f332(f332(f290(x82991),x82992),x82993)),f332(f332(f290(x82991),x82994),x82995))) % 165.30/165.06 [8300]~P129(x83001)+~P24(f332(f332(f246(x83001),x83003),x83005))+~P24(f332(f332(f246(x83001),f2(x83001)),x83002))+~P24(f332(f332(f247(x83001),x83002),x83004))+~P24(f332(f332(f247(x83001),f2(x83001)),x83003))+P24(f332(f332(f247(x83001),f332(f332(f82(x83001),x83002),x83003)),f332(f332(f82(x83001),x83004),x83005))) % 165.30/165.06 [8301]~P129(x83011)+~P24(f332(f332(f246(x83011),x83012),x83014))+~P24(f332(f332(f246(x83011),f2(x83011)),x83013))+~P24(f332(f332(f247(x83011),x83013),x83015))+~P24(f332(f332(f247(x83011),f2(x83011)),x83012))+P24(f332(f332(f247(x83011),f332(f332(f82(x83011),x83012),x83013)),f332(f332(f82(x83011),x83014),x83015))) % 165.30/165.06 [8302]~P129(x83021)+~P24(f332(f332(f246(x83021),f2(x83021)),x83023))+~P24(f332(f332(f246(x83021),f2(x83021)),x83022))+~P24(f332(f332(f247(x83021),x83023),x83025))+~P24(f332(f332(f247(x83021),x83022),x83024))+P24(f332(f332(f247(x83021),f332(f332(f82(x83021),x83022),x83023)),f332(f332(f82(x83021),x83024),x83025))) % 165.30/165.06 [8303]~P129(x83031)+~P24(f332(f332(f246(x83031),f2(x83031)),x83033))+~P24(f332(f332(f247(x83031),x83033),x83035))+~P24(f332(f332(f247(x83031),x83032),x83034))+~P24(f332(f332(f247(x83031),f2(x83031)),x83034))+P24(f332(f332(f247(x83031),f332(f332(f82(x83031),x83032),x83033)),f332(f332(f82(x83031),x83034),x83035))) % 165.30/165.06 [8304]~P63(x83041)+~P24(f332(f332(f246(x83041),x83045),x83043))+~P24(f332(f332(f246(x83041),f2(x83041)),x83042))+~P24(f332(f332(f247(x83041),x83042),x83044))+~P24(f332(f332(f247(x83041),f2(x83041)),x83045))+P24(f332(f332(f247(x83041),f332(f332(f290(x83041),x83042),x83043)),f332(f332(f290(x83041),x83044),x83045))) % 165.30/165.06 [8305]~P63(x83051)+~P24(f332(f332(f246(x83051),x83052),x83054))+~P24(f332(f332(f247(x83051),x83055),x83053))+~P24(f332(f332(f247(x83051),f2(x83051)),x83055))+~P24(f332(f332(f247(x83051),f2(x83051)),x83052))+P24(f332(f332(f247(x83051),f332(f332(f290(x83051),x83052),x83053)),f332(f332(f290(x83051),x83054),x83055))) % 165.30/165.06 [9629]~P86(x96295)+~P74(x96295)+E(x96291,f196(f875(x96292,a862)))+~P24(f332(f62(x96292),x96291))+P24(f332(f332(f334(x96292),f841(x96293,x96294,x96291,x96292,x96295)),x96291))+P24(f332(f332(f247(x96295),f332(f332(f6(x96292,x96295),x96294),x96291)),f332(f332(f6(x96292,x96295),x96293),x96291))) % 165.30/165.06 [9748]~P84(x97481)+~P74(x97481)+~P24(f332(f62(x97482),x97485))+~P24(f332(f332(f246(x97481),f2(x97481)),f332(x97483,f861(x97483,x97484,x97485,x97482,x97481))))+P24(f332(f332(f246(x97481),f332(f332(f6(x97482,x97481),x97483),x97484)),f332(f332(f6(x97482,x97481),x97483),x97485)))+~P24(f332(f332(f246(f875(x97482,a862)),x97484),x97485)) % 165.30/165.06 [9915]~P86(x99153)+~P74(x99153)+E(x99151,f196(f875(x99152,a862)))+~P24(f332(f62(x99152),x99151))+~P24(f332(f332(f247(x99153),f332(x99154,f841(x99155,x99154,x99151,x99152,x99153))),f332(x99155,f841(x99155,x99154,x99151,x99152,x99153))))+P24(f332(f332(f247(x99153),f332(f332(f6(x99152,x99153),x99154),x99151)),f332(f332(f6(x99152,x99153),x99155),x99151))) % 165.30/165.06 [7038]~P13(x70382,x70385,x70384)+E(x70381,f196(f875(x70382,a862)))+E(x70383,f196(f875(x70382,a862)))+~P24(f332(f62(x70382),x70381))+~P24(f332(f62(x70382),x70383))+E(f332(x70384,f332(f332(f113(f875(x70382,a862)),x70383),x70381)),f332(f332(x70385,f332(x70384,x70383)),f332(x70384,x70381))) % 165.30/165.06 [7620]~P145(x76201,x76203,x76204)+P24(f332(x76201,x76202))+~P24(f332(f332(f247(a1),x76204),f2(a1)))+~P24(f332(f332(f246(a1),x76205),f2(a1)))+~E(x76203,f332(f332(f81(a1),f332(f332(f82(a1),x76204),x76202)),x76205))+~P24(f332(f332(f247(a1),x76204),x76205)) % 165.30/165.06 [7621]~P144(x76211,x76213,x76214)+P24(f332(x76211,x76212))+~P24(f332(f332(f247(a1),x76214),f2(a1)))+~P24(f332(f332(f246(a1),x76212),f2(a1)))+~E(x76213,f332(f332(f81(a1),f332(f332(f82(a1),x76214),x76215)),x76212))+~P24(f332(f332(f247(a1),x76214),x76212)) % 165.30/165.06 [7663]~P145(x76631,x76633,x76634)+P24(f332(x76631,x76632))+~E(x76633,f332(f332(f81(a1),f332(f332(f82(a1),x76634),x76632)),x76635))+~P24(f332(f332(f246(a1),f2(a1)),x76635))+~P24(f332(f332(f247(a1),f2(a1)),x76634))+~P24(f332(f332(f247(a1),x76635),x76634)) % 165.30/165.06 [7664]~P144(x76641,x76643,x76644)+P24(f332(x76641,x76642))+~E(x76643,f332(f332(f81(a1),f332(f332(f82(a1),x76644),x76645)),x76642))+~P24(f332(f332(f246(a1),f2(a1)),x76642))+~P24(f332(f332(f247(a1),f2(a1)),x76644))+~P24(f332(f332(f247(a1),x76642),x76644)) % 165.30/165.06 [8580]P24(f332(f332(x85801,x85802),x85803))+~P24(f332(f332(x85801,f332(f332(f39(a1),x85804),x85805)),f45(a1,x85804,x85805)))+~P24(f332(f332(f247(a1),x85805),f2(a1)))+~P24(f332(f332(f246(a1),x85803),f2(a1)))+~E(x85804,f332(f332(f81(a1),f332(f332(f82(a1),x85805),x85802)),x85803))+~P24(f332(f332(f247(a1),x85805),x85803)) % 165.30/165.06 [8587]P24(f332(f332(x85871,x85872),x85873))+~P24(f332(f332(x85871,f332(f332(f39(a1),x85874),x85875)),f45(a1,x85874,x85875)))+~E(x85874,f332(f332(f81(a1),f332(f332(f82(a1),x85875),x85872)),x85873))+~P24(f332(f332(f246(a1),f2(a1)),x85873))+~P24(f332(f332(f247(a1),f2(a1)),x85875))+~P24(f332(f332(f247(a1),x85873),x85875)) % 165.30/165.06 [8823]E(x88231,x88232)+~P54(x88233,x88235,x88234)+~P24(f332(f332(f334(x88233),x88232),x88235))+~P24(f332(f332(f334(x88233),x88231),x88235))+P24(f332(f332(f334(f874(x88233,x88233)),f332(f332(f267(x88233,x88233),x88231),x88232)),x88234))+P24(f332(f332(f334(f874(x88233,x88233)),f332(f332(f267(x88233,x88233),x88232),x88231)),x88234)) % 165.30/165.06 [9656]~P84(x96565)+~P74(x96565)+~P24(f332(f62(x96561),x96564))+P24(f332(f332(f246(x96565),f332(f332(f6(x96561,x96565),x96562),x96563)),f332(f332(f6(x96561,x96565),x96562),x96564)))+~P24(f332(f332(f246(f875(x96561,a862)),x96563),x96564))+P24(f332(f332(f334(x96561),f861(x96562,x96563,x96564,x96561,x96565)),f332(f332(f22(f875(x96561,a862)),x96564),x96563))) % 165.30/165.06 [9756]E(x97561,f196(f875(x97562,a862)))+~P24(f332(f62(x97562),x97563))+~P24(f332(f62(x97562),x97561))+P24(f332(f332(f334(f874(f875(x97562,a862),f875(x97562,a862))),f332(f332(f267(f875(x97562,a862),f875(x97562,a862)),x97563),x97561)),f323(x97562,x97564)))+~P24(f332(f332(f334(x97562),x97565),x97561))+~P24(f332(f332(f334(f874(x97562,x97562)),f332(f332(f267(x97562,x97562),f674(x97564,x97561,x97563,x97562)),x97565)),x97564)) % 165.30/165.06 [9757]E(x97571,f196(f875(x97572,a862)))+~P24(f332(f62(x97572),x97573))+~P24(f332(f62(x97572),x97571))+P24(f332(f332(f334(f874(f875(x97572,a862),f875(x97572,a862))),f332(f332(f267(f875(x97572,a862),f875(x97572,a862)),x97573),x97571)),f323(x97572,x97574)))+~P24(f332(f332(f334(x97572),x97575),x97571))+~P24(f332(f332(f334(f874(x97572,x97572)),f332(f332(f267(x97572,x97572),f721(x97574,x97571,x97573,x97572)),x97575)),x97574)) % 165.30/165.06 [9919]~P77(x99191)+~E(f332(f332(f6(x99195,x99191),x99192),x99196),x99194)+~P24(f332(f62(x99195),x99196))+P24(f332(f332(f334(x99195),f358(x99193,x99194,x99192,x99196,x99195,x99191)),x99196))+P24(f332(f332(f246(x99191),f332(x99192,x99193)),x99194))+~P24(f332(f332(f334(x99195),x99193),x99196)) % 165.30/165.06 [9966]~P77(x99661)+~E(f332(f332(f6(x99665,x99661),x99662),x99666),x99664)+~P24(f332(f62(x99665),x99666))+~P24(f332(f332(f334(x99665),x99663),x99666))+~P24(f332(f332(f246(x99661),f2(x99661)),f332(x99662,f358(x99663,x99664,x99662,x99666,x99665,x99661))))+P24(f332(f332(f246(x99661),f332(x99662,x99663)),x99664)) % 165.30/165.06 [10077]~E(x100775,x100778)+~E(x100774,x100777)+~P105(x100771)+~P74(x100772)+E(f332(f332(f6(x100771,x100772),x100773),f332(f302(x100771,x100774),x100775)),f332(f332(f6(x100771,x100772),x100776),f332(f302(x100771,x100777),x100778)))+P24(f332(f332(f246(x100771),x100774),f729(x100773,x100776,x100775,x100778,x100774,x100777,x100771,x100772))) % 165.30/165.06 [10094]~E(x100947,x100944)+~E(x100948,x100945)+~P105(x100941)+~P74(x100942)+~E(f332(x100943,f729(x100946,x100943,x100948,x100945,x100947,x100944,x100941,x100942)),f332(x100946,f729(x100946,x100943,x100948,x100945,x100947,x100944,x100941,x100942)))+E(f332(f332(f6(x100941,x100942),x100943),f332(f302(x100941,x100944),x100945)),f332(f332(f6(x100941,x100942),x100946),f332(f302(x100941,x100947),x100948))) % 165.30/165.06 [10096]~E(x100964,x100967)+~E(x100965,x100968)+~P105(x100961)+~P74(x100962)+E(f332(f332(f6(x100961,x100962),x100963),f332(f302(x100961,x100964),x100965)),f332(f332(f6(x100961,x100962),x100966),f332(f302(x100961,x100967),x100968)))+P24(f332(f332(f247(x100961),f729(x100963,x100966,x100965,x100968,x100964,x100967,x100961,x100962)),x100965)) % 165.30/165.06 [9762]~P6(x97625,x97629,x97626)+~P6(x97621,x976210,x97623)+~P10(x97621,x97625,f875(x97622,a862),x97623,x97626,x97628)+~P24(f332(f332(f334(x97625),x97627),x97629))+~P24(f332(f332(f334(x97621),x97624),x976210))+E(f332(f332(f42(x97621,f875(x97622,a862)),f332(f286(x97621,x97621,x97623),f332(f332(f310(x97621),x97624),f196(f875(x97621,a862))))),f332(f332(f8(f875(x97625,f875(x97622,a862)),f875(x97622,a862),x97621),f332(f42(x97625,f875(x97622,a862)),f332(f286(x97625,x97625,x97626),f332(f332(f310(x97625),x97627),f196(f875(x97625,a862)))))),x97628)),f332(f332(x97628,x97624),x97627)) % 165.30/165.06 [5581]~P106(x55813)+~P32(x55813,x55812)+~P32(x55813,x55811)+E(x55811,x55812)+~E(f332(f174(x55813),x55811),f332(f174(x55813),x55812))+~P24(f332(f138(x55813),x55812))+~P24(f332(f138(x55813),x55811)) % 165.30/165.06 [4912]~P127(x49122)+~P128(x49122)+~P141(x49122)+~P110(x49122)+~E(x49123,f2(x49122))+E(x49121,f2(a868))+E(f332(f332(f257(x49122),x49123),x49121),f2(x49122)) % 165.30/165.06 [9080]E(x90801,f2(a868))+~E(x90802,f332(f332(f81(a868),f332(f332(f82(a868),f332(f266(a868,a868),x90803)),x90801)),f332(f270(a868,a868),x90803)))+P24(f332(f48(x90802,x90801),x90803))+~P24(f332(f332(f246(a868),f332(f270(a868,a868),x90803)),f2(a868)))+~P24(f332(f332(f246(a868),f2(a868)),f332(f270(a868,a868),x90803)))+~P24(f332(f332(f247(a868),x90801),f332(f270(a868,a868),x90803)))+~P24(f332(f332(f247(a868),f332(f270(a868,a868),x90803)),x90801)) % 165.30/165.06 [9089]~E(f332(f266(a868,a868),x90893),f2(a868))+~E(x90891,f332(f332(f81(a868),f332(f332(f82(a868),f332(f266(a868,a868),x90893)),x90892)),f332(f270(a868,a868),x90893)))+P24(f332(f48(x90891,x90892),x90893))+~P24(f332(f332(f246(a868),f332(f270(a868,a868),x90893)),f2(a868)))+~P24(f332(f332(f246(a868),f2(a868)),f332(f270(a868,a868),x90893)))+~P24(f332(f332(f247(a868),x90892),f332(f270(a868,a868),x90893)))+~P24(f332(f332(f247(a868),f332(f270(a868,a868),x90893)),x90892)) % 165.30/165.06 [7972]~P71(x79722)+E(x79721,f196(f875(x79722,a862)))+E(x79723,f196(f875(x79722,a862)))+~P24(f332(f62(x79722),x79721))+~P24(f332(f62(x79722),x79723))+~E(f332(f332(f104(f875(x79722,a862)),x79723),x79721),f196(f875(x79722,a862)))+E(f332(f332(f82(x79722),f332(f64(x79722,f82(x79722)),x79723)),f332(f64(x79722,f82(x79722)),x79721)),f332(f64(x79722,f82(x79722)),f332(f332(f113(f875(x79722,a862)),x79723),x79721))) % 165.30/165.06 [7759]E(x77591,f2(a1))+E(f332(f332(f39(a1),x77592),x77591),x77593)+~P24(f332(f332(f246(a1),x77594),f2(a1)))+~E(x77592,f332(f332(f81(a1),f332(f332(f82(a1),x77591),x77593)),x77594))+~P24(f332(f332(f246(a1),f2(a1)),x77594))+~P24(f332(f332(f247(a1),x77594),x77591))+~P24(f332(f332(f247(a1),x77591),x77594)) % 165.30/165.06 [7768]E(f45(a1,x77682,x77681),x77683)+E(x77681,f2(a1))+~P24(f332(f332(f246(a1),x77683),f2(a1)))+~E(x77682,f332(f332(f81(a1),f332(f332(f82(a1),x77681),x77684)),x77683))+~P24(f332(f332(f246(a1),f2(a1)),x77683))+~P24(f332(f332(f247(a1),x77683),x77681))+~P24(f332(f332(f247(a1),x77681),x77683)) % 165.30/165.06 [7672]~P14(x76722,x76725,x76724)+E(x76721,f196(f875(x76722,a862)))+E(x76723,f196(f875(x76722,a862)))+~P24(f332(f62(x76722),x76721))+~P24(f332(f62(x76722),x76723))+~E(f332(f332(f104(f875(x76722,a862)),x76723),x76721),f196(f875(x76722,a862)))+E(f332(x76724,f332(f332(f113(f875(x76722,a862)),x76723),x76721)),f332(f332(x76725,f332(x76724,x76723)),f332(x76724,x76721))) % 165.30/165.06 [9311]~P21(x93113,x93111,x93115,x93114)+~P21(x93111,x93113,x93116,x93112)+E(f332(f38(x93111),x93112),f332(f38(x93113),x93114))+~P24(f332(f62(x93113),x93114))+~P24(f332(f62(x93111),x93112))+~P24(f332(f332(f246(f875(x93113,a862)),f332(f311(x93111,x93113,x93116),x93112)),x93114))+~P24(f332(f332(f246(f875(x93111,a862)),f332(f311(x93113,x93111,x93115),x93114)),x93112)) % 165.30/165.06 [9256]~P24(f332(f332(f247(a1),f332(f332(f81(a1),f332(f332(f82(a1),x92565),x92561)),x92566)),f2(a1)))+~E(f332(f332(f81(a1),f332(f332(f82(a1),x92563),x92562)),x92564),f332(f332(f81(a1),f332(f332(f82(a1),x92565),x92561)),x92566))+~P24(f332(f332(f246(a1),f2(a1)),x92566))+~P24(f332(f332(f247(a1),f2(a1)),x92565))+~P24(f332(f332(f246(a1),x92565),x92563))+~P24(f332(f332(f247(a1),x92564),x92563))+P24(f332(f332(f246(a1),x92561),x92562)) % 165.30/165.06 [9032]~E(f332(f332(f81(a1),f332(f332(f82(a1),x90323),x90321)),x90324),f332(f332(f81(a1),f332(f332(f82(a1),x90325),x90322)),x90326))+~P24(f332(f332(f246(a1),f2(a1)),x90324))+~P24(f332(f332(f247(a1),f2(a1)),x90325))+~P24(f332(f332(f246(a1),x90325),x90323))+~P24(f332(f332(f247(a1),x90326),x90325))+P24(f332(f332(f246(a1),x90321),x90322))+~P24(f332(f332(f246(a1),f2(a1)),f332(f332(f81(a1),f332(f332(f82(a1),x90325),x90322)),x90326))) % 165.30/165.06 [9202]~P131(x92021)+~E(f332(f332(f81(x92021),x92022),x92024),f79(x92021))+~P24(f332(f332(f246(x92021),x92025),x92026))+~P24(f332(f332(f246(x92021),x92023),x92026))+~P24(f332(f332(f246(x92021),f2(x92021)),x92024))+~P24(f332(f332(f246(x92021),f2(x92021)),x92022))+P24(f332(f332(f246(x92021),f332(f332(f81(x92021),f332(f332(f82(x92021),x92022),x92023)),f332(f332(f82(x92021),x92024),x92025))),x92026)) % 165.30/165.06 [9203]~P132(x92031)+~E(f332(f332(f81(x92031),x92032),x92034),f79(x92031))+~P24(f332(f332(f246(x92031),f2(x92031)),x92034))+~P24(f332(f332(f246(x92031),f2(x92031)),x92032))+~P24(f332(f332(f247(x92031),x92035),x92036))+~P24(f332(f332(f247(x92031),x92033),x92036))+P24(f332(f332(f247(x92031),f332(f332(f81(x92031),f332(f332(f82(x92031),x92032),x92033)),f332(f332(f82(x92031),x92034),x92035))),x92036)) % 165.30/165.06 [10011]~P6(x100117,x100116,x100115)+E(x100111,x100112)+~P9(x100117,f875(x100114,a862),x100115,x100113)+E(f332(x100113,f499(x100111,x100112,x100113,x100114,x100115,x100116,x100117)),f332(x100113,f500(x100111,x100112,x100113,x100114,x100115,x100116,x100117)))+~E(f332(f332(f42(x100117,f875(x100114,a862)),x100111),x100113),f332(f332(f42(x100117,f875(x100114,a862)),x100112),x100113))+~P24(f332(f332(f334(f875(x100117,a862)),x100112),f332(f332(f61(x100117),x100116),x100115)))+~P24(f332(f332(f334(f875(x100117,a862)),x100111),f332(f332(f61(x100117),x100116),x100115))) % 165.30/165.06 [10044]~P6(x100443,x100447,x100446)+E(x100441,x100442)+~P9(x100443,f875(x100445,a862),x100446,x100444)+~E(f332(f332(f42(x100443,f875(x100445,a862)),x100441),x100444),f332(f332(f42(x100443,f875(x100445,a862)),x100442),x100444))+P24(f332(f332(f334(x100443),f500(x100441,x100442,x100444,x100445,x100446,x100447,x100443)),x100447))+~P24(f332(f332(f334(f875(x100443,a862)),x100442),f332(f332(f61(x100443),x100447),x100446)))+~P24(f332(f332(f334(f875(x100443,a862)),x100441),f332(f332(f61(x100443),x100447),x100446))) % 165.30/165.06 [10045]~P6(x100453,x100457,x100456)+E(x100451,x100452)+~P9(x100453,f875(x100455,a862),x100456,x100454)+~E(f332(f332(f42(x100453,f875(x100455,a862)),x100451),x100454),f332(f332(f42(x100453,f875(x100455,a862)),x100452),x100454))+P24(f332(f332(f334(x100453),f499(x100451,x100452,x100454,x100455,x100456,x100457,x100453)),x100457))+~P24(f332(f332(f334(f875(x100453,a862)),x100452),f332(f332(f61(x100453),x100457),x100456)))+~P24(f332(f332(f334(f875(x100453,a862)),x100451),f332(f332(f61(x100453),x100457),x100456))) % 165.30/165.06 [10113]E(x101131,x101132)+~P6(x101133,x101136,x101137)+~P9(x101133,f875(x101134,a862),x101137,x101135)+~E(f332(f332(f42(x101133,f875(x101134,a862)),x101131),x101135),f332(f332(f42(x101133,f875(x101134,a862)),x101132),x101135))+~P24(f332(f332(f334(f874(x101133,x101133)),f332(f332(f267(x101133,x101133),f500(x101131,x101132,x101135,x101134,x101137,x101136,x101133)),f499(x101131,x101132,x101135,x101134,x101137,x101136,x101133))),x101137))+~P24(f332(f332(f334(f875(x101133,a862)),x101132),f332(f332(f61(x101133),x101136),x101137)))+~P24(f332(f332(f334(f875(x101133,a862)),x101131),f332(f332(f61(x101133),x101136),x101137))) % 165.30/165.06 [9031]~P6(x90311,x90317,x90314)+~E(x90315,x90316)+~P24(f332(f332(f334(x90311),x90313),x90316))+~P24(f332(f332(f334(x90311),x90312),x90315))+~P24(f332(f332(f334(f875(x90311,a862)),x90316),f332(f332(f61(x90311),x90317),x90314)))+~P24(f332(f332(f334(f875(x90311,a862)),x90315),f332(f332(f61(x90311),x90317),x90314)))+P24(f332(f332(f334(f874(x90311,x90311)),f332(f332(f267(x90311,x90311),x90312),x90313)),x90314)) % 165.30/165.06 [9164]E(x91641,x91642)+~P6(x91643,x91644,x91645)+~P24(f332(f332(f334(x91643),x91646),x91642))+~P24(f332(f332(f334(x91643),x91647),x91641))+~P24(f332(f332(f334(f875(x91643,a862)),x91642),f332(f332(f61(x91643),x91644),x91645)))+~P24(f332(f332(f334(f875(x91643,a862)),x91641),f332(f332(f61(x91643),x91644),x91645)))+~P24(f332(f332(f334(f874(x91643,x91643)),f332(f332(f267(x91643,x91643),x91647),x91646)),x91645)) % 165.30/165.06 [10132]~P6(x101329,x101328,x101327)+~P6(x101321,x1013211,x1013210)+~P10(x101321,x101329,f875(x101326,a862),x1013210,x101327,x101325)+P24(f332(f332(f334(x101321),f493(x101322,x101323,x101324,x101325,x101326,x101327,x101328,x101329,x1013210,x1013211,x101321)),x1013211))+~P24(f332(f332(f334(f875(x101329,a862)),x101323),f332(f332(f61(x101329),x101328),x101327)))+~P24(f332(f332(f334(f875(x101321,a862)),x101324),f332(f332(f61(x101321),x1013211),x1013210)))+P24(f332(f332(f334(f875(x101326,a862)),f332(f332(f42(x101321,f875(x101326,a862)),x101324),f332(f332(f8(f875(x101329,f875(x101326,a862)),f875(x101326,a862),x101321),f332(f42(x101329,f875(x101326,a862)),x101323)),x101325))),x101322)) % 165.30/165.06 [10133]~P6(x1013311,x1013310,x101339)+~P6(x101331,x101338,x101337)+~P10(x1013311,x101331,f875(x101336,a862),x101339,x101337,x101335)+P24(f332(f332(f334(x101331),f494(x101332,x101333,x101334,x101335,x101336,x101337,x101338,x101331,x101339,x1013310,x1013311)),x101338))+~P24(f332(f332(f334(f875(x1013311,a862)),x101334),f332(f332(f61(x1013311),x1013310),x101339)))+~P24(f332(f332(f334(f875(x101331,a862)),x101333),f332(f332(f61(x101331),x101338),x101337)))+P24(f332(f332(f334(f875(x101336,a862)),f332(f332(f42(x1013311,f875(x101336,a862)),x101334),f332(f332(f8(f875(x101331,f875(x101336,a862)),f875(x101336,a862),x1013311),f332(f42(x101331,f875(x101336,a862)),x101333)),x101335))),x101332)) % 165.30/165.06 [10136]~P6(x101362,x101368,x101369)+~P6(x101364,x1013610,x1013611)+~P10(x101362,x101364,f875(x101361,a862),x101369,x1013611,x101366)+~P24(f332(f332(f334(f875(x101362,a862)),x101363),f332(f332(f61(x101362),x101368),x101369)))+~P24(f332(f332(f334(f875(x101364,a862)),x101365),f332(f332(f61(x101364),x1013610),x1013611)))+~P24(f332(f332(f334(f875(x101361,a862)),f332(f332(x101366,f493(x101367,x101365,x101363,x101366,x101361,x1013611,x1013610,x101364,x101369,x101368,x101362)),f494(x101367,x101365,x101363,x101366,x101361,x1013611,x1013610,x101364,x101369,x101368,x101362))),x101367))+P24(f332(f332(f334(f875(x101361,a862)),f332(f332(f42(x101362,f875(x101361,a862)),x101363),f332(f332(f8(f875(x101364,f875(x101361,a862)),f875(x101361,a862),x101362),f332(f42(x101364,f875(x101361,a862)),x101365)),x101366))),x101367)) % 165.30/165.06 [9067]E(x90671,x90672)+~P106(x90674)+~P21(x90673,x90674,x90675,f332(f332(f113(f875(x90673,a862)),f332(f174(x90673),x90671)),f332(f174(x90673),x90672)))+~E(f332(f174(x90673),x90671),f332(f174(x90673),x90672))+~P32(x90674,f332(f332(f155(x90673,x90674),x90675),x90672))+~P32(x90674,f332(f332(f155(x90673,x90674),x90675),x90671))+~P24(f332(f138(x90674),f332(f332(f155(x90673,x90674),x90675),x90672)))+~P24(f332(f138(x90674),f332(f332(f155(x90673,x90674),x90675),x90671))) % 165.30/165.06 %EqnAxiom % 165.30/165.06 [1]E(x11,x11) % 165.30/165.06 [2]E(x22,x21)+~E(x21,x22) % 165.30/165.06 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 165.30/165.06 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 165.30/165.06 [5]~E(x51,x52)+E(f103(x51),f103(x52)) % 165.30/165.06 [6]~E(x61,x62)+E(f22(x61),f22(x62)) % 165.30/165.06 [7]~E(x71,x72)+E(f196(x71),f196(x72)) % 165.30/165.06 [8]~E(x81,x82)+E(f332(x81,x83),f332(x82,x83)) % 165.30/165.06 [9]~E(x91,x92)+E(f332(x93,x91),f332(x93,x92)) % 165.30/165.06 [10]~E(x101,x102)+E(f32(x101),f32(x102)) % 165.30/165.06 [11]~E(x111,x112)+E(f174(x111),f174(x112)) % 165.30/165.06 [12]~E(x121,x122)+E(f104(x121),f104(x122)) % 165.30/165.06 [13]~E(x131,x132)+E(f244(x131),f244(x132)) % 165.30/165.06 [14]~E(x141,x142)+E(f113(x141),f113(x142)) % 165.30/165.06 [15]~E(x151,x152)+E(f245(x151),f245(x152)) % 165.30/165.06 [16]~E(x161,x162)+E(f105(x161),f105(x162)) % 165.30/165.06 [17]~E(x171,x172)+E(f35(x171),f35(x172)) % 165.30/165.06 [18]~E(x181,x182)+E(f85(x181),f85(x182)) % 165.30/165.06 [19]~E(x191,x192)+E(f716(x191,x193,x194,x195,x196,x197,x198),f716(x192,x193,x194,x195,x196,x197,x198)) % 165.30/165.06 [20]~E(x201,x202)+E(f716(x203,x201,x204,x205,x206,x207,x208),f716(x203,x202,x204,x205,x206,x207,x208)) % 165.30/165.06 [21]~E(x211,x212)+E(f716(x213,x214,x211,x215,x216,x217,x218),f716(x213,x214,x212,x215,x216,x217,x218)) % 165.30/165.06 [22]~E(x221,x222)+E(f716(x223,x224,x225,x221,x226,x227,x228),f716(x223,x224,x225,x222,x226,x227,x228)) % 165.30/165.06 [23]~E(x231,x232)+E(f716(x233,x234,x235,x236,x231,x237,x238),f716(x233,x234,x235,x236,x232,x237,x238)) % 165.30/165.06 [24]~E(x241,x242)+E(f716(x243,x244,x245,x246,x247,x241,x248),f716(x243,x244,x245,x246,x247,x242,x248)) % 165.30/165.06 [25]~E(x251,x252)+E(f716(x253,x254,x255,x256,x257,x258,x251),f716(x253,x254,x255,x256,x257,x258,x252)) % 165.30/165.06 [26]~E(x261,x262)+E(f246(x261),f246(x262)) % 165.30/165.06 [27]~E(x271,x272)+E(f494(x271,x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x2712),f494(x272,x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x2712)) % 165.30/165.06 [28]~E(x281,x282)+E(f494(x283,x281,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812),f494(x283,x282,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812)) % 165.30/165.06 [29]~E(x291,x292)+E(f494(x293,x294,x291,x295,x296,x297,x298,x299,x2910,x2911,x2912),f494(x293,x294,x292,x295,x296,x297,x298,x299,x2910,x2911,x2912)) % 165.30/165.06 [30]~E(x301,x302)+E(f494(x303,x304,x305,x301,x306,x307,x308,x309,x3010,x3011,x3012),f494(x303,x304,x305,x302,x306,x307,x308,x309,x3010,x3011,x3012)) % 165.30/165.06 [31]~E(x311,x312)+E(f494(x313,x314,x315,x316,x311,x317,x318,x319,x3110,x3111,x3112),f494(x313,x314,x315,x316,x312,x317,x318,x319,x3110,x3111,x3112)) % 165.30/165.06 [32]~E(x321,x322)+E(f494(x323,x324,x325,x326,x327,x321,x328,x329,x3210,x3211,x3212),f494(x323,x324,x325,x326,x327,x322,x328,x329,x3210,x3211,x3212)) % 165.30/165.06 [33]~E(x331,x332)+E(f494(x333,x334,x335,x336,x337,x338,x331,x339,x3310,x3311,x3312),f494(x333,x334,x335,x336,x337,x338,x332,x339,x3310,x3311,x3312)) % 165.30/165.06 [34]~E(x341,x342)+E(f494(x343,x344,x345,x346,x347,x348,x349,x341,x3410,x3411,x3412),f494(x343,x344,x345,x346,x347,x348,x349,x342,x3410,x3411,x3412)) % 165.30/165.06 [35]~E(x351,x352)+E(f494(x353,x354,x355,x356,x357,x358,x359,x3510,x351,x3511,x3512),f494(x353,x354,x355,x356,x357,x358,x359,x3510,x352,x3511,x3512)) % 165.30/165.06 [36]~E(x361,x362)+E(f494(x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x361,x3612),f494(x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x362,x3612)) % 165.30/165.06 [37]~E(x371,x372)+E(f494(x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712,x371),f494(x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712,x372)) % 165.30/165.06 [38]~E(x381,x382)+E(f79(x381),f79(x382)) % 165.30/165.06 [39]~E(x391,x392)+E(f334(x391),f334(x392)) % 165.30/165.06 [40]~E(x401,x402)+E(f493(x401,x403,x404,x405,x406,x407,x408,x409,x4010,x4011,x4012),f493(x402,x403,x404,x405,x406,x407,x408,x409,x4010,x4011,x4012)) % 165.30/165.06 [41]~E(x411,x412)+E(f493(x413,x411,x414,x415,x416,x417,x418,x419,x4110,x4111,x4112),f493(x413,x412,x414,x415,x416,x417,x418,x419,x4110,x4111,x4112)) % 165.30/165.06 [42]~E(x421,x422)+E(f493(x423,x424,x421,x425,x426,x427,x428,x429,x4210,x4211,x4212),f493(x423,x424,x422,x425,x426,x427,x428,x429,x4210,x4211,x4212)) % 165.30/165.06 [43]~E(x431,x432)+E(f493(x433,x434,x435,x431,x436,x437,x438,x439,x4310,x4311,x4312),f493(x433,x434,x435,x432,x436,x437,x438,x439,x4310,x4311,x4312)) % 165.30/165.06 [44]~E(x441,x442)+E(f493(x443,x444,x445,x446,x441,x447,x448,x449,x4410,x4411,x4412),f493(x443,x444,x445,x446,x442,x447,x448,x449,x4410,x4411,x4412)) % 165.30/165.06 [45]~E(x451,x452)+E(f493(x453,x454,x455,x456,x457,x451,x458,x459,x4510,x4511,x4512),f493(x453,x454,x455,x456,x457,x452,x458,x459,x4510,x4511,x4512)) % 165.30/165.06 [46]~E(x461,x462)+E(f493(x463,x464,x465,x466,x467,x468,x461,x469,x4610,x4611,x4612),f493(x463,x464,x465,x466,x467,x468,x462,x469,x4610,x4611,x4612)) % 165.30/165.06 [47]~E(x471,x472)+E(f493(x473,x474,x475,x476,x477,x478,x479,x471,x4710,x4711,x4712),f493(x473,x474,x475,x476,x477,x478,x479,x472,x4710,x4711,x4712)) % 165.30/165.06 [48]~E(x481,x482)+E(f493(x483,x484,x485,x486,x487,x488,x489,x4810,x481,x4811,x4812),f493(x483,x484,x485,x486,x487,x488,x489,x4810,x482,x4811,x4812)) % 165.30/165.06 [49]~E(x491,x492)+E(f493(x493,x494,x495,x496,x497,x498,x499,x4910,x4911,x491,x4912),f493(x493,x494,x495,x496,x497,x498,x499,x4910,x4911,x492,x4912)) % 165.30/165.06 [50]~E(x501,x502)+E(f493(x503,x504,x505,x506,x507,x508,x509,x5010,x5011,x5012,x501),f493(x503,x504,x505,x506,x507,x508,x509,x5010,x5011,x5012,x502)) % 165.30/165.06 [51]~E(x511,x512)+E(f114(x511),f114(x512)) % 165.30/165.06 [52]~E(x521,x522)+E(f184(x521,x523),f184(x522,x523)) % 165.30/165.06 [53]~E(x531,x532)+E(f184(x533,x531),f184(x533,x532)) % 165.30/165.06 [54]~E(x541,x542)+E(f875(x541,x543),f875(x542,x543)) % 165.30/165.06 [55]~E(x551,x552)+E(f875(x553,x551),f875(x553,x552)) % 165.30/165.06 [56]~E(x561,x562)+E(f4(x561),f4(x562)) % 165.30/165.06 [57]~E(x571,x572)+E(f137(x571,x573),f137(x572,x573)) % 165.30/165.06 [58]~E(x581,x582)+E(f137(x583,x581),f137(x583,x582)) % 165.30/165.06 [59]~E(x591,x592)+E(f867(x591),f867(x592)) % 165.30/165.06 [60]~E(x601,x602)+E(f872(x601),f872(x602)) % 165.30/165.06 [61]~E(x611,x612)+E(f869(x611),f869(x612)) % 165.30/165.06 [62]~E(x621,x622)+E(f870(x621),f870(x622)) % 165.30/165.06 [63]~E(x631,x632)+E(f81(x631),f81(x632)) % 165.30/165.06 [64]~E(x641,x642)+E(f82(x641),f82(x642)) % 165.30/165.06 [65]~E(x651,x652)+E(f39(x651),f39(x652)) % 165.30/165.06 [66]~E(x661,x662)+E(f7(x661,x663,x664),f7(x662,x663,x664)) % 165.30/165.06 [67]~E(x671,x672)+E(f7(x673,x671,x674),f7(x673,x672,x674)) % 165.30/165.06 [68]~E(x681,x682)+E(f7(x683,x684,x681),f7(x683,x684,x682)) % 165.30/165.06 [69]~E(x691,x692)+E(f80(x691),f80(x692)) % 165.30/165.06 [70]~E(x701,x702)+E(f152(x701),f152(x702)) % 165.30/165.06 [71]~E(x711,x712)+E(f197(x711),f197(x712)) % 165.30/165.06 [72]~E(x721,x722)+E(f247(x721),f247(x722)) % 165.30/165.06 [73]~E(x731,x732)+E(f106(x731),f106(x732)) % 165.30/165.06 [74]~E(x741,x742)+E(f135(x741),f135(x742)) % 165.30/165.06 [75]~E(x751,x752)+E(f257(x751),f257(x752)) % 165.30/165.06 [76]~E(x761,x762)+E(f138(x761),f138(x762)) % 165.30/165.06 [77]~E(x771,x772)+E(f290(x771),f290(x772)) % 165.30/165.06 [78]~E(x781,x782)+E(f45(x781,x783,x784),f45(x782,x783,x784)) % 165.30/165.06 [79]~E(x791,x792)+E(f45(x793,x791,x794),f45(x793,x792,x794)) % 165.30/165.06 [80]~E(x801,x802)+E(f45(x803,x804,x801),f45(x803,x804,x802)) % 165.30/165.06 [81]~E(x811,x812)+E(f718(x811,x813,x814,x815,x816,x817,x818),f718(x812,x813,x814,x815,x816,x817,x818)) % 165.30/165.06 [82]~E(x821,x822)+E(f718(x823,x821,x824,x825,x826,x827,x828),f718(x823,x822,x824,x825,x826,x827,x828)) % 165.30/165.06 [83]~E(x831,x832)+E(f718(x833,x834,x831,x835,x836,x837,x838),f718(x833,x834,x832,x835,x836,x837,x838)) % 165.30/165.06 [84]~E(x841,x842)+E(f718(x843,x844,x845,x841,x846,x847,x848),f718(x843,x844,x845,x842,x846,x847,x848)) % 165.30/165.06 [85]~E(x851,x852)+E(f718(x853,x854,x855,x856,x851,x857,x858),f718(x853,x854,x855,x856,x852,x857,x858)) % 165.30/165.06 [86]~E(x861,x862)+E(f718(x863,x864,x865,x866,x867,x861,x868),f718(x863,x864,x865,x866,x867,x862,x868)) % 165.30/165.06 [87]~E(x871,x872)+E(f718(x873,x874,x875,x876,x877,x878,x871),f718(x873,x874,x875,x876,x877,x878,x872)) % 165.30/165.06 [88]~E(x881,x882)+E(f874(x881,x883),f874(x882,x883)) % 165.30/165.06 [89]~E(x891,x892)+E(f874(x893,x891),f874(x893,x892)) % 165.30/165.06 [90]~E(x901,x902)+E(f33(x901,x903),f33(x902,x903)) % 165.30/165.06 [91]~E(x911,x912)+E(f33(x913,x911),f33(x913,x912)) % 165.30/165.06 [92]~E(x921,x922)+E(f10(x921,x923),f10(x922,x923)) % 165.30/165.06 [93]~E(x931,x932)+E(f10(x933,x931),f10(x933,x932)) % 165.30/165.06 [94]~E(x941,x942)+E(f169(x941),f169(x942)) % 165.30/165.06 [95]~E(x951,x952)+E(f172(x951,x953,x954),f172(x952,x953,x954)) % 165.30/165.06 [96]~E(x961,x962)+E(f172(x963,x961,x964),f172(x963,x962,x964)) % 165.30/165.06 [97]~E(x971,x972)+E(f172(x973,x974,x971),f172(x973,x974,x972)) % 165.30/165.06 [98]~E(x981,x982)+E(f310(x981),f310(x982)) % 165.30/165.06 [99]~E(x991,x992)+E(f61(x991),f61(x992)) % 165.30/165.06 [100]~E(x1001,x1002)+E(f8(x1001,x1003,x1004),f8(x1002,x1003,x1004)) % 165.30/165.06 [101]~E(x1011,x1012)+E(f8(x1013,x1011,x1014),f8(x1013,x1012,x1014)) % 165.30/165.06 [102]~E(x1021,x1022)+E(f8(x1023,x1024,x1021),f8(x1023,x1024,x1022)) % 165.30/165.06 [103]~E(x1031,x1032)+E(f759(x1031,x1033,x1034,x1035),f759(x1032,x1033,x1034,x1035)) % 165.30/165.06 [104]~E(x1041,x1042)+E(f759(x1043,x1041,x1044,x1045),f759(x1043,x1042,x1044,x1045)) % 165.30/165.06 [105]~E(x1051,x1052)+E(f759(x1053,x1054,x1051,x1055),f759(x1053,x1054,x1052,x1055)) % 165.30/165.06 [106]~E(x1061,x1062)+E(f759(x1063,x1064,x1065,x1061),f759(x1063,x1064,x1065,x1062)) % 165.30/165.06 [107]~E(x1071,x1072)+E(f269(x1071,x1073),f269(x1072,x1073)) % 165.30/165.06 [108]~E(x1081,x1082)+E(f269(x1083,x1081),f269(x1083,x1082)) % 165.30/165.06 [109]~E(x1091,x1092)+E(f170(x1091),f170(x1092)) % 165.30/165.06 [110]~E(x1101,x1102)+E(f209(x1101),f209(x1102)) % 165.30/165.06 [111]~E(x1111,x1112)+E(f798(x1111,x1113,x1114,x1115),f798(x1112,x1113,x1114,x1115)) % 165.30/165.06 [112]~E(x1121,x1122)+E(f798(x1123,x1121,x1124,x1125),f798(x1123,x1122,x1124,x1125)) % 165.30/165.06 [113]~E(x1131,x1132)+E(f798(x1133,x1134,x1131,x1135),f798(x1133,x1134,x1132,x1135)) % 165.30/165.06 [114]~E(x1141,x1142)+E(f798(x1143,x1144,x1145,x1141),f798(x1143,x1144,x1145,x1142)) % 165.30/165.06 [115]~E(x1151,x1152)+E(f267(x1151,x1153),f267(x1152,x1153)) % 165.30/165.06 [116]~E(x1161,x1162)+E(f267(x1163,x1161),f267(x1163,x1162)) % 165.30/165.06 [117]~E(x1171,x1172)+E(f6(x1171,x1173),f6(x1172,x1173)) % 165.30/165.06 [118]~E(x1181,x1182)+E(f6(x1183,x1181),f6(x1183,x1182)) % 165.30/165.06 [119]~E(x1191,x1192)+E(f18(x1191,x1193,x1194),f18(x1192,x1193,x1194)) % 165.30/165.06 [120]~E(x1201,x1202)+E(f18(x1203,x1201,x1204),f18(x1203,x1202,x1204)) % 165.30/165.06 [121]~E(x1211,x1212)+E(f18(x1213,x1214,x1211),f18(x1213,x1214,x1212)) % 165.30/165.06 [122]~E(x1221,x1222)+E(f14(x1221,x1223),f14(x1222,x1223)) % 165.30/165.06 [123]~E(x1231,x1232)+E(f14(x1233,x1231),f14(x1233,x1232)) % 165.30/165.06 [124]~E(x1241,x1242)+E(f64(x1241,x1243),f64(x1242,x1243)) % 165.30/165.06 [125]~E(x1251,x1252)+E(f64(x1253,x1251),f64(x1253,x1252)) % 165.30/165.06 [126]~E(x1261,x1262)+E(f76(x1261),f76(x1262)) % 165.30/165.06 [127]~E(x1271,x1272)+E(f116(x1271),f116(x1272)) % 165.30/165.06 [128]~E(x1281,x1282)+E(f311(x1281,x1283,x1284),f311(x1282,x1283,x1284)) % 165.30/165.06 [129]~E(x1291,x1292)+E(f311(x1293,x1291,x1294),f311(x1293,x1292,x1294)) % 165.30/165.06 [130]~E(x1301,x1302)+E(f311(x1303,x1304,x1301),f311(x1303,x1304,x1302)) % 165.30/165.06 [131]~E(x1311,x1312)+E(f16(x1311,x1313),f16(x1312,x1313)) % 165.30/165.06 [132]~E(x1321,x1322)+E(f16(x1323,x1321),f16(x1323,x1322)) % 165.30/165.06 [133]~E(x1331,x1332)+E(f155(x1331,x1333),f155(x1332,x1333)) % 165.30/165.06 [134]~E(x1341,x1342)+E(f155(x1343,x1341),f155(x1343,x1342)) % 165.30/165.06 [135]~E(x1351,x1352)+E(f252(x1351),f252(x1352)) % 165.30/165.06 [136]~E(x1361,x1362)+E(f42(x1361,x1363),f42(x1362,x1363)) % 165.30/165.06 [137]~E(x1371,x1372)+E(f42(x1373,x1371),f42(x1373,x1372)) % 165.30/165.06 [138]~E(x1381,x1382)+E(f38(x1381),f38(x1382)) % 165.30/165.06 [139]~E(x1391,x1392)+E(f758(x1391,x1393,x1394,x1395),f758(x1392,x1393,x1394,x1395)) % 165.30/165.06 [140]~E(x1401,x1402)+E(f758(x1403,x1401,x1404,x1405),f758(x1403,x1402,x1404,x1405)) % 165.30/165.06 [141]~E(x1411,x1412)+E(f758(x1413,x1414,x1411,x1415),f758(x1413,x1414,x1412,x1415)) % 165.30/165.06 [142]~E(x1421,x1422)+E(f758(x1423,x1424,x1425,x1421),f758(x1423,x1424,x1425,x1422)) % 165.30/165.06 [143]~E(x1431,x1432)+E(f166(x1431),f166(x1432)) % 165.30/165.06 [144]~E(x1441,x1442)+E(f301(x1441),f301(x1442)) % 165.30/165.06 [145]~E(x1451,x1452)+E(f112(x1451),f112(x1452)) % 165.30/165.06 [146]~E(x1461,x1462)+E(f253(x1461),f253(x1462)) % 165.30/165.06 [147]~E(x1471,x1472)+E(f140(x1471,x1473),f140(x1472,x1473)) % 165.30/165.06 [148]~E(x1481,x1482)+E(f140(x1483,x1481),f140(x1483,x1482)) % 165.30/165.06 [149]~E(x1491,x1492)+E(f62(x1491),f62(x1492)) % 165.30/165.06 [150]~E(x1501,x1502)+E(f43(x1501,x1503),f43(x1502,x1503)) % 165.30/165.06 [151]~E(x1511,x1512)+E(f43(x1513,x1511),f43(x1513,x1512)) % 165.30/165.06 [152]~E(x1521,x1522)+E(f108(x1521),f108(x1522)) % 165.30/165.06 [153]~E(x1531,x1532)+E(f110(x1531),f110(x1532)) % 165.30/165.06 [154]~E(x1541,x1542)+E(f333(x1541),f333(x1542)) % 165.30/165.06 [155]~E(x1551,x1552)+E(f160(x1551,x1553),f160(x1552,x1553)) % 165.30/165.06 [156]~E(x1561,x1562)+E(f160(x1563,x1561),f160(x1563,x1562)) % 165.30/165.06 [157]~E(x1571,x1572)+E(f264(x1571,x1573),f264(x1572,x1573)) % 165.30/165.06 [158]~E(x1581,x1582)+E(f264(x1583,x1581),f264(x1583,x1582)) % 165.30/165.06 [159]~E(x1591,x1592)+E(f427(x1591,x1593),f427(x1592,x1593)) % 165.30/165.06 [160]~E(x1601,x1602)+E(f427(x1603,x1601),f427(x1603,x1602)) % 165.30/165.06 [161]~E(x1611,x1612)+E(f88(x1611),f88(x1612)) % 165.30/165.06 [162]~E(x1621,x1622)+E(f5(x1621),f5(x1622)) % 165.30/165.06 [163]~E(x1631,x1632)+E(f41(x1631,x1633),f41(x1632,x1633)) % 165.30/165.06 [164]~E(x1641,x1642)+E(f41(x1643,x1641),f41(x1643,x1642)) % 165.30/165.06 [165]~E(x1651,x1652)+E(f180(x1651,x1653),f180(x1652,x1653)) % 165.30/165.06 [166]~E(x1661,x1662)+E(f180(x1663,x1661),f180(x1663,x1662)) % 165.30/165.06 [167]~E(x1671,x1672)+E(f159(x1671,x1673),f159(x1672,x1673)) % 165.30/165.06 [168]~E(x1681,x1682)+E(f159(x1683,x1681),f159(x1683,x1682)) % 165.30/165.06 [169]~E(x1691,x1692)+E(f321(x1691,x1693),f321(x1692,x1693)) % 165.30/165.06 [170]~E(x1701,x1702)+E(f321(x1703,x1701),f321(x1703,x1702)) % 165.30/165.06 [171]~E(x1711,x1712)+E(f847(x1711,x1713,x1714,x1715),f847(x1712,x1713,x1714,x1715)) % 165.30/165.06 [172]~E(x1721,x1722)+E(f847(x1723,x1721,x1724,x1725),f847(x1723,x1722,x1724,x1725)) % 165.30/165.06 [173]~E(x1731,x1732)+E(f847(x1733,x1734,x1731,x1735),f847(x1733,x1734,x1732,x1735)) % 165.30/165.06 [174]~E(x1741,x1742)+E(f847(x1743,x1744,x1745,x1741),f847(x1743,x1744,x1745,x1742)) % 165.30/165.06 [175]~E(x1751,x1752)+E(f74(x1751,x1753,x1754,x1755),f74(x1752,x1753,x1754,x1755)) % 165.30/165.06 [176]~E(x1761,x1762)+E(f74(x1763,x1761,x1764,x1765),f74(x1763,x1762,x1764,x1765)) % 165.30/165.06 [177]~E(x1771,x1772)+E(f74(x1773,x1774,x1771,x1775),f74(x1773,x1774,x1772,x1775)) % 165.30/165.06 [178]~E(x1781,x1782)+E(f74(x1783,x1784,x1785,x1781),f74(x1783,x1784,x1785,x1782)) % 165.30/165.06 [179]~E(x1791,x1792)+E(f145(x1791,x1793),f145(x1792,x1793)) % 165.30/165.06 [180]~E(x1801,x1802)+E(f145(x1803,x1801),f145(x1803,x1802)) % 165.30/165.06 [181]~E(x1811,x1812)+E(f419(x1811,x1813,x1814),f419(x1812,x1813,x1814)) % 165.30/165.06 [182]~E(x1821,x1822)+E(f419(x1823,x1821,x1824),f419(x1823,x1822,x1824)) % 165.30/165.06 [183]~E(x1831,x1832)+E(f419(x1833,x1834,x1831),f419(x1833,x1834,x1832)) % 165.30/165.06 [184]~E(x1841,x1842)+E(f420(x1841,x1843,x1844),f420(x1842,x1843,x1844)) % 165.30/165.06 [185]~E(x1851,x1852)+E(f420(x1853,x1851,x1854),f420(x1853,x1852,x1854)) % 165.30/165.06 [186]~E(x1861,x1862)+E(f420(x1863,x1864,x1861),f420(x1863,x1864,x1862)) % 165.30/165.06 [187]~E(x1871,x1872)+E(f357(x1871,x1873,x1874,x1875,x1876),f357(x1872,x1873,x1874,x1875,x1876)) % 165.30/165.06 [188]~E(x1881,x1882)+E(f357(x1883,x1881,x1884,x1885,x1886),f357(x1883,x1882,x1884,x1885,x1886)) % 165.30/165.06 [189]~E(x1891,x1892)+E(f357(x1893,x1894,x1891,x1895,x1896),f357(x1893,x1894,x1892,x1895,x1896)) % 165.30/165.06 [190]~E(x1901,x1902)+E(f357(x1903,x1904,x1905,x1901,x1906),f357(x1903,x1904,x1905,x1902,x1906)) % 165.30/165.06 [191]~E(x1911,x1912)+E(f357(x1913,x1914,x1915,x1916,x1911),f357(x1913,x1914,x1915,x1916,x1912)) % 165.30/165.06 [192]~E(x1921,x1922)+E(f75(x1921,x1923),f75(x1922,x1923)) % 165.30/165.06 [193]~E(x1931,x1932)+E(f75(x1933,x1931),f75(x1933,x1932)) % 165.30/165.06 [194]~E(x1941,x1942)+E(f161(x1941,x1943),f161(x1942,x1943)) % 165.30/165.06 [195]~E(x1951,x1952)+E(f161(x1953,x1951),f161(x1953,x1952)) % 165.30/165.06 [196]~E(x1961,x1962)+E(f846(x1961,x1963,x1964),f846(x1962,x1963,x1964)) % 165.30/165.06 [197]~E(x1971,x1972)+E(f846(x1973,x1971,x1974),f846(x1973,x1972,x1974)) % 165.30/165.06 [198]~E(x1981,x1982)+E(f846(x1983,x1984,x1981),f846(x1983,x1984,x1982)) % 165.30/165.06 [199]~E(x1991,x1992)+E(f186(x1991,x1993,x1994),f186(x1992,x1993,x1994)) % 165.30/165.06 [200]~E(x2001,x2002)+E(f186(x2003,x2001,x2004),f186(x2003,x2002,x2004)) % 165.30/165.06 [201]~E(x2011,x2012)+E(f186(x2013,x2014,x2011),f186(x2013,x2014,x2012)) % 165.30/165.06 [202]~E(x2021,x2022)+E(f191(x2021,x2023),f191(x2022,x2023)) % 165.30/165.06 [203]~E(x2031,x2032)+E(f191(x2033,x2031),f191(x2033,x2032)) % 165.30/165.06 [204]~E(x2041,x2042)+E(f374(x2041,x2043,x2044),f374(x2042,x2043,x2044)) % 165.30/165.06 [205]~E(x2051,x2052)+E(f374(x2053,x2051,x2054),f374(x2053,x2052,x2054)) % 165.30/165.06 [206]~E(x2061,x2062)+E(f374(x2063,x2064,x2061),f374(x2063,x2064,x2062)) % 165.30/165.06 [207]~E(x2071,x2072)+E(f271(x2071,x2073,x2074),f271(x2072,x2073,x2074)) % 165.30/165.06 [208]~E(x2081,x2082)+E(f271(x2083,x2081,x2084),f271(x2083,x2082,x2084)) % 165.30/165.06 [209]~E(x2091,x2092)+E(f271(x2093,x2094,x2091),f271(x2093,x2094,x2092)) % 165.30/165.06 [210]~E(x2101,x2102)+E(f320(x2101,x2103),f320(x2102,x2103)) % 165.30/165.06 [211]~E(x2111,x2112)+E(f320(x2113,x2111),f320(x2113,x2112)) % 165.30/165.06 [212]~E(x2121,x2122)+E(f139(x2121),f139(x2122)) % 165.30/165.06 [213]~E(x2131,x2132)+E(f289(x2131,x2133,x2134),f289(x2132,x2133,x2134)) % 165.30/165.06 [214]~E(x2141,x2142)+E(f289(x2143,x2141,x2144),f289(x2143,x2142,x2144)) % 165.30/165.06 [215]~E(x2151,x2152)+E(f289(x2153,x2154,x2151),f289(x2153,x2154,x2152)) % 165.30/165.06 [216]~E(x2161,x2162)+E(f48(x2161,x2163),f48(x2162,x2163)) % 165.30/165.06 [217]~E(x2171,x2172)+E(f48(x2173,x2171),f48(x2173,x2172)) % 165.30/165.06 [218]~E(x2181,x2182)+E(f308(x2181,x2183),f308(x2182,x2183)) % 165.30/165.06 [219]~E(x2191,x2192)+E(f308(x2193,x2191),f308(x2193,x2192)) % 165.30/165.06 [220]~E(x2201,x2202)+E(f168(x2201,x2203,x2204),f168(x2202,x2203,x2204)) % 165.30/165.06 [221]~E(x2211,x2212)+E(f168(x2213,x2211,x2214),f168(x2213,x2212,x2214)) % 165.30/165.06 [222]~E(x2221,x2222)+E(f168(x2223,x2224,x2221),f168(x2223,x2224,x2222)) % 165.30/165.06 [223]~E(x2231,x2232)+E(f9(x2231,x2233),f9(x2232,x2233)) % 165.30/165.06 [224]~E(x2241,x2242)+E(f9(x2243,x2241),f9(x2243,x2242)) % 165.30/165.06 [225]~E(x2251,x2252)+E(f302(x2251,x2253),f302(x2252,x2253)) % 165.30/165.06 [226]~E(x2261,x2262)+E(f302(x2263,x2261),f302(x2263,x2262)) % 165.30/165.06 [227]~E(x2271,x2272)+E(f93(x2271),f93(x2272)) % 165.30/165.06 [228]~E(x2281,x2282)+E(f822(x2281,x2283),f822(x2282,x2283)) % 165.30/165.06 [229]~E(x2291,x2292)+E(f822(x2293,x2291),f822(x2293,x2292)) % 165.30/165.06 [230]~E(x2301,x2302)+E(f291(x2301,x2303),f291(x2302,x2303)) % 165.30/165.06 [231]~E(x2311,x2312)+E(f291(x2313,x2311),f291(x2313,x2312)) % 165.30/165.06 [232]~E(x2321,x2322)+E(f234(x2321,x2323,x2324,x2325),f234(x2322,x2323,x2324,x2325)) % 165.30/165.06 [233]~E(x2331,x2332)+E(f234(x2333,x2331,x2334,x2335),f234(x2333,x2332,x2334,x2335)) % 165.30/165.06 [234]~E(x2341,x2342)+E(f234(x2343,x2344,x2341,x2345),f234(x2343,x2344,x2342,x2345)) % 165.30/165.06 [235]~E(x2351,x2352)+E(f234(x2353,x2354,x2355,x2351),f234(x2353,x2354,x2355,x2352)) % 165.30/165.06 [236]~E(x2361,x2362)+E(f804(x2361,x2363,x2364),f804(x2362,x2363,x2364)) % 165.30/165.06 [237]~E(x2371,x2372)+E(f804(x2373,x2371,x2374),f804(x2373,x2372,x2374)) % 165.30/165.06 [238]~E(x2381,x2382)+E(f804(x2383,x2384,x2381),f804(x2383,x2384,x2382)) % 165.30/165.06 [239]~E(x2391,x2392)+E(f208(x2391),f208(x2392)) % 165.30/165.06 [240]~E(x2401,x2402)+E(f266(x2401,x2403),f266(x2402,x2403)) % 165.30/165.06 [241]~E(x2411,x2412)+E(f266(x2413,x2411),f266(x2413,x2412)) % 165.30/165.06 [242]~E(x2421,x2422)+E(f298(x2421,x2423,x2424),f298(x2422,x2423,x2424)) % 165.30/165.06 [243]~E(x2431,x2432)+E(f298(x2433,x2431,x2434),f298(x2433,x2432,x2434)) % 165.30/165.06 [244]~E(x2441,x2442)+E(f298(x2443,x2444,x2441),f298(x2443,x2444,x2442)) % 165.30/165.06 [245]~E(x2451,x2452)+E(f83(x2451,x2453),f83(x2452,x2453)) % 165.30/165.06 [246]~E(x2461,x2462)+E(f83(x2463,x2461),f83(x2463,x2462)) % 165.30/165.06 [247]~E(x2471,x2472)+E(f177(x2471),f177(x2472)) % 165.30/165.06 [248]~E(x2481,x2482)+E(f256(x2481,x2483,x2484),f256(x2482,x2483,x2484)) % 165.30/165.06 [249]~E(x2491,x2492)+E(f256(x2493,x2491,x2494),f256(x2493,x2492,x2494)) % 165.30/165.06 [250]~E(x2501,x2502)+E(f256(x2503,x2504,x2501),f256(x2503,x2504,x2502)) % 165.30/165.06 [251]~E(x2511,x2512)+E(f117(x2511,x2513),f117(x2512,x2513)) % 165.30/165.06 [252]~E(x2521,x2522)+E(f117(x2523,x2521),f117(x2523,x2522)) % 165.30/165.06 [253]~E(x2531,x2532)+E(f272(x2531,x2533,x2534,x2535,x2536,x2537),f272(x2532,x2533,x2534,x2535,x2536,x2537)) % 165.30/165.06 [254]~E(x2541,x2542)+E(f272(x2543,x2541,x2544,x2545,x2546,x2547),f272(x2543,x2542,x2544,x2545,x2546,x2547)) % 165.30/165.06 [255]~E(x2551,x2552)+E(f272(x2553,x2554,x2551,x2555,x2556,x2557),f272(x2553,x2554,x2552,x2555,x2556,x2557)) % 165.30/165.06 [256]~E(x2561,x2562)+E(f272(x2563,x2564,x2565,x2561,x2566,x2567),f272(x2563,x2564,x2565,x2562,x2566,x2567)) % 165.30/165.06 [257]~E(x2571,x2572)+E(f272(x2573,x2574,x2575,x2576,x2571,x2577),f272(x2573,x2574,x2575,x2576,x2572,x2577)) % 165.30/165.06 [258]~E(x2581,x2582)+E(f272(x2583,x2584,x2585,x2586,x2587,x2581),f272(x2583,x2584,x2585,x2586,x2587,x2582)) % 165.30/165.06 [259]~E(x2591,x2592)+E(f542(x2591,x2593,x2594,x2595),f542(x2592,x2593,x2594,x2595)) % 165.30/165.06 [260]~E(x2601,x2602)+E(f542(x2603,x2601,x2604,x2605),f542(x2603,x2602,x2604,x2605)) % 165.30/165.06 [261]~E(x2611,x2612)+E(f542(x2613,x2614,x2611,x2615),f542(x2613,x2614,x2612,x2615)) % 165.30/165.06 [262]~E(x2621,x2622)+E(f542(x2623,x2624,x2625,x2621),f542(x2623,x2624,x2625,x2622)) % 165.30/165.06 [263]~E(x2631,x2632)+E(f153(x2631,x2633),f153(x2632,x2633)) % 165.30/165.06 [264]~E(x2641,x2642)+E(f153(x2643,x2641),f153(x2643,x2642)) % 165.30/165.06 [265]~E(x2651,x2652)+E(f158(x2651,x2653),f158(x2652,x2653)) % 165.30/165.06 [266]~E(x2661,x2662)+E(f158(x2663,x2661),f158(x2663,x2662)) % 165.30/165.06 [267]~E(x2671,x2672)+E(f199(x2671),f199(x2672)) % 165.30/165.06 [268]~E(x2681,x2682)+E(f305(x2681,x2683,x2684),f305(x2682,x2683,x2684)) % 165.30/165.06 [269]~E(x2691,x2692)+E(f305(x2693,x2691,x2694),f305(x2693,x2692,x2694)) % 165.30/165.06 [270]~E(x2701,x2702)+E(f305(x2703,x2704,x2701),f305(x2703,x2704,x2702)) % 165.30/165.06 [271]~E(x2711,x2712)+E(f118(x2711),f118(x2712)) % 165.30/165.06 [272]~E(x2721,x2722)+E(f73(x2721,x2723),f73(x2722,x2723)) % 165.30/165.06 [273]~E(x2731,x2732)+E(f73(x2733,x2731),f73(x2733,x2732)) % 165.30/165.06 [274]~E(x2741,x2742)+E(f579(x2741,x2743,x2744,x2745,x2746,x2747),f579(x2742,x2743,x2744,x2745,x2746,x2747)) % 165.30/165.06 [275]~E(x2751,x2752)+E(f579(x2753,x2751,x2754,x2755,x2756,x2757),f579(x2753,x2752,x2754,x2755,x2756,x2757)) % 165.30/165.06 [276]~E(x2761,x2762)+E(f579(x2763,x2764,x2761,x2765,x2766,x2767),f579(x2763,x2764,x2762,x2765,x2766,x2767)) % 165.30/165.06 [277]~E(x2771,x2772)+E(f579(x2773,x2774,x2775,x2771,x2776,x2777),f579(x2773,x2774,x2775,x2772,x2776,x2777)) % 165.30/165.06 [278]~E(x2781,x2782)+E(f579(x2783,x2784,x2785,x2786,x2781,x2787),f579(x2783,x2784,x2785,x2786,x2782,x2787)) % 165.30/165.06 [279]~E(x2791,x2792)+E(f579(x2793,x2794,x2795,x2796,x2797,x2791),f579(x2793,x2794,x2795,x2796,x2797,x2792)) % 165.30/165.06 [280]~E(x2801,x2802)+E(f555(x2801,x2803,x2804,x2805),f555(x2802,x2803,x2804,x2805)) % 165.30/165.06 [281]~E(x2811,x2812)+E(f555(x2813,x2811,x2814,x2815),f555(x2813,x2812,x2814,x2815)) % 165.30/165.06 [282]~E(x2821,x2822)+E(f555(x2823,x2824,x2821,x2825),f555(x2823,x2824,x2822,x2825)) % 165.30/165.06 [283]~E(x2831,x2832)+E(f555(x2833,x2834,x2835,x2831),f555(x2833,x2834,x2835,x2832)) % 165.30/165.06 [284]~E(x2841,x2842)+E(f747(x2841,x2843,x2844,x2845,x2846),f747(x2842,x2843,x2844,x2845,x2846)) % 165.30/165.06 [285]~E(x2851,x2852)+E(f747(x2853,x2851,x2854,x2855,x2856),f747(x2853,x2852,x2854,x2855,x2856)) % 165.30/165.06 [286]~E(x2861,x2862)+E(f747(x2863,x2864,x2861,x2865,x2866),f747(x2863,x2864,x2862,x2865,x2866)) % 165.30/165.06 [287]~E(x2871,x2872)+E(f747(x2873,x2874,x2875,x2871,x2876),f747(x2873,x2874,x2875,x2872,x2876)) % 165.30/165.06 [288]~E(x2881,x2882)+E(f747(x2883,x2884,x2885,x2886,x2881),f747(x2883,x2884,x2885,x2886,x2882)) % 165.30/165.06 [289]~E(x2891,x2892)+E(f149(x2891,x2893,x2894),f149(x2892,x2893,x2894)) % 165.30/165.06 [290]~E(x2901,x2902)+E(f149(x2903,x2901,x2904),f149(x2903,x2902,x2904)) % 165.30/165.06 [291]~E(x2911,x2912)+E(f149(x2913,x2914,x2911),f149(x2913,x2914,x2912)) % 165.30/165.06 [292]~E(x2921,x2922)+E(f690(x2921,x2923),f690(x2922,x2923)) % 165.30/165.06 [293]~E(x2931,x2932)+E(f690(x2933,x2931),f690(x2933,x2932)) % 165.30/165.06 [294]~E(x2941,x2942)+E(f29(x2941,x2943,x2944),f29(x2942,x2943,x2944)) % 165.30/165.06 [295]~E(x2951,x2952)+E(f29(x2953,x2951,x2954),f29(x2953,x2952,x2954)) % 165.30/165.06 [296]~E(x2961,x2962)+E(f29(x2963,x2964,x2961),f29(x2963,x2964,x2962)) % 165.30/165.06 [297]~E(x2971,x2972)+E(f786(x2971,x2973,x2974,x2975,x2976,x2977),f786(x2972,x2973,x2974,x2975,x2976,x2977)) % 165.30/165.06 [298]~E(x2981,x2982)+E(f786(x2983,x2981,x2984,x2985,x2986,x2987),f786(x2983,x2982,x2984,x2985,x2986,x2987)) % 165.30/165.06 [299]~E(x2991,x2992)+E(f786(x2993,x2994,x2991,x2995,x2996,x2997),f786(x2993,x2994,x2992,x2995,x2996,x2997)) % 165.30/165.06 [300]~E(x3001,x3002)+E(f786(x3003,x3004,x3005,x3001,x3006,x3007),f786(x3003,x3004,x3005,x3002,x3006,x3007)) % 165.30/165.06 [301]~E(x3011,x3012)+E(f786(x3013,x3014,x3015,x3016,x3011,x3017),f786(x3013,x3014,x3015,x3016,x3012,x3017)) % 165.30/165.06 [302]~E(x3021,x3022)+E(f786(x3023,x3024,x3025,x3026,x3027,x3021),f786(x3023,x3024,x3025,x3026,x3027,x3022)) % 165.30/165.06 [303]~E(x3031,x3032)+E(f92(x3031),f92(x3032)) % 165.30/165.06 [304]~E(x3041,x3042)+E(f270(x3041,x3043),f270(x3042,x3043)) % 165.30/165.06 [305]~E(x3051,x3052)+E(f270(x3053,x3051),f270(x3053,x3052)) % 165.30/165.06 [306]~E(x3061,x3062)+E(f876(x3061,x3063),f876(x3062,x3063)) % 165.30/165.06 [307]~E(x3071,x3072)+E(f876(x3073,x3071),f876(x3073,x3072)) % 165.30/165.06 [308]~E(x3081,x3082)+E(f154(x3081,x3083),f154(x3082,x3083)) % 165.30/165.06 [309]~E(x3091,x3092)+E(f154(x3093,x3091),f154(x3093,x3092)) % 165.30/165.06 [310]~E(x3101,x3102)+E(f304(x3101),f304(x3102)) % 165.30/165.06 [311]~E(x3111,x3112)+E(f255(x3111),f255(x3112)) % 165.30/165.06 [312]~E(x3121,x3122)+E(f286(x3121,x3123,x3124),f286(x3122,x3123,x3124)) % 165.30/165.06 [313]~E(x3131,x3132)+E(f286(x3133,x3131,x3134),f286(x3133,x3132,x3134)) % 165.30/165.06 [314]~E(x3141,x3142)+E(f286(x3143,x3144,x3141),f286(x3143,x3144,x3142)) % 165.30/165.06 [315]~E(x3151,x3152)+E(f66(x3151,x3153,x3154),f66(x3152,x3153,x3154)) % 165.30/165.06 [316]~E(x3161,x3162)+E(f66(x3163,x3161,x3164),f66(x3163,x3162,x3164)) % 165.30/165.06 [317]~E(x3171,x3172)+E(f66(x3173,x3174,x3171),f66(x3173,x3174,x3172)) % 165.30/165.06 [318]~E(x3181,x3182)+E(f171(x3181,x3183,x3184),f171(x3182,x3183,x3184)) % 165.30/165.06 [319]~E(x3191,x3192)+E(f171(x3193,x3191,x3194),f171(x3193,x3192,x3194)) % 165.30/165.06 [320]~E(x3201,x3202)+E(f171(x3203,x3204,x3201),f171(x3203,x3204,x3202)) % 165.30/165.06 [321]~E(x3211,x3212)+E(f173(x3211),f173(x3212)) % 165.30/165.06 [322]~E(x3221,x3222)+E(f167(x3221),f167(x3222)) % 165.30/165.06 [323]~E(x3231,x3232)+E(f711(x3231,x3233,x3234,x3235),f711(x3232,x3233,x3234,x3235)) % 165.30/165.06 [324]~E(x3241,x3242)+E(f711(x3243,x3241,x3244,x3245),f711(x3243,x3242,x3244,x3245)) % 165.30/165.06 [325]~E(x3251,x3252)+E(f711(x3253,x3254,x3251,x3255),f711(x3253,x3254,x3252,x3255)) % 165.30/165.06 [326]~E(x3261,x3262)+E(f711(x3263,x3264,x3265,x3261),f711(x3263,x3264,x3265,x3262)) % 165.30/165.06 [327]~E(x3271,x3272)+E(f143(x3271,x3273,x3274,x3275),f143(x3272,x3273,x3274,x3275)) % 165.30/165.06 [328]~E(x3281,x3282)+E(f143(x3283,x3281,x3284,x3285),f143(x3283,x3282,x3284,x3285)) % 165.30/165.06 [329]~E(x3291,x3292)+E(f143(x3293,x3294,x3291,x3295),f143(x3293,x3294,x3292,x3295)) % 165.30/165.06 [330]~E(x3301,x3302)+E(f143(x3303,x3304,x3305,x3301),f143(x3303,x3304,x3305,x3302)) % 165.30/165.06 [331]~E(x3311,x3312)+E(f620(x3311,x3313,x3314),f620(x3312,x3313,x3314)) % 165.30/165.06 [332]~E(x3321,x3322)+E(f620(x3323,x3321,x3324),f620(x3323,x3322,x3324)) % 165.30/165.06 [333]~E(x3331,x3332)+E(f620(x3333,x3334,x3331),f620(x3333,x3334,x3332)) % 165.30/165.06 [334]~E(x3341,x3342)+E(f435(x3341,x3343,x3344,x3345,x3346,x3347),f435(x3342,x3343,x3344,x3345,x3346,x3347)) % 165.30/165.06 [335]~E(x3351,x3352)+E(f435(x3353,x3351,x3354,x3355,x3356,x3357),f435(x3353,x3352,x3354,x3355,x3356,x3357)) % 165.30/165.06 [336]~E(x3361,x3362)+E(f435(x3363,x3364,x3361,x3365,x3366,x3367),f435(x3363,x3364,x3362,x3365,x3366,x3367)) % 165.30/165.06 [337]~E(x3371,x3372)+E(f435(x3373,x3374,x3375,x3371,x3376,x3377),f435(x3373,x3374,x3375,x3372,x3376,x3377)) % 165.30/165.06 [338]~E(x3381,x3382)+E(f435(x3383,x3384,x3385,x3386,x3381,x3387),f435(x3383,x3384,x3385,x3386,x3382,x3387)) % 165.30/165.06 [339]~E(x3391,x3392)+E(f435(x3393,x3394,x3395,x3396,x3397,x3391),f435(x3393,x3394,x3395,x3396,x3397,x3392)) % 165.30/165.06 [340]~E(x3401,x3402)+E(f77(x3401,x3403,x3404,x3405,x3406),f77(x3402,x3403,x3404,x3405,x3406)) % 165.30/165.06 [341]~E(x3411,x3412)+E(f77(x3413,x3411,x3414,x3415,x3416),f77(x3413,x3412,x3414,x3415,x3416)) % 165.30/165.06 [342]~E(x3421,x3422)+E(f77(x3423,x3424,x3421,x3425,x3426),f77(x3423,x3424,x3422,x3425,x3426)) % 165.30/165.06 [343]~E(x3431,x3432)+E(f77(x3433,x3434,x3435,x3431,x3436),f77(x3433,x3434,x3435,x3432,x3436)) % 165.30/165.06 [344]~E(x3441,x3442)+E(f77(x3443,x3444,x3445,x3446,x3441),f77(x3443,x3444,x3445,x3446,x3442)) % 165.30/165.06 [345]~E(x3451,x3452)+E(f210(x3451,x3453),f210(x3452,x3453)) % 165.30/165.06 [346]~E(x3461,x3462)+E(f210(x3463,x3461),f210(x3463,x3462)) % 165.30/165.06 [347]~E(x3471,x3472)+E(f490(x3471,x3473,x3474),f490(x3472,x3473,x3474)) % 165.30/165.06 [348]~E(x3481,x3482)+E(f490(x3483,x3481,x3484),f490(x3483,x3482,x3484)) % 165.30/165.06 [349]~E(x3491,x3492)+E(f490(x3493,x3494,x3491),f490(x3493,x3494,x3492)) % 165.30/165.06 [350]~E(x3501,x3502)+E(f193(x3501,x3503,x3504,x3505),f193(x3502,x3503,x3504,x3505)) % 165.30/165.06 [351]~E(x3511,x3512)+E(f193(x3513,x3511,x3514,x3515),f193(x3513,x3512,x3514,x3515)) % 165.30/165.06 [352]~E(x3521,x3522)+E(f193(x3523,x3524,x3521,x3525),f193(x3523,x3524,x3522,x3525)) % 165.30/165.06 [353]~E(x3531,x3532)+E(f193(x3533,x3534,x3535,x3531),f193(x3533,x3534,x3535,x3532)) % 165.30/165.06 [354]~E(x3541,x3542)+E(f659(x3541,x3543,x3544,x3545,x3546),f659(x3542,x3543,x3544,x3545,x3546)) % 165.30/165.06 [355]~E(x3551,x3552)+E(f659(x3553,x3551,x3554,x3555,x3556),f659(x3553,x3552,x3554,x3555,x3556)) % 165.30/165.06 [356]~E(x3561,x3562)+E(f659(x3563,x3564,x3561,x3565,x3566),f659(x3563,x3564,x3562,x3565,x3566)) % 165.30/165.06 [357]~E(x3571,x3572)+E(f659(x3573,x3574,x3575,x3571,x3576),f659(x3573,x3574,x3575,x3572,x3576)) % 165.30/165.06 [358]~E(x3581,x3582)+E(f659(x3583,x3584,x3585,x3586,x3581),f659(x3583,x3584,x3585,x3586,x3582)) % 165.30/165.06 [359]~E(x3591,x3592)+E(f179(x3591,x3593,x3594),f179(x3592,x3593,x3594)) % 165.30/165.06 [360]~E(x3601,x3602)+E(f179(x3603,x3601,x3604),f179(x3603,x3602,x3604)) % 165.30/165.06 [361]~E(x3611,x3612)+E(f179(x3613,x3614,x3611),f179(x3613,x3614,x3612)) % 165.30/165.06 [362]~E(x3621,x3622)+E(f131(x3621,x3623,x3624,x3625,x3626),f131(x3622,x3623,x3624,x3625,x3626)) % 165.30/165.06 [363]~E(x3631,x3632)+E(f131(x3633,x3631,x3634,x3635,x3636),f131(x3633,x3632,x3634,x3635,x3636)) % 165.30/165.06 [364]~E(x3641,x3642)+E(f131(x3643,x3644,x3641,x3645,x3646),f131(x3643,x3644,x3642,x3645,x3646)) % 165.30/165.06 [365]~E(x3651,x3652)+E(f131(x3653,x3654,x3655,x3651,x3656),f131(x3653,x3654,x3655,x3652,x3656)) % 165.30/165.06 [366]~E(x3661,x3662)+E(f131(x3663,x3664,x3665,x3666,x3661),f131(x3663,x3664,x3665,x3666,x3662)) % 165.30/165.06 [367]~E(x3671,x3672)+E(f309(x3671),f309(x3672)) % 165.30/165.06 [368]~E(x3681,x3682)+E(f312(x3681,x3683,x3684),f312(x3682,x3683,x3684)) % 165.30/165.06 [369]~E(x3691,x3692)+E(f312(x3693,x3691,x3694),f312(x3693,x3692,x3694)) % 165.30/165.06 [370]~E(x3701,x3702)+E(f312(x3703,x3704,x3701),f312(x3703,x3704,x3702)) % 165.30/165.06 [371]~E(x3711,x3712)+E(f323(x3711,x3713),f323(x3712,x3713)) % 165.30/165.06 [372]~E(x3721,x3722)+E(f323(x3723,x3721),f323(x3723,x3722)) % 165.30/165.06 [373]~E(x3731,x3732)+E(f228(x3731,x3733),f228(x3732,x3733)) % 165.30/165.06 [374]~E(x3741,x3742)+E(f228(x3743,x3741),f228(x3743,x3742)) % 165.30/165.06 [375]~E(x3751,x3752)+E(f325(x3751,x3753),f325(x3752,x3753)) % 165.30/165.06 [376]~E(x3761,x3762)+E(f325(x3763,x3761),f325(x3763,x3762)) % 165.30/165.06 [377]~E(x3771,x3772)+E(f56(x3771),f56(x3772)) % 165.30/165.06 [378]~E(x3781,x3782)+E(f15(x3781,x3783),f15(x3782,x3783)) % 165.30/165.06 [379]~E(x3791,x3792)+E(f15(x3793,x3791),f15(x3793,x3792)) % 165.30/165.06 [380]~E(x3801,x3802)+E(f802(x3801,x3803,x3804),f802(x3802,x3803,x3804)) % 165.30/165.06 [381]~E(x3811,x3812)+E(f802(x3813,x3811,x3814),f802(x3813,x3812,x3814)) % 165.30/165.06 [382]~E(x3821,x3822)+E(f802(x3823,x3824,x3821),f802(x3823,x3824,x3822)) % 165.30/165.06 [383]~E(x3831,x3832)+E(f67(x3831,x3833,x3834,x3835,x3836),f67(x3832,x3833,x3834,x3835,x3836)) % 165.30/165.06 [384]~E(x3841,x3842)+E(f67(x3843,x3841,x3844,x3845,x3846),f67(x3843,x3842,x3844,x3845,x3846)) % 165.30/165.06 [385]~E(x3851,x3852)+E(f67(x3853,x3854,x3851,x3855,x3856),f67(x3853,x3854,x3852,x3855,x3856)) % 165.30/165.06 [386]~E(x3861,x3862)+E(f67(x3863,x3864,x3865,x3861,x3866),f67(x3863,x3864,x3865,x3862,x3866)) % 165.30/165.06 [387]~E(x3871,x3872)+E(f67(x3873,x3874,x3875,x3876,x3871),f67(x3873,x3874,x3875,x3876,x3872)) % 165.30/165.06 [388]~E(x3881,x3882)+E(f353(x3881,x3883,x3884),f353(x3882,x3883,x3884)) % 165.30/165.06 [389]~E(x3891,x3892)+E(f353(x3893,x3891,x3894),f353(x3893,x3892,x3894)) % 165.30/165.06 [390]~E(x3901,x3902)+E(f353(x3903,x3904,x3901),f353(x3903,x3904,x3902)) % 165.30/165.06 [391]~E(x3911,x3912)+E(f190(x3911,x3913,x3914,x3915),f190(x3912,x3913,x3914,x3915)) % 165.30/165.06 [392]~E(x3921,x3922)+E(f190(x3923,x3921,x3924,x3925),f190(x3923,x3922,x3924,x3925)) % 165.30/165.06 [393]~E(x3931,x3932)+E(f190(x3933,x3934,x3931,x3935),f190(x3933,x3934,x3932,x3935)) % 165.30/165.06 [394]~E(x3941,x3942)+E(f190(x3943,x3944,x3945,x3941),f190(x3943,x3944,x3945,x3942)) % 165.30/165.06 [395]~E(x3951,x3952)+E(f640(x3951,x3953,x3954),f640(x3952,x3953,x3954)) % 165.30/165.06 [396]~E(x3961,x3962)+E(f640(x3963,x3961,x3964),f640(x3963,x3962,x3964)) % 165.30/165.06 [397]~E(x3971,x3972)+E(f640(x3973,x3974,x3971),f640(x3973,x3974,x3972)) % 165.30/165.06 [398]~E(x3981,x3982)+E(f806(x3981,x3983,x3984),f806(x3982,x3983,x3984)) % 165.30/165.06 [399]~E(x3991,x3992)+E(f806(x3993,x3991,x3994),f806(x3993,x3992,x3994)) % 165.30/165.06 [400]~E(x4001,x4002)+E(f806(x4003,x4004,x4001),f806(x4003,x4004,x4002)) % 165.30/165.06 [401]~E(x4011,x4012)+E(f144(x4011,x4013),f144(x4012,x4013)) % 165.30/165.06 [402]~E(x4021,x4022)+E(f144(x4023,x4021),f144(x4023,x4022)) % 165.30/165.06 [403]~E(x4031,x4032)+E(f811(x4031,x4033,x4034),f811(x4032,x4033,x4034)) % 165.30/165.06 [404]~E(x4041,x4042)+E(f811(x4043,x4041,x4044),f811(x4043,x4042,x4044)) % 165.30/165.06 [405]~E(x4051,x4052)+E(f811(x4053,x4054,x4051),f811(x4053,x4054,x4052)) % 165.30/165.06 [406]~E(x4061,x4062)+E(f389(x4061,x4063,x4064,x4065),f389(x4062,x4063,x4064,x4065)) % 165.30/165.06 [407]~E(x4071,x4072)+E(f389(x4073,x4071,x4074,x4075),f389(x4073,x4072,x4074,x4075)) % 165.30/165.06 [408]~E(x4081,x4082)+E(f389(x4083,x4084,x4081,x4085),f389(x4083,x4084,x4082,x4085)) % 165.30/165.06 [409]~E(x4091,x4092)+E(f389(x4093,x4094,x4095,x4091),f389(x4093,x4094,x4095,x4092)) % 165.30/165.06 [410]~E(x4101,x4102)+E(f182(x4101,x4103),f182(x4102,x4103)) % 165.30/165.06 [411]~E(x4111,x4112)+E(f182(x4113,x4111),f182(x4113,x4112)) % 165.30/165.06 [412]~E(x4121,x4122)+E(f801(x4121,x4123),f801(x4122,x4123)) % 165.30/165.06 [413]~E(x4131,x4132)+E(f801(x4133,x4131),f801(x4133,x4132)) % 165.30/165.06 [414]~E(x4141,x4142)+E(f126(x4141,x4143),f126(x4142,x4143)) % 165.30/165.06 [415]~E(x4151,x4152)+E(f126(x4153,x4151),f126(x4153,x4152)) % 165.30/165.06 [416]~E(x4161,x4162)+E(f47(x4161,x4163),f47(x4162,x4163)) % 165.30/165.06 [417]~E(x4171,x4172)+E(f47(x4173,x4171),f47(x4173,x4172)) % 165.30/165.06 [418]~E(x4181,x4182)+E(f738(x4181,x4183),f738(x4182,x4183)) % 165.30/165.06 [419]~E(x4191,x4192)+E(f738(x4193,x4191),f738(x4193,x4192)) % 165.30/165.06 [420]~E(x4201,x4202)+E(f86(x4201,x4203),f86(x4202,x4203)) % 165.30/165.06 [421]~E(x4211,x4212)+E(f86(x4213,x4211),f86(x4213,x4212)) % 165.30/165.06 [422]~E(x4221,x4222)+E(f303(x4221,x4223,x4224),f303(x4222,x4223,x4224)) % 165.30/165.06 [423]~E(x4231,x4232)+E(f303(x4233,x4231,x4234),f303(x4233,x4232,x4234)) % 165.30/165.06 [424]~E(x4241,x4242)+E(f303(x4243,x4244,x4241),f303(x4243,x4244,x4242)) % 165.30/165.06 [425]~E(x4251,x4252)+E(f91(x4251,x4253),f91(x4252,x4253)) % 165.30/165.06 [426]~E(x4261,x4262)+E(f91(x4263,x4261),f91(x4263,x4262)) % 165.30/165.06 [427]~E(x4271,x4272)+E(f181(x4271,x4273),f181(x4272,x4273)) % 165.30/165.06 [428]~E(x4281,x4282)+E(f181(x4283,x4281),f181(x4283,x4282)) % 165.30/165.06 [429]~E(x4291,x4292)+E(f224(x4291),f224(x4292)) % 165.30/165.06 [430]~E(x4301,x4302)+E(f265(x4301,x4303),f265(x4302,x4303)) % 165.30/165.06 [431]~E(x4311,x4312)+E(f265(x4313,x4311),f265(x4313,x4312)) % 165.30/165.06 [432]~E(x4321,x4322)+E(f556(x4321,x4323,x4324,x4325),f556(x4322,x4323,x4324,x4325)) % 165.30/165.06 [433]~E(x4331,x4332)+E(f556(x4333,x4331,x4334,x4335),f556(x4333,x4332,x4334,x4335)) % 165.30/165.06 [434]~E(x4341,x4342)+E(f556(x4343,x4344,x4341,x4345),f556(x4343,x4344,x4342,x4345)) % 165.30/165.06 [435]~E(x4351,x4352)+E(f556(x4353,x4354,x4355,x4351),f556(x4353,x4354,x4355,x4352)) % 165.30/165.06 [436]~E(x4361,x4362)+E(f99(x4361),f99(x4362)) % 165.30/165.06 [437]~E(x4371,x4372)+E(f717(x4371,x4373,x4374,x4375,x4376,x4377),f717(x4372,x4373,x4374,x4375,x4376,x4377)) % 165.30/165.06 [438]~E(x4381,x4382)+E(f717(x4383,x4381,x4384,x4385,x4386,x4387),f717(x4383,x4382,x4384,x4385,x4386,x4387)) % 165.30/165.06 [439]~E(x4391,x4392)+E(f717(x4393,x4394,x4391,x4395,x4396,x4397),f717(x4393,x4394,x4392,x4395,x4396,x4397)) % 165.30/165.06 [440]~E(x4401,x4402)+E(f717(x4403,x4404,x4405,x4401,x4406,x4407),f717(x4403,x4404,x4405,x4402,x4406,x4407)) % 165.30/165.06 [441]~E(x4411,x4412)+E(f717(x4413,x4414,x4415,x4416,x4411,x4417),f717(x4413,x4414,x4415,x4416,x4412,x4417)) % 165.30/165.06 [442]~E(x4421,x4422)+E(f717(x4423,x4424,x4425,x4426,x4427,x4421),f717(x4423,x4424,x4425,x4426,x4427,x4422)) % 165.30/165.06 [443]~E(x4431,x4432)+E(f40(x4431,x4433),f40(x4432,x4433)) % 165.30/165.06 [444]~E(x4441,x4442)+E(f40(x4443,x4441),f40(x4443,x4442)) % 165.30/165.06 [445]~E(x4451,x4452)+E(f87(x4451,x4453),f87(x4452,x4453)) % 165.30/165.06 [446]~E(x4461,x4462)+E(f87(x4463,x4461),f87(x4463,x4462)) % 165.30/165.06 [447]~E(x4471,x4472)+E(f65(x4471,x4473,x4474),f65(x4472,x4473,x4474)) % 165.30/165.06 [448]~E(x4481,x4482)+E(f65(x4483,x4481,x4484),f65(x4483,x4482,x4484)) % 165.30/165.06 [449]~E(x4491,x4492)+E(f65(x4493,x4494,x4491),f65(x4493,x4494,x4492)) % 165.30/165.06 [450]~E(x4501,x4502)+E(f243(x4501),f243(x4502)) % 165.30/165.06 [451]~E(x4511,x4512)+E(f187(x4511,x4513,x4514,x4515),f187(x4512,x4513,x4514,x4515)) % 165.30/165.06 [452]~E(x4521,x4522)+E(f187(x4523,x4521,x4524,x4525),f187(x4523,x4522,x4524,x4525)) % 165.30/165.06 [453]~E(x4531,x4532)+E(f187(x4533,x4534,x4531,x4535),f187(x4533,x4534,x4532,x4535)) % 165.30/165.06 [454]~E(x4541,x4542)+E(f187(x4543,x4544,x4545,x4541),f187(x4543,x4544,x4545,x4542)) % 165.30/165.06 [455]~E(x4551,x4552)+E(f810(x4551,x4553,x4554),f810(x4552,x4553,x4554)) % 165.30/165.06 [456]~E(x4561,x4562)+E(f810(x4563,x4561,x4564),f810(x4563,x4562,x4564)) % 165.30/165.06 [457]~E(x4571,x4572)+E(f810(x4573,x4574,x4571),f810(x4573,x4574,x4572)) % 165.30/165.06 [458]~E(x4581,x4582)+E(f421(x4581,x4583,x4584),f421(x4582,x4583,x4584)) % 165.30/165.06 [459]~E(x4591,x4592)+E(f421(x4593,x4591,x4594),f421(x4593,x4592,x4594)) % 165.30/165.06 [460]~E(x4601,x4602)+E(f421(x4603,x4604,x4601),f421(x4603,x4604,x4602)) % 165.30/165.06 [461]~E(x4611,x4612)+E(f782(x4611,x4613,x4614),f782(x4612,x4613,x4614)) % 165.30/165.06 [462]~E(x4621,x4622)+E(f782(x4623,x4621,x4624),f782(x4623,x4622,x4624)) % 165.30/165.06 [463]~E(x4631,x4632)+E(f782(x4633,x4634,x4631),f782(x4633,x4634,x4632)) % 165.30/165.06 [464]~E(x4641,x4642)+E(f653(x4641,x4643,x4644),f653(x4642,x4643,x4644)) % 165.30/165.06 [465]~E(x4651,x4652)+E(f653(x4653,x4651,x4654),f653(x4653,x4652,x4654)) % 165.30/165.06 [466]~E(x4661,x4662)+E(f653(x4663,x4664,x4661),f653(x4663,x4664,x4662)) % 165.30/165.06 [467]~E(x4671,x4672)+E(f585(x4671,x4673,x4674,x4675,x4676),f585(x4672,x4673,x4674,x4675,x4676)) % 165.30/165.06 [468]~E(x4681,x4682)+E(f585(x4683,x4681,x4684,x4685,x4686),f585(x4683,x4682,x4684,x4685,x4686)) % 165.30/165.06 [469]~E(x4691,x4692)+E(f585(x4693,x4694,x4691,x4695,x4696),f585(x4693,x4694,x4692,x4695,x4696)) % 165.30/165.06 [470]~E(x4701,x4702)+E(f585(x4703,x4704,x4705,x4701,x4706),f585(x4703,x4704,x4705,x4702,x4706)) % 165.30/165.06 [471]~E(x4711,x4712)+E(f585(x4713,x4714,x4715,x4716,x4711),f585(x4713,x4714,x4715,x4716,x4712)) % 165.30/165.06 [472]~E(x4721,x4722)+E(f162(x4721,x4723),f162(x4722,x4723)) % 165.30/165.06 [473]~E(x4731,x4732)+E(f162(x4733,x4731),f162(x4733,x4732)) % 165.30/165.06 [474]~E(x4741,x4742)+E(f164(x4741,x4743,x4744,x4745),f164(x4742,x4743,x4744,x4745)) % 165.30/165.06 [475]~E(x4751,x4752)+E(f164(x4753,x4751,x4754,x4755),f164(x4753,x4752,x4754,x4755)) % 165.30/165.06 [476]~E(x4761,x4762)+E(f164(x4763,x4764,x4761,x4765),f164(x4763,x4764,x4762,x4765)) % 165.30/165.06 [477]~E(x4771,x4772)+E(f164(x4773,x4774,x4775,x4771),f164(x4773,x4774,x4775,x4772)) % 165.30/165.06 [478]~E(x4781,x4782)+E(f194(x4781),f194(x4782)) % 165.30/165.06 [479]~E(x4791,x4792)+E(f148(x4791,x4793),f148(x4792,x4793)) % 165.30/165.06 [480]~E(x4801,x4802)+E(f148(x4803,x4801),f148(x4803,x4802)) % 165.30/165.06 [481]~E(x4811,x4812)+E(f805(x4811,x4813,x4814),f805(x4812,x4813,x4814)) % 165.30/165.06 [482]~E(x4821,x4822)+E(f805(x4823,x4821,x4824),f805(x4823,x4822,x4824)) % 165.30/165.06 [483]~E(x4831,x4832)+E(f805(x4833,x4834,x4831),f805(x4833,x4834,x4832)) % 165.30/165.06 [484]~E(x4841,x4842)+E(f287(x4841,x4843),f287(x4842,x4843)) % 165.30/165.06 [485]~E(x4851,x4852)+E(f287(x4853,x4851),f287(x4853,x4852)) % 165.30/165.06 [486]~E(x4861,x4862)+E(f443(x4861,x4863),f443(x4862,x4863)) % 165.30/165.06 [487]~E(x4871,x4872)+E(f443(x4873,x4871),f443(x4873,x4872)) % 165.30/165.06 [488]~E(x4881,x4882)+E(f13(x4881,x4883,x4884),f13(x4882,x4883,x4884)) % 165.30/165.06 [489]~E(x4891,x4892)+E(f13(x4893,x4891,x4894),f13(x4893,x4892,x4894)) % 165.30/165.06 [490]~E(x4901,x4902)+E(f13(x4903,x4904,x4901),f13(x4903,x4904,x4902)) % 165.30/165.06 [491]~E(x4911,x4912)+E(f189(x4911,x4913,x4914,x4915,x4916),f189(x4912,x4913,x4914,x4915,x4916)) % 165.30/165.06 [492]~E(x4921,x4922)+E(f189(x4923,x4921,x4924,x4925,x4926),f189(x4923,x4922,x4924,x4925,x4926)) % 165.30/165.06 [493]~E(x4931,x4932)+E(f189(x4933,x4934,x4931,x4935,x4936),f189(x4933,x4934,x4932,x4935,x4936)) % 165.30/165.06 [494]~E(x4941,x4942)+E(f189(x4943,x4944,x4945,x4941,x4946),f189(x4943,x4944,x4945,x4942,x4946)) % 165.30/165.06 [495]~E(x4951,x4952)+E(f189(x4953,x4954,x4955,x4956,x4951),f189(x4953,x4954,x4955,x4956,x4952)) % 165.30/165.06 [496]~E(x4961,x4962)+E(f499(x4961,x4963,x4964,x4965,x4966,x4967,x4968),f499(x4962,x4963,x4964,x4965,x4966,x4967,x4968)) % 165.30/165.06 [497]~E(x4971,x4972)+E(f499(x4973,x4971,x4974,x4975,x4976,x4977,x4978),f499(x4973,x4972,x4974,x4975,x4976,x4977,x4978)) % 165.30/165.06 [498]~E(x4981,x4982)+E(f499(x4983,x4984,x4981,x4985,x4986,x4987,x4988),f499(x4983,x4984,x4982,x4985,x4986,x4987,x4988)) % 165.30/165.06 [499]~E(x4991,x4992)+E(f499(x4993,x4994,x4995,x4991,x4996,x4997,x4998),f499(x4993,x4994,x4995,x4992,x4996,x4997,x4998)) % 165.30/165.06 [500]~E(x5001,x5002)+E(f499(x5003,x5004,x5005,x5006,x5001,x5007,x5008),f499(x5003,x5004,x5005,x5006,x5002,x5007,x5008)) % 165.30/165.06 [501]~E(x5011,x5012)+E(f499(x5013,x5014,x5015,x5016,x5017,x5011,x5018),f499(x5013,x5014,x5015,x5016,x5017,x5012,x5018)) % 165.30/165.06 [502]~E(x5021,x5022)+E(f499(x5023,x5024,x5025,x5026,x5027,x5028,x5021),f499(x5023,x5024,x5025,x5026,x5027,x5028,x5022)) % 165.30/165.06 [503]~E(x5031,x5032)+E(f468(x5031,x5033,x5034,x5035,x5036),f468(x5032,x5033,x5034,x5035,x5036)) % 165.30/165.06 [504]~E(x5041,x5042)+E(f468(x5043,x5041,x5044,x5045,x5046),f468(x5043,x5042,x5044,x5045,x5046)) % 165.30/165.06 [505]~E(x5051,x5052)+E(f468(x5053,x5054,x5051,x5055,x5056),f468(x5053,x5054,x5052,x5055,x5056)) % 165.30/165.06 [506]~E(x5061,x5062)+E(f468(x5063,x5064,x5065,x5061,x5066),f468(x5063,x5064,x5065,x5062,x5066)) % 165.30/165.06 [507]~E(x5071,x5072)+E(f468(x5073,x5074,x5075,x5076,x5071),f468(x5073,x5074,x5075,x5076,x5072)) % 165.30/165.06 [508]~E(x5081,x5082)+E(f656(x5081,x5083,x5084,x5085,x5086),f656(x5082,x5083,x5084,x5085,x5086)) % 165.30/165.06 [509]~E(x5091,x5092)+E(f656(x5093,x5091,x5094,x5095,x5096),f656(x5093,x5092,x5094,x5095,x5096)) % 165.30/165.06 [510]~E(x5101,x5102)+E(f656(x5103,x5104,x5101,x5105,x5106),f656(x5103,x5104,x5102,x5105,x5106)) % 165.30/165.06 [511]~E(x5111,x5112)+E(f656(x5113,x5114,x5115,x5111,x5116),f656(x5113,x5114,x5115,x5112,x5116)) % 165.30/165.06 [512]~E(x5121,x5122)+E(f656(x5123,x5124,x5125,x5126,x5121),f656(x5123,x5124,x5125,x5126,x5122)) % 165.30/165.06 [513]~E(x5131,x5132)+E(f596(x5131,x5133,x5134),f596(x5132,x5133,x5134)) % 165.30/165.06 [514]~E(x5141,x5142)+E(f596(x5143,x5141,x5144),f596(x5143,x5142,x5144)) % 165.30/165.06 [515]~E(x5151,x5152)+E(f596(x5153,x5154,x5151),f596(x5153,x5154,x5152)) % 165.30/165.06 [516]~E(x5161,x5162)+E(f128(x5161,x5163,x5164),f128(x5162,x5163,x5164)) % 165.30/165.06 [517]~E(x5171,x5172)+E(f128(x5173,x5171,x5174),f128(x5173,x5172,x5174)) % 165.30/165.06 [518]~E(x5181,x5182)+E(f128(x5183,x5184,x5181),f128(x5183,x5184,x5182)) % 165.30/165.06 [519]~E(x5191,x5192)+E(f409(x5191,x5193,x5194,x5195),f409(x5192,x5193,x5194,x5195)) % 165.30/165.06 [520]~E(x5201,x5202)+E(f409(x5203,x5201,x5204,x5205),f409(x5203,x5202,x5204,x5205)) % 165.30/165.06 [521]~E(x5211,x5212)+E(f409(x5213,x5214,x5211,x5215),f409(x5213,x5214,x5212,x5215)) % 165.30/165.06 [522]~E(x5221,x5222)+E(f409(x5223,x5224,x5225,x5221),f409(x5223,x5224,x5225,x5222)) % 165.30/165.06 [523]~E(x5231,x5232)+E(f307(x5231),f307(x5232)) % 165.30/165.06 [524]~E(x5241,x5242)+E(f770(x5241,x5243,x5244,x5245),f770(x5242,x5243,x5244,x5245)) % 165.30/165.06 [525]~E(x5251,x5252)+E(f770(x5253,x5251,x5254,x5255),f770(x5253,x5252,x5254,x5255)) % 165.30/165.06 [526]~E(x5261,x5262)+E(f770(x5263,x5264,x5261,x5265),f770(x5263,x5264,x5262,x5265)) % 165.30/165.06 [527]~E(x5271,x5272)+E(f770(x5273,x5274,x5275,x5271),f770(x5273,x5274,x5275,x5272)) % 165.30/165.06 [528]~E(x5281,x5282)+E(f698(x5281,x5283,x5284,x5285,x5286,x5287),f698(x5282,x5283,x5284,x5285,x5286,x5287)) % 165.30/165.06 [529]~E(x5291,x5292)+E(f698(x5293,x5291,x5294,x5295,x5296,x5297),f698(x5293,x5292,x5294,x5295,x5296,x5297)) % 165.30/165.06 [530]~E(x5301,x5302)+E(f698(x5303,x5304,x5301,x5305,x5306,x5307),f698(x5303,x5304,x5302,x5305,x5306,x5307)) % 165.30/165.06 [531]~E(x5311,x5312)+E(f698(x5313,x5314,x5315,x5311,x5316,x5317),f698(x5313,x5314,x5315,x5312,x5316,x5317)) % 165.30/165.06 [532]~E(x5321,x5322)+E(f698(x5323,x5324,x5325,x5326,x5321,x5327),f698(x5323,x5324,x5325,x5326,x5322,x5327)) % 165.30/165.06 [533]~E(x5331,x5332)+E(f698(x5333,x5334,x5335,x5336,x5337,x5331),f698(x5333,x5334,x5335,x5336,x5337,x5332)) % 165.30/165.06 [534]~E(x5341,x5342)+E(f697(x5341,x5343,x5344,x5345,x5346,x5347),f697(x5342,x5343,x5344,x5345,x5346,x5347)) % 165.30/165.06 [535]~E(x5351,x5352)+E(f697(x5353,x5351,x5354,x5355,x5356,x5357),f697(x5353,x5352,x5354,x5355,x5356,x5357)) % 165.30/165.06 [536]~E(x5361,x5362)+E(f697(x5363,x5364,x5361,x5365,x5366,x5367),f697(x5363,x5364,x5362,x5365,x5366,x5367)) % 165.30/165.06 [537]~E(x5371,x5372)+E(f697(x5373,x5374,x5375,x5371,x5376,x5377),f697(x5373,x5374,x5375,x5372,x5376,x5377)) % 165.30/165.06 [538]~E(x5381,x5382)+E(f697(x5383,x5384,x5385,x5386,x5381,x5387),f697(x5383,x5384,x5385,x5386,x5382,x5387)) % 165.30/165.06 [539]~E(x5391,x5392)+E(f697(x5393,x5394,x5395,x5396,x5397,x5391),f697(x5393,x5394,x5395,x5396,x5397,x5392)) % 165.30/165.06 [540]~E(x5401,x5402)+E(f710(x5401,x5403,x5404),f710(x5402,x5403,x5404)) % 165.30/165.06 [541]~E(x5411,x5412)+E(f710(x5413,x5411,x5414),f710(x5413,x5412,x5414)) % 165.30/165.06 [542]~E(x5421,x5422)+E(f710(x5423,x5424,x5421),f710(x5423,x5424,x5422)) % 165.30/165.06 [543]~E(x5431,x5432)+E(f771(x5431,x5433,x5434,x5435,x5436,x5437,x5438),f771(x5432,x5433,x5434,x5435,x5436,x5437,x5438)) % 165.30/165.06 [544]~E(x5441,x5442)+E(f771(x5443,x5441,x5444,x5445,x5446,x5447,x5448),f771(x5443,x5442,x5444,x5445,x5446,x5447,x5448)) % 165.30/165.06 [545]~E(x5451,x5452)+E(f771(x5453,x5454,x5451,x5455,x5456,x5457,x5458),f771(x5453,x5454,x5452,x5455,x5456,x5457,x5458)) % 165.30/165.06 [546]~E(x5461,x5462)+E(f771(x5463,x5464,x5465,x5461,x5466,x5467,x5468),f771(x5463,x5464,x5465,x5462,x5466,x5467,x5468)) % 165.30/165.06 [547]~E(x5471,x5472)+E(f771(x5473,x5474,x5475,x5476,x5471,x5477,x5478),f771(x5473,x5474,x5475,x5476,x5472,x5477,x5478)) % 165.30/165.06 [548]~E(x5481,x5482)+E(f771(x5483,x5484,x5485,x5486,x5487,x5481,x5488),f771(x5483,x5484,x5485,x5486,x5487,x5482,x5488)) % 165.30/165.06 [549]~E(x5491,x5492)+E(f771(x5493,x5494,x5495,x5496,x5497,x5498,x5491),f771(x5493,x5494,x5495,x5496,x5497,x5498,x5492)) % 165.30/165.06 [550]~E(x5501,x5502)+E(f142(x5501),f142(x5502)) % 165.30/165.06 [551]~E(x5511,x5512)+E(f550(x5511,x5513,x5514,x5515,x5516,x5517),f550(x5512,x5513,x5514,x5515,x5516,x5517)) % 165.30/165.06 [552]~E(x5521,x5522)+E(f550(x5523,x5521,x5524,x5525,x5526,x5527),f550(x5523,x5522,x5524,x5525,x5526,x5527)) % 165.30/165.06 [553]~E(x5531,x5532)+E(f550(x5533,x5534,x5531,x5535,x5536,x5537),f550(x5533,x5534,x5532,x5535,x5536,x5537)) % 165.30/165.06 [554]~E(x5541,x5542)+E(f550(x5543,x5544,x5545,x5541,x5546,x5547),f550(x5543,x5544,x5545,x5542,x5546,x5547)) % 165.30/165.06 [555]~E(x5551,x5552)+E(f550(x5553,x5554,x5555,x5556,x5551,x5557),f550(x5553,x5554,x5555,x5556,x5552,x5557)) % 165.30/165.06 [556]~E(x5561,x5562)+E(f550(x5563,x5564,x5565,x5566,x5567,x5561),f550(x5563,x5564,x5565,x5566,x5567,x5562)) % 165.30/165.06 [557]~E(x5571,x5572)+E(f783(x5571,x5573,x5574),f783(x5572,x5573,x5574)) % 165.30/165.06 [558]~E(x5581,x5582)+E(f783(x5583,x5581,x5584),f783(x5583,x5582,x5584)) % 165.30/165.06 [559]~E(x5591,x5592)+E(f783(x5593,x5594,x5591),f783(x5593,x5594,x5592)) % 165.30/165.06 [560]~E(x5601,x5602)+E(f259(x5601,x5603,x5604),f259(x5602,x5603,x5604)) % 165.30/165.06 [561]~E(x5611,x5612)+E(f259(x5613,x5611,x5614),f259(x5613,x5612,x5614)) % 165.30/165.06 [562]~E(x5621,x5622)+E(f259(x5623,x5624,x5621),f259(x5623,x5624,x5622)) % 165.30/165.06 [563]~E(x5631,x5632)+E(f34(x5631,x5633),f34(x5632,x5633)) % 165.30/165.06 [564]~E(x5641,x5642)+E(f34(x5643,x5641),f34(x5643,x5642)) % 165.30/165.06 [565]~E(x5651,x5652)+E(f146(x5651,x5653),f146(x5652,x5653)) % 165.30/165.06 [566]~E(x5661,x5662)+E(f146(x5663,x5661),f146(x5663,x5662)) % 165.30/165.06 [567]~E(x5671,x5672)+E(f254(x5671),f254(x5672)) % 165.30/165.06 [568]~E(x5681,x5682)+E(f219(x5681,x5683,x5684,x5685),f219(x5682,x5683,x5684,x5685)) % 165.30/165.06 [569]~E(x5691,x5692)+E(f219(x5693,x5691,x5694,x5695),f219(x5693,x5692,x5694,x5695)) % 165.30/165.06 [570]~E(x5701,x5702)+E(f219(x5703,x5704,x5701,x5705),f219(x5703,x5704,x5702,x5705)) % 165.30/165.06 [571]~E(x5711,x5712)+E(f219(x5713,x5714,x5715,x5711),f219(x5713,x5714,x5715,x5712)) % 165.30/165.06 [572]~E(x5721,x5722)+E(f175(x5721,x5723,x5724),f175(x5722,x5723,x5724)) % 165.30/165.06 [573]~E(x5731,x5732)+E(f175(x5733,x5731,x5734),f175(x5733,x5732,x5734)) % 165.30/165.06 [574]~E(x5741,x5742)+E(f175(x5743,x5744,x5741),f175(x5743,x5744,x5742)) % 165.30/165.06 [575]~E(x5751,x5752)+E(f241(x5751,x5753,x5754,x5755),f241(x5752,x5753,x5754,x5755)) % 165.30/165.06 [576]~E(x5761,x5762)+E(f241(x5763,x5761,x5764,x5765),f241(x5763,x5762,x5764,x5765)) % 165.30/165.06 [577]~E(x5771,x5772)+E(f241(x5773,x5774,x5771,x5775),f241(x5773,x5774,x5772,x5775)) % 165.30/165.06 [578]~E(x5781,x5782)+E(f241(x5783,x5784,x5785,x5781),f241(x5783,x5784,x5785,x5782)) % 165.30/165.06 [579]~E(x5791,x5792)+E(f178(x5791,x5793,x5794),f178(x5792,x5793,x5794)) % 165.30/165.06 [580]~E(x5801,x5802)+E(f178(x5803,x5801,x5804),f178(x5803,x5802,x5804)) % 165.30/165.06 [581]~E(x5811,x5812)+E(f178(x5813,x5814,x5811),f178(x5813,x5814,x5812)) % 165.30/165.06 [582]~E(x5821,x5822)+E(f276(x5821,x5823),f276(x5822,x5823)) % 165.30/165.06 [583]~E(x5831,x5832)+E(f276(x5833,x5831),f276(x5833,x5832)) % 165.30/165.06 [584]~E(x5841,x5842)+E(f59(x5841),f59(x5842)) % 165.30/165.06 [585]~E(x5851,x5852)+E(f470(x5851,x5853,x5854,x5855,x5856),f470(x5852,x5853,x5854,x5855,x5856)) % 165.30/165.06 [586]~E(x5861,x5862)+E(f470(x5863,x5861,x5864,x5865,x5866),f470(x5863,x5862,x5864,x5865,x5866)) % 165.30/165.06 [587]~E(x5871,x5872)+E(f470(x5873,x5874,x5871,x5875,x5876),f470(x5873,x5874,x5872,x5875,x5876)) % 165.30/165.06 [588]~E(x5881,x5882)+E(f470(x5883,x5884,x5885,x5881,x5886),f470(x5883,x5884,x5885,x5882,x5886)) % 165.30/165.06 [589]~E(x5891,x5892)+E(f470(x5893,x5894,x5895,x5896,x5891),f470(x5893,x5894,x5895,x5896,x5892)) % 165.30/165.06 [590]~E(x5901,x5902)+E(f654(x5901,x5903,x5904),f654(x5902,x5903,x5904)) % 165.30/165.06 [591]~E(x5911,x5912)+E(f654(x5913,x5911,x5914),f654(x5913,x5912,x5914)) % 165.30/165.06 [592]~E(x5921,x5922)+E(f654(x5923,x5924,x5921),f654(x5923,x5924,x5922)) % 165.30/165.06 [593]~E(x5931,x5932)+E(f306(x5931,x5933,x5934),f306(x5932,x5933,x5934)) % 165.30/165.06 [594]~E(x5941,x5942)+E(f306(x5943,x5941,x5944),f306(x5943,x5942,x5944)) % 165.30/165.06 [595]~E(x5951,x5952)+E(f306(x5953,x5954,x5951),f306(x5953,x5954,x5952)) % 165.30/165.06 [596]~E(x5961,x5962)+E(f511(x5961,x5963,x5964),f511(x5962,x5963,x5964)) % 165.30/165.06 [597]~E(x5971,x5972)+E(f511(x5973,x5971,x5974),f511(x5973,x5972,x5974)) % 165.30/165.06 [598]~E(x5981,x5982)+E(f511(x5983,x5984,x5981),f511(x5983,x5984,x5982)) % 165.30/165.06 [599]~E(x5991,x5992)+E(f574(x5991,x5993,x5994),f574(x5992,x5993,x5994)) % 165.30/165.06 [600]~E(x6001,x6002)+E(f574(x6003,x6001,x6004),f574(x6003,x6002,x6004)) % 165.30/165.06 [601]~E(x6011,x6012)+E(f574(x6013,x6014,x6011),f574(x6013,x6014,x6012)) % 165.30/165.06 [602]~E(x6021,x6022)+E(f368(x6021,x6023),f368(x6022,x6023)) % 165.30/165.06 [603]~E(x6031,x6032)+E(f368(x6033,x6031),f368(x6033,x6032)) % 165.30/165.06 [604]~E(x6041,x6042)+E(f398(x6041,x6043),f398(x6042,x6043)) % 165.30/165.06 [605]~E(x6051,x6052)+E(f398(x6053,x6051),f398(x6053,x6052)) % 165.30/165.06 [606]~E(x6061,x6062)+E(f743(x6061,x6063),f743(x6062,x6063)) % 165.30/165.06 [607]~E(x6071,x6072)+E(f743(x6073,x6071),f743(x6073,x6072)) % 165.30/165.06 [608]~E(x6081,x6082)+E(f239(x6081,x6083),f239(x6082,x6083)) % 165.30/165.06 [609]~E(x6091,x6092)+E(f239(x6093,x6091),f239(x6093,x6092)) % 165.30/165.06 [610]~E(x6101,x6102)+E(f739(x6101,x6103,x6104),f739(x6102,x6103,x6104)) % 165.30/165.06 [611]~E(x6111,x6112)+E(f739(x6113,x6111,x6114),f739(x6113,x6112,x6114)) % 165.30/165.06 [612]~E(x6121,x6122)+E(f739(x6123,x6124,x6121),f739(x6123,x6124,x6122)) % 165.30/165.06 [613]~E(x6131,x6132)+E(f285(x6131),f285(x6132)) % 165.30/165.06 [614]~E(x6141,x6142)+E(f746(x6141,x6143,x6144,x6145,x6146),f746(x6142,x6143,x6144,x6145,x6146)) % 165.30/165.06 [615]~E(x6151,x6152)+E(f746(x6153,x6151,x6154,x6155,x6156),f746(x6153,x6152,x6154,x6155,x6156)) % 165.30/165.06 [616]~E(x6161,x6162)+E(f746(x6163,x6164,x6161,x6165,x6166),f746(x6163,x6164,x6162,x6165,x6166)) % 165.30/165.06 [617]~E(x6171,x6172)+E(f746(x6173,x6174,x6175,x6171,x6176),f746(x6173,x6174,x6175,x6172,x6176)) % 165.30/165.06 [618]~E(x6181,x6182)+E(f746(x6183,x6184,x6185,x6186,x6181),f746(x6183,x6184,x6185,x6186,x6182)) % 165.30/165.06 [619]~E(x6191,x6192)+E(f644(x6191,x6193,x6194,x6195),f644(x6192,x6193,x6194,x6195)) % 165.30/165.06 [620]~E(x6201,x6202)+E(f644(x6203,x6201,x6204,x6205),f644(x6203,x6202,x6204,x6205)) % 165.30/165.06 [621]~E(x6211,x6212)+E(f644(x6213,x6214,x6211,x6215),f644(x6213,x6214,x6212,x6215)) % 165.30/165.06 [622]~E(x6221,x6222)+E(f644(x6223,x6224,x6225,x6221),f644(x6223,x6224,x6225,x6222)) % 165.30/165.06 [623]~E(x6231,x6232)+E(f31(x6231,x6233,x6234),f31(x6232,x6233,x6234)) % 165.30/165.06 [624]~E(x6241,x6242)+E(f31(x6243,x6241,x6244),f31(x6243,x6242,x6244)) % 165.30/165.06 [625]~E(x6251,x6252)+E(f31(x6253,x6254,x6251),f31(x6253,x6254,x6252)) % 165.30/165.06 [626]~E(x6261,x6262)+E(f651(x6261,x6263),f651(x6262,x6263)) % 165.30/165.06 [627]~E(x6271,x6272)+E(f651(x6273,x6271),f651(x6273,x6272)) % 165.30/165.06 [628]~E(x6281,x6282)+E(f702(x6281,x6283,x6284,x6285,x6286,x6287,x6288),f702(x6282,x6283,x6284,x6285,x6286,x6287,x6288)) % 165.30/165.06 [629]~E(x6291,x6292)+E(f702(x6293,x6291,x6294,x6295,x6296,x6297,x6298),f702(x6293,x6292,x6294,x6295,x6296,x6297,x6298)) % 165.30/165.06 [630]~E(x6301,x6302)+E(f702(x6303,x6304,x6301,x6305,x6306,x6307,x6308),f702(x6303,x6304,x6302,x6305,x6306,x6307,x6308)) % 165.30/165.06 [631]~E(x6311,x6312)+E(f702(x6313,x6314,x6315,x6311,x6316,x6317,x6318),f702(x6313,x6314,x6315,x6312,x6316,x6317,x6318)) % 165.30/165.06 [632]~E(x6321,x6322)+E(f702(x6323,x6324,x6325,x6326,x6321,x6327,x6328),f702(x6323,x6324,x6325,x6326,x6322,x6327,x6328)) % 165.30/165.06 [633]~E(x6331,x6332)+E(f702(x6333,x6334,x6335,x6336,x6337,x6331,x6338),f702(x6333,x6334,x6335,x6336,x6337,x6332,x6338)) % 165.30/165.06 [634]~E(x6341,x6342)+E(f702(x6343,x6344,x6345,x6346,x6347,x6348,x6341),f702(x6343,x6344,x6345,x6346,x6347,x6348,x6342)) % 165.30/165.06 [635]~E(x6351,x6352)+E(f772(x6351,x6353,x6354),f772(x6352,x6353,x6354)) % 165.30/165.06 [636]~E(x6361,x6362)+E(f772(x6363,x6361,x6364),f772(x6363,x6362,x6364)) % 165.30/165.06 [637]~E(x6371,x6372)+E(f772(x6373,x6374,x6371),f772(x6373,x6374,x6372)) % 165.30/165.06 [638]~E(x6381,x6382)+E(f538(x6381,x6383,x6384,x6385),f538(x6382,x6383,x6384,x6385)) % 165.30/165.06 [639]~E(x6391,x6392)+E(f538(x6393,x6391,x6394,x6395),f538(x6393,x6392,x6394,x6395)) % 165.30/165.06 [640]~E(x6401,x6402)+E(f538(x6403,x6404,x6401,x6405),f538(x6403,x6404,x6402,x6405)) % 165.30/165.06 [641]~E(x6411,x6412)+E(f538(x6413,x6414,x6415,x6411),f538(x6413,x6414,x6415,x6412)) % 165.30/165.06 [642]~E(x6421,x6422)+E(f11(x6421,x6423),f11(x6422,x6423)) % 165.30/165.06 [643]~E(x6431,x6432)+E(f11(x6433,x6431),f11(x6433,x6432)) % 165.30/165.06 [644]~E(x6441,x6442)+E(f273(x6441,x6443,x6444,x6445),f273(x6442,x6443,x6444,x6445)) % 165.30/165.06 [645]~E(x6451,x6452)+E(f273(x6453,x6451,x6454,x6455),f273(x6453,x6452,x6454,x6455)) % 165.30/165.06 [646]~E(x6461,x6462)+E(f273(x6463,x6464,x6461,x6465),f273(x6463,x6464,x6462,x6465)) % 165.30/165.06 [647]~E(x6471,x6472)+E(f273(x6473,x6474,x6475,x6471),f273(x6473,x6474,x6475,x6472)) % 165.30/165.06 [648]~E(x6481,x6482)+E(f549(x6481,x6483,x6484),f549(x6482,x6483,x6484)) % 165.30/165.06 [649]~E(x6491,x6492)+E(f549(x6493,x6491,x6494),f549(x6493,x6492,x6494)) % 165.30/165.06 [650]~E(x6501,x6502)+E(f549(x6503,x6504,x6501),f549(x6503,x6504,x6502)) % 165.30/165.06 [651]~E(x6511,x6512)+E(f661(x6511,x6513,x6514),f661(x6512,x6513,x6514)) % 165.30/165.06 [652]~E(x6521,x6522)+E(f661(x6523,x6521,x6524),f661(x6523,x6522,x6524)) % 165.30/165.06 [653]~E(x6531,x6532)+E(f661(x6533,x6534,x6531),f661(x6533,x6534,x6532)) % 165.30/165.06 [654]~E(x6541,x6542)+E(f268(x6541,x6543,x6544,x6545,x6546),f268(x6542,x6543,x6544,x6545,x6546)) % 165.30/165.06 [655]~E(x6551,x6552)+E(f268(x6553,x6551,x6554,x6555,x6556),f268(x6553,x6552,x6554,x6555,x6556)) % 165.30/165.06 [656]~E(x6561,x6562)+E(f268(x6563,x6564,x6561,x6565,x6566),f268(x6563,x6564,x6562,x6565,x6566)) % 165.30/165.06 [657]~E(x6571,x6572)+E(f268(x6573,x6574,x6575,x6571,x6576),f268(x6573,x6574,x6575,x6572,x6576)) % 165.30/165.06 [658]~E(x6581,x6582)+E(f268(x6583,x6584,x6585,x6586,x6581),f268(x6583,x6584,x6585,x6586,x6582)) % 165.30/165.06 [659]~E(x6591,x6592)+E(f662(x6591,x6593),f662(x6592,x6593)) % 165.30/165.06 [660]~E(x6601,x6602)+E(f662(x6603,x6601),f662(x6603,x6602)) % 165.30/165.06 [661]~E(x6611,x6612)+E(f12(x6611,x6613,x6614),f12(x6612,x6613,x6614)) % 165.30/165.06 [662]~E(x6621,x6622)+E(f12(x6623,x6621,x6624),f12(x6623,x6622,x6624)) % 165.30/165.06 [663]~E(x6631,x6632)+E(f12(x6633,x6634,x6631),f12(x6633,x6634,x6632)) % 165.30/165.06 [664]~E(x6641,x6642)+E(f559(x6641,x6643,x6644,x6645),f559(x6642,x6643,x6644,x6645)) % 165.30/165.06 [665]~E(x6651,x6652)+E(f559(x6653,x6651,x6654,x6655),f559(x6653,x6652,x6654,x6655)) % 165.30/165.06 [666]~E(x6661,x6662)+E(f559(x6663,x6664,x6661,x6665),f559(x6663,x6664,x6662,x6665)) % 165.30/165.06 [667]~E(x6671,x6672)+E(f559(x6673,x6674,x6675,x6671),f559(x6673,x6674,x6675,x6672)) % 165.30/165.06 [668]~E(x6681,x6682)+E(f732(x6681,x6683,x6684),f732(x6682,x6683,x6684)) % 165.30/165.06 [669]~E(x6691,x6692)+E(f732(x6693,x6691,x6694),f732(x6693,x6692,x6694)) % 165.30/165.06 [670]~E(x6701,x6702)+E(f732(x6703,x6704,x6701),f732(x6703,x6704,x6702)) % 165.30/165.06 [671]~E(x6711,x6712)+E(f668(x6711,x6713),f668(x6712,x6713)) % 165.30/165.06 [672]~E(x6721,x6722)+E(f668(x6723,x6721),f668(x6723,x6722)) % 165.30/165.06 [673]~E(x6731,x6732)+E(f165(x6731,x6733,x6734,x6735),f165(x6732,x6733,x6734,x6735)) % 165.30/165.06 [674]~E(x6741,x6742)+E(f165(x6743,x6741,x6744,x6745),f165(x6743,x6742,x6744,x6745)) % 165.30/165.06 [675]~E(x6751,x6752)+E(f165(x6753,x6754,x6751,x6755),f165(x6753,x6754,x6752,x6755)) % 165.30/165.06 [676]~E(x6761,x6762)+E(f165(x6763,x6764,x6765,x6761),f165(x6763,x6764,x6765,x6762)) % 165.30/165.06 [677]~E(x6771,x6772)+E(f625(x6771,x6773),f625(x6772,x6773)) % 165.30/165.06 [678]~E(x6781,x6782)+E(f625(x6783,x6781),f625(x6783,x6782)) % 165.30/165.06 [679]~E(x6791,x6792)+E(f157(x6791,x6793,x6794,x6795),f157(x6792,x6793,x6794,x6795)) % 165.30/165.06 [680]~E(x6801,x6802)+E(f157(x6803,x6801,x6804,x6805),f157(x6803,x6802,x6804,x6805)) % 165.30/165.06 [681]~E(x6811,x6812)+E(f157(x6813,x6814,x6811,x6815),f157(x6813,x6814,x6812,x6815)) % 165.30/165.06 [682]~E(x6821,x6822)+E(f157(x6823,x6824,x6825,x6821),f157(x6823,x6824,x6825,x6822)) % 165.30/165.06 [683]~E(x6831,x6832)+E(f150(x6831,x6833,x6834,x6835,x6836),f150(x6832,x6833,x6834,x6835,x6836)) % 165.30/165.06 [684]~E(x6841,x6842)+E(f150(x6843,x6841,x6844,x6845,x6846),f150(x6843,x6842,x6844,x6845,x6846)) % 165.30/165.06 [685]~E(x6851,x6852)+E(f150(x6853,x6854,x6851,x6855,x6856),f150(x6853,x6854,x6852,x6855,x6856)) % 165.30/165.06 [686]~E(x6861,x6862)+E(f150(x6863,x6864,x6865,x6861,x6866),f150(x6863,x6864,x6865,x6862,x6866)) % 165.30/165.06 [687]~E(x6871,x6872)+E(f150(x6873,x6874,x6875,x6876,x6871),f150(x6873,x6874,x6875,x6876,x6872)) % 165.30/165.06 [688]~E(x6881,x6882)+E(f537(x6881,x6883,x6884),f537(x6882,x6883,x6884)) % 165.30/165.06 [689]~E(x6891,x6892)+E(f537(x6893,x6891,x6894),f537(x6893,x6892,x6894)) % 165.30/165.06 [690]~E(x6901,x6902)+E(f537(x6903,x6904,x6901),f537(x6903,x6904,x6902)) % 165.30/165.06 [691]~E(x6911,x6912)+E(f643(x6911,x6913,x6914),f643(x6912,x6913,x6914)) % 165.30/165.06 [692]~E(x6921,x6922)+E(f643(x6923,x6921,x6924),f643(x6923,x6922,x6924)) % 165.30/165.06 [693]~E(x6931,x6932)+E(f643(x6933,x6934,x6931),f643(x6933,x6934,x6932)) % 165.30/165.06 [694]~E(x6941,x6942)+E(f757(x6941,x6943,x6944,x6945,x6946),f757(x6942,x6943,x6944,x6945,x6946)) % 165.30/165.06 [695]~E(x6951,x6952)+E(f757(x6953,x6951,x6954,x6955,x6956),f757(x6953,x6952,x6954,x6955,x6956)) % 165.30/165.06 [696]~E(x6961,x6962)+E(f757(x6963,x6964,x6961,x6965,x6966),f757(x6963,x6964,x6962,x6965,x6966)) % 165.30/165.06 [697]~E(x6971,x6972)+E(f757(x6973,x6974,x6975,x6971,x6976),f757(x6973,x6974,x6975,x6972,x6976)) % 165.30/165.06 [698]~E(x6981,x6982)+E(f757(x6983,x6984,x6985,x6986,x6981),f757(x6983,x6984,x6985,x6986,x6982)) % 165.30/165.06 [699]~E(x6991,x6992)+E(f677(x6991,x6993,x6994,x6995),f677(x6992,x6993,x6994,x6995)) % 165.30/165.06 [700]~E(x7001,x7002)+E(f677(x7003,x7001,x7004,x7005),f677(x7003,x7002,x7004,x7005)) % 165.30/165.06 [701]~E(x7011,x7012)+E(f677(x7013,x7014,x7011,x7015),f677(x7013,x7014,x7012,x7015)) % 165.30/165.06 [702]~E(x7021,x7022)+E(f677(x7023,x7024,x7025,x7021),f677(x7023,x7024,x7025,x7022)) % 165.30/165.06 [703]~E(x7031,x7032)+E(f460(x7031,x7033,x7034),f460(x7032,x7033,x7034)) % 165.30/165.06 [704]~E(x7041,x7042)+E(f460(x7043,x7041,x7044),f460(x7043,x7042,x7044)) % 165.30/165.06 [705]~E(x7051,x7052)+E(f460(x7053,x7054,x7051),f460(x7053,x7054,x7052)) % 165.30/165.06 [706]~E(x7061,x7062)+E(f670(x7061,x7063,x7064,x7065),f670(x7062,x7063,x7064,x7065)) % 165.30/165.06 [707]~E(x7071,x7072)+E(f670(x7073,x7071,x7074,x7075),f670(x7073,x7072,x7074,x7075)) % 165.30/165.06 [708]~E(x7081,x7082)+E(f670(x7083,x7084,x7081,x7085),f670(x7083,x7084,x7082,x7085)) % 165.30/165.06 [709]~E(x7091,x7092)+E(f670(x7093,x7094,x7095,x7091),f670(x7093,x7094,x7095,x7092)) % 165.30/165.06 [710]~E(x7101,x7102)+E(f526(x7101,x7103,x7104,x7105,x7106,x7107),f526(x7102,x7103,x7104,x7105,x7106,x7107)) % 165.30/165.06 [711]~E(x7111,x7112)+E(f526(x7113,x7111,x7114,x7115,x7116,x7117),f526(x7113,x7112,x7114,x7115,x7116,x7117)) % 165.30/165.06 [712]~E(x7121,x7122)+E(f526(x7123,x7124,x7121,x7125,x7126,x7127),f526(x7123,x7124,x7122,x7125,x7126,x7127)) % 165.30/165.06 [713]~E(x7131,x7132)+E(f526(x7133,x7134,x7135,x7131,x7136,x7137),f526(x7133,x7134,x7135,x7132,x7136,x7137)) % 165.30/165.06 [714]~E(x7141,x7142)+E(f526(x7143,x7144,x7145,x7146,x7141,x7147),f526(x7143,x7144,x7145,x7146,x7142,x7147)) % 165.30/165.06 [715]~E(x7151,x7152)+E(f526(x7153,x7154,x7155,x7156,x7157,x7151),f526(x7153,x7154,x7155,x7156,x7157,x7152)) % 165.30/165.06 [716]~E(x7161,x7162)+E(f319(x7161,x7163,x7164,x7165),f319(x7162,x7163,x7164,x7165)) % 165.30/165.06 [717]~E(x7171,x7172)+E(f319(x7173,x7171,x7174,x7175),f319(x7173,x7172,x7174,x7175)) % 165.30/165.06 [718]~E(x7181,x7182)+E(f319(x7183,x7184,x7181,x7185),f319(x7183,x7184,x7182,x7185)) % 165.30/165.06 [719]~E(x7191,x7192)+E(f319(x7193,x7194,x7195,x7191),f319(x7193,x7194,x7195,x7192)) % 165.30/165.06 [720]~E(x7201,x7202)+E(f367(x7201,x7203),f367(x7202,x7203)) % 165.30/165.06 [721]~E(x7211,x7212)+E(f367(x7213,x7211),f367(x7213,x7212)) % 165.30/165.06 [722]~E(x7221,x7222)+E(f824(x7221,x7223,x7224),f824(x7222,x7223,x7224)) % 165.30/165.06 [723]~E(x7231,x7232)+E(f824(x7233,x7231,x7234),f824(x7233,x7232,x7234)) % 165.30/165.06 [724]~E(x7241,x7242)+E(f824(x7243,x7244,x7241),f824(x7243,x7244,x7242)) % 165.30/165.06 [725]~E(x7251,x7252)+E(f814(x7251,x7253),f814(x7252,x7253)) % 165.30/165.06 [726]~E(x7261,x7262)+E(f814(x7263,x7261),f814(x7263,x7262)) % 165.30/165.06 [727]~E(x7271,x7272)+E(f363(x7271,x7273),f363(x7272,x7273)) % 165.30/165.06 [728]~E(x7281,x7282)+E(f363(x7283,x7281),f363(x7283,x7282)) % 165.30/165.06 [729]~E(x7291,x7292)+E(f453(x7291,x7293,x7294,x7295),f453(x7292,x7293,x7294,x7295)) % 165.30/165.06 [730]~E(x7301,x7302)+E(f453(x7303,x7301,x7304,x7305),f453(x7303,x7302,x7304,x7305)) % 165.30/165.06 [731]~E(x7311,x7312)+E(f453(x7313,x7314,x7311,x7315),f453(x7313,x7314,x7312,x7315)) % 165.30/165.06 [732]~E(x7321,x7322)+E(f453(x7323,x7324,x7325,x7321),f453(x7323,x7324,x7325,x7322)) % 165.30/165.06 [733]~E(x7331,x7332)+E(f294(x7331,x7333,x7334),f294(x7332,x7333,x7334)) % 165.30/165.06 [734]~E(x7341,x7342)+E(f294(x7343,x7341,x7344),f294(x7343,x7342,x7344)) % 165.30/165.06 [735]~E(x7351,x7352)+E(f294(x7353,x7354,x7351),f294(x7353,x7354,x7352)) % 165.30/165.06 [736]~E(x7361,x7362)+E(f709(x7361,x7363,x7364),f709(x7362,x7363,x7364)) % 165.30/165.06 [737]~E(x7371,x7372)+E(f709(x7373,x7371,x7374),f709(x7373,x7372,x7374)) % 165.30/165.06 [738]~E(x7381,x7382)+E(f709(x7383,x7384,x7381),f709(x7383,x7384,x7382)) % 165.30/165.06 [739]~E(x7391,x7392)+E(f347(x7391,x7393),f347(x7392,x7393)) % 165.30/165.06 [740]~E(x7401,x7402)+E(f347(x7403,x7401),f347(x7403,x7402)) % 165.30/165.06 [741]~E(x7411,x7412)+E(f288(x7411,x7413),f288(x7412,x7413)) % 165.30/165.06 [742]~E(x7421,x7422)+E(f288(x7423,x7421),f288(x7423,x7422)) % 165.30/165.06 [743]~E(x7431,x7432)+E(f477(x7431,x7433,x7434,x7435,x7436),f477(x7432,x7433,x7434,x7435,x7436)) % 165.30/165.06 [744]~E(x7441,x7442)+E(f477(x7443,x7441,x7444,x7445,x7446),f477(x7443,x7442,x7444,x7445,x7446)) % 165.30/165.06 [745]~E(x7451,x7452)+E(f477(x7453,x7454,x7451,x7455,x7456),f477(x7453,x7454,x7452,x7455,x7456)) % 165.30/165.06 [746]~E(x7461,x7462)+E(f477(x7463,x7464,x7465,x7461,x7466),f477(x7463,x7464,x7465,x7462,x7466)) % 165.30/165.06 [747]~E(x7471,x7472)+E(f477(x7473,x7474,x7475,x7476,x7471),f477(x7473,x7474,x7475,x7476,x7472)) % 165.30/165.06 [748]~E(x7481,x7482)+E(f513(x7481,x7483,x7484),f513(x7482,x7483,x7484)) % 165.30/165.06 [749]~E(x7491,x7492)+E(f513(x7493,x7491,x7494),f513(x7493,x7492,x7494)) % 165.30/165.06 [750]~E(x7501,x7502)+E(f513(x7503,x7504,x7501),f513(x7503,x7504,x7502)) % 165.30/165.06 [751]~E(x7511,x7512)+E(f745(x7511,x7513,x7514,x7515,x7516),f745(x7512,x7513,x7514,x7515,x7516)) % 165.30/165.06 [752]~E(x7521,x7522)+E(f745(x7523,x7521,x7524,x7525,x7526),f745(x7523,x7522,x7524,x7525,x7526)) % 165.30/165.06 [753]~E(x7531,x7532)+E(f745(x7533,x7534,x7531,x7535,x7536),f745(x7533,x7534,x7532,x7535,x7536)) % 165.30/165.06 [754]~E(x7541,x7542)+E(f745(x7543,x7544,x7545,x7541,x7546),f745(x7543,x7544,x7545,x7542,x7546)) % 165.30/165.06 [755]~E(x7551,x7552)+E(f745(x7553,x7554,x7555,x7556,x7551),f745(x7553,x7554,x7555,x7556,x7552)) % 165.30/165.06 [756]~E(x7561,x7562)+E(f527(x7561,x7563,x7564,x7565,x7566,x7567),f527(x7562,x7563,x7564,x7565,x7566,x7567)) % 165.30/165.06 [757]~E(x7571,x7572)+E(f527(x7573,x7571,x7574,x7575,x7576,x7577),f527(x7573,x7572,x7574,x7575,x7576,x7577)) % 165.30/165.06 [758]~E(x7581,x7582)+E(f527(x7583,x7584,x7581,x7585,x7586,x7587),f527(x7583,x7584,x7582,x7585,x7586,x7587)) % 165.30/165.06 [759]~E(x7591,x7592)+E(f527(x7593,x7594,x7595,x7591,x7596,x7597),f527(x7593,x7594,x7595,x7592,x7596,x7597)) % 165.30/165.06 [760]~E(x7601,x7602)+E(f527(x7603,x7604,x7605,x7606,x7601,x7607),f527(x7603,x7604,x7605,x7606,x7602,x7607)) % 165.30/165.06 [761]~E(x7611,x7612)+E(f527(x7613,x7614,x7615,x7616,x7617,x7611),f527(x7613,x7614,x7615,x7616,x7617,x7612)) % 165.30/165.06 [762]~E(x7621,x7622)+E(f641(x7621,x7623,x7624),f641(x7622,x7623,x7624)) % 165.30/165.06 [763]~E(x7631,x7632)+E(f641(x7633,x7631,x7634),f641(x7633,x7632,x7634)) % 165.30/165.06 [764]~E(x7641,x7642)+E(f641(x7643,x7644,x7641),f641(x7643,x7644,x7642)) % 165.30/165.06 [765]~E(x7651,x7652)+E(f30(x7651,x7653,x7654),f30(x7652,x7653,x7654)) % 165.30/165.06 [766]~E(x7661,x7662)+E(f30(x7663,x7661,x7664),f30(x7663,x7662,x7664)) % 165.30/165.06 [767]~E(x7671,x7672)+E(f30(x7673,x7674,x7671),f30(x7673,x7674,x7672)) % 165.30/165.06 [768]~E(x7681,x7682)+E(f521(x7681,x7683),f521(x7682,x7683)) % 165.30/165.06 [769]~E(x7691,x7692)+E(f521(x7693,x7691),f521(x7693,x7692)) % 165.30/165.06 [770]~E(x7701,x7702)+E(f508(x7701,x7703,x7704,x7705),f508(x7702,x7703,x7704,x7705)) % 165.30/165.06 [771]~E(x7711,x7712)+E(f508(x7713,x7711,x7714,x7715),f508(x7713,x7712,x7714,x7715)) % 165.30/165.06 [772]~E(x7721,x7722)+E(f508(x7723,x7724,x7721,x7725),f508(x7723,x7724,x7722,x7725)) % 165.30/165.06 [773]~E(x7731,x7732)+E(f508(x7733,x7734,x7735,x7731),f508(x7733,x7734,x7735,x7732)) % 165.30/165.06 [774]~E(x7741,x7742)+E(f727(x7741,x7743,x7744,x7745,x7746,x7747,x7748,x7749),f727(x7742,x7743,x7744,x7745,x7746,x7747,x7748,x7749)) % 165.30/165.06 [775]~E(x7751,x7752)+E(f727(x7753,x7751,x7754,x7755,x7756,x7757,x7758,x7759),f727(x7753,x7752,x7754,x7755,x7756,x7757,x7758,x7759)) % 165.30/165.06 [776]~E(x7761,x7762)+E(f727(x7763,x7764,x7761,x7765,x7766,x7767,x7768,x7769),f727(x7763,x7764,x7762,x7765,x7766,x7767,x7768,x7769)) % 165.30/165.06 [777]~E(x7771,x7772)+E(f727(x7773,x7774,x7775,x7771,x7776,x7777,x7778,x7779),f727(x7773,x7774,x7775,x7772,x7776,x7777,x7778,x7779)) % 165.30/165.06 [778]~E(x7781,x7782)+E(f727(x7783,x7784,x7785,x7786,x7781,x7787,x7788,x7789),f727(x7783,x7784,x7785,x7786,x7782,x7787,x7788,x7789)) % 165.30/165.06 [779]~E(x7791,x7792)+E(f727(x7793,x7794,x7795,x7796,x7797,x7791,x7798,x7799),f727(x7793,x7794,x7795,x7796,x7797,x7792,x7798,x7799)) % 165.30/165.06 [780]~E(x7801,x7802)+E(f727(x7803,x7804,x7805,x7806,x7807,x7808,x7801,x7809),f727(x7803,x7804,x7805,x7806,x7807,x7808,x7802,x7809)) % 165.30/165.06 [781]~E(x7811,x7812)+E(f727(x7813,x7814,x7815,x7816,x7817,x7818,x7819,x7811),f727(x7813,x7814,x7815,x7816,x7817,x7818,x7819,x7812)) % 165.30/165.06 [782]~E(x7821,x7822)+E(f156(x7821,x7823,x7824),f156(x7822,x7823,x7824)) % 165.30/165.06 [783]~E(x7831,x7832)+E(f156(x7833,x7831,x7834),f156(x7833,x7832,x7834)) % 165.30/165.06 [784]~E(x7841,x7842)+E(f156(x7843,x7844,x7841),f156(x7843,x7844,x7842)) % 165.30/165.06 [785]~E(x7851,x7852)+E(f519(x7851),f519(x7852)) % 165.30/165.06 [786]~E(x7861,x7862)+E(f261(x7861,x7863,x7864),f261(x7862,x7863,x7864)) % 165.30/165.06 [787]~E(x7871,x7872)+E(f261(x7873,x7871,x7874),f261(x7873,x7872,x7874)) % 165.30/165.06 [788]~E(x7881,x7882)+E(f261(x7883,x7884,x7881),f261(x7883,x7884,x7882)) % 165.30/165.06 [789]~E(x7891,x7892)+E(f423(x7891,x7893,x7894),f423(x7892,x7893,x7894)) % 165.30/165.06 [790]~E(x7901,x7902)+E(f423(x7903,x7901,x7904),f423(x7903,x7902,x7904)) % 165.30/165.06 [791]~E(x7911,x7912)+E(f423(x7913,x7914,x7911),f423(x7913,x7914,x7912)) % 165.30/165.06 [792]~E(x7921,x7922)+E(f407(x7921,x7923,x7924,x7925),f407(x7922,x7923,x7924,x7925)) % 165.30/165.06 [793]~E(x7931,x7932)+E(f407(x7933,x7931,x7934,x7935),f407(x7933,x7932,x7934,x7935)) % 165.30/165.06 [794]~E(x7941,x7942)+E(f407(x7943,x7944,x7941,x7945),f407(x7943,x7944,x7942,x7945)) % 165.30/165.06 [795]~E(x7951,x7952)+E(f407(x7953,x7954,x7955,x7951),f407(x7953,x7954,x7955,x7952)) % 165.30/165.06 [796]~E(x7961,x7962)+E(f669(x7961,x7963,x7964,x7965),f669(x7962,x7963,x7964,x7965)) % 165.30/165.06 [797]~E(x7971,x7972)+E(f669(x7973,x7971,x7974,x7975),f669(x7973,x7972,x7974,x7975)) % 165.30/165.06 [798]~E(x7981,x7982)+E(f669(x7983,x7984,x7981,x7985),f669(x7983,x7984,x7982,x7985)) % 165.30/165.06 [799]~E(x7991,x7992)+E(f669(x7993,x7994,x7995,x7991),f669(x7993,x7994,x7995,x7992)) % 165.30/165.06 [800]~E(x8001,x8002)+E(f517(x8001,x8003,x8004),f517(x8002,x8003,x8004)) % 165.30/165.06 [801]~E(x8011,x8012)+E(f517(x8013,x8011,x8014),f517(x8013,x8012,x8014)) % 165.30/165.06 [802]~E(x8021,x8022)+E(f517(x8023,x8024,x8021),f517(x8023,x8024,x8022)) % 165.30/165.06 [803]~E(x8031,x8032)+E(f813(x8031,x8033,x8034),f813(x8032,x8033,x8034)) % 165.30/165.06 [804]~E(x8041,x8042)+E(f813(x8043,x8041,x8044),f813(x8043,x8042,x8044)) % 165.30/165.06 [805]~E(x8051,x8052)+E(f813(x8053,x8054,x8051),f813(x8053,x8054,x8052)) % 165.30/165.06 [806]~E(x8061,x8062)+E(f263(x8061,x8063),f263(x8062,x8063)) % 165.30/165.06 [807]~E(x8071,x8072)+E(f263(x8073,x8071),f263(x8073,x8072)) % 165.30/165.06 [808]~E(x8081,x8082)+E(f366(x8081,x8083),f366(x8082,x8083)) % 165.30/165.06 [809]~E(x8091,x8092)+E(f366(x8093,x8091),f366(x8093,x8092)) % 165.30/165.06 [810]~E(x8101,x8102)+E(f729(x8101,x8103,x8104,x8105,x8106,x8107,x8108,x8109),f729(x8102,x8103,x8104,x8105,x8106,x8107,x8108,x8109)) % 165.30/165.06 [811]~E(x8111,x8112)+E(f729(x8113,x8111,x8114,x8115,x8116,x8117,x8118,x8119),f729(x8113,x8112,x8114,x8115,x8116,x8117,x8118,x8119)) % 165.30/165.06 [812]~E(x8121,x8122)+E(f729(x8123,x8124,x8121,x8125,x8126,x8127,x8128,x8129),f729(x8123,x8124,x8122,x8125,x8126,x8127,x8128,x8129)) % 165.30/165.06 [813]~E(x8131,x8132)+E(f729(x8133,x8134,x8135,x8131,x8136,x8137,x8138,x8139),f729(x8133,x8134,x8135,x8132,x8136,x8137,x8138,x8139)) % 165.30/165.06 [814]~E(x8141,x8142)+E(f729(x8143,x8144,x8145,x8146,x8141,x8147,x8148,x8149),f729(x8143,x8144,x8145,x8146,x8142,x8147,x8148,x8149)) % 165.30/165.06 [815]~E(x8151,x8152)+E(f729(x8153,x8154,x8155,x8156,x8157,x8151,x8158,x8159),f729(x8153,x8154,x8155,x8156,x8157,x8152,x8158,x8159)) % 165.30/165.06 [816]~E(x8161,x8162)+E(f729(x8163,x8164,x8165,x8166,x8167,x8168,x8161,x8169),f729(x8163,x8164,x8165,x8166,x8167,x8168,x8162,x8169)) % 165.30/165.06 [817]~E(x8171,x8172)+E(f729(x8173,x8174,x8175,x8176,x8177,x8178,x8179,x8171),f729(x8173,x8174,x8175,x8176,x8177,x8178,x8179,x8172)) % 165.30/165.06 [818]~E(x8181,x8182)+E(f450(x8181,x8183),f450(x8182,x8183)) % 165.30/165.06 [819]~E(x8191,x8192)+E(f450(x8193,x8191),f450(x8193,x8192)) % 165.30/165.06 [820]~E(x8201,x8202)+E(f512(x8201,x8203,x8204),f512(x8202,x8203,x8204)) % 165.30/165.06 [821]~E(x8211,x8212)+E(f512(x8213,x8211,x8214),f512(x8213,x8212,x8214)) % 165.30/165.06 [822]~E(x8221,x8222)+E(f512(x8223,x8224,x8221),f512(x8223,x8224,x8222)) % 165.30/165.06 [823]~E(x8231,x8232)+E(f46(x8231,x8233),f46(x8232,x8233)) % 165.30/165.06 [824]~E(x8241,x8242)+E(f46(x8243,x8241),f46(x8243,x8242)) % 165.30/165.06 [825]~E(x8251,x8252)+E(f58(x8251),f58(x8252)) % 165.30/165.06 [826]~E(x8261,x8262)+E(f127(x8261),f127(x8262)) % 165.30/165.06 [827]~E(x8271,x8272)+E(f249(x8271,x8273),f249(x8272,x8273)) % 165.30/165.06 [828]~E(x8281,x8282)+E(f249(x8283,x8281),f249(x8283,x8282)) % 165.30/165.06 [829]~E(x8291,x8292)+E(f726(x8291,x8293,x8294,x8295),f726(x8292,x8293,x8294,x8295)) % 165.30/165.06 [830]~E(x8301,x8302)+E(f726(x8303,x8301,x8304,x8305),f726(x8303,x8302,x8304,x8305)) % 165.30/165.06 [831]~E(x8311,x8312)+E(f726(x8313,x8314,x8311,x8315),f726(x8313,x8314,x8312,x8315)) % 165.30/165.06 [832]~E(x8321,x8322)+E(f726(x8323,x8324,x8325,x8321),f726(x8323,x8324,x8325,x8322)) % 165.30/165.06 [833]~E(x8331,x8332)+E(f851(x8331,x8333,x8334),f851(x8332,x8333,x8334)) % 165.30/165.06 [834]~E(x8341,x8342)+E(f851(x8343,x8341,x8344),f851(x8343,x8342,x8344)) % 165.30/165.06 [835]~E(x8351,x8352)+E(f851(x8353,x8354,x8351),f851(x8353,x8354,x8352)) % 165.30/165.06 [836]~E(x8361,x8362)+E(f724(x8361,x8363,x8364),f724(x8362,x8363,x8364)) % 165.30/165.06 [837]~E(x8371,x8372)+E(f724(x8373,x8371,x8374),f724(x8373,x8372,x8374)) % 165.30/165.06 [838]~E(x8381,x8382)+E(f724(x8383,x8384,x8381),f724(x8383,x8384,x8382)) % 165.30/165.06 [839]~E(x8391,x8392)+E(f664(x8391,x8393),f664(x8392,x8393)) % 165.30/165.06 [840]~E(x8401,x8402)+E(f664(x8403,x8401),f664(x8403,x8402)) % 165.30/165.06 [841]~E(x8411,x8412)+E(f638(x8411,x8413,x8414),f638(x8412,x8413,x8414)) % 165.30/165.06 [842]~E(x8421,x8422)+E(f638(x8423,x8421,x8424),f638(x8423,x8422,x8424)) % 165.30/165.06 [843]~E(x8431,x8432)+E(f638(x8433,x8434,x8431),f638(x8433,x8434,x8432)) % 165.30/165.06 [844]~E(x8441,x8442)+E(f429(x8441,x8443,x8444),f429(x8442,x8443,x8444)) % 165.30/165.06 [845]~E(x8451,x8452)+E(f429(x8453,x8451,x8454),f429(x8453,x8452,x8454)) % 165.30/165.06 [846]~E(x8461,x8462)+E(f429(x8463,x8464,x8461),f429(x8463,x8464,x8462)) % 165.30/165.06 [847]~E(x8471,x8472)+E(f50(x8471,x8473),f50(x8472,x8473)) % 165.30/165.06 [848]~E(x8481,x8482)+E(f50(x8483,x8481),f50(x8483,x8482)) % 165.30/165.06 [849]~E(x8491,x8492)+E(f548(x8491,x8493,x8494),f548(x8492,x8493,x8494)) % 165.30/165.06 [850]~E(x8501,x8502)+E(f548(x8503,x8501,x8504),f548(x8503,x8502,x8504)) % 165.30/165.06 [851]~E(x8511,x8512)+E(f548(x8513,x8514,x8511),f548(x8513,x8514,x8512)) % 165.30/165.06 [852]~E(x8521,x8522)+E(f242(x8521,x8523,x8524,x8525,x8526),f242(x8522,x8523,x8524,x8525,x8526)) % 165.30/165.06 [853]~E(x8531,x8532)+E(f242(x8533,x8531,x8534,x8535,x8536),f242(x8533,x8532,x8534,x8535,x8536)) % 165.30/165.06 [854]~E(x8541,x8542)+E(f242(x8543,x8544,x8541,x8545,x8546),f242(x8543,x8544,x8542,x8545,x8546)) % 165.30/165.06 [855]~E(x8551,x8552)+E(f242(x8553,x8554,x8555,x8551,x8556),f242(x8553,x8554,x8555,x8552,x8556)) % 165.30/165.06 [856]~E(x8561,x8562)+E(f242(x8563,x8564,x8565,x8566,x8561),f242(x8563,x8564,x8565,x8566,x8562)) % 165.30/165.06 [857]~E(x8571,x8572)+E(f543(x8571,x8573,x8574,x8575),f543(x8572,x8573,x8574,x8575)) % 165.30/165.06 [858]~E(x8581,x8582)+E(f543(x8583,x8581,x8584,x8585),f543(x8583,x8582,x8584,x8585)) % 165.30/165.06 [859]~E(x8591,x8592)+E(f543(x8593,x8594,x8591,x8595),f543(x8593,x8594,x8592,x8595)) % 165.30/165.06 [860]~E(x8601,x8602)+E(f543(x8603,x8604,x8605,x8601),f543(x8603,x8604,x8605,x8602)) % 165.30/165.06 [861]~E(x8611,x8612)+E(f133(x8611,x8613),f133(x8612,x8613)) % 165.30/165.06 [862]~E(x8621,x8622)+E(f133(x8623,x8621),f133(x8623,x8622)) % 165.30/165.06 [863]~E(x8631,x8632)+E(f832(x8631,x8633,x8634,x8635,x8636),f832(x8632,x8633,x8634,x8635,x8636)) % 165.30/165.06 [864]~E(x8641,x8642)+E(f832(x8643,x8641,x8644,x8645,x8646),f832(x8643,x8642,x8644,x8645,x8646)) % 165.30/165.06 [865]~E(x8651,x8652)+E(f832(x8653,x8654,x8651,x8655,x8656),f832(x8653,x8654,x8652,x8655,x8656)) % 165.30/165.06 [866]~E(x8661,x8662)+E(f832(x8663,x8664,x8665,x8661,x8666),f832(x8663,x8664,x8665,x8662,x8666)) % 165.30/165.06 [867]~E(x8671,x8672)+E(f832(x8673,x8674,x8675,x8676,x8671),f832(x8673,x8674,x8675,x8676,x8672)) % 165.30/165.06 [868]~E(x8681,x8682)+E(f361(x8681),f361(x8682)) % 165.30/165.06 [869]~E(x8691,x8692)+E(f616(x8691,x8693),f616(x8692,x8693)) % 165.30/165.06 [870]~E(x8701,x8702)+E(f616(x8703,x8701),f616(x8703,x8702)) % 165.30/165.06 [871]~E(x8711,x8712)+E(f176(x8711,x8713,x8714),f176(x8712,x8713,x8714)) % 165.30/165.06 [872]~E(x8721,x8722)+E(f176(x8723,x8721,x8724),f176(x8723,x8722,x8724)) % 165.30/165.06 [873]~E(x8731,x8732)+E(f176(x8733,x8734,x8731),f176(x8733,x8734,x8732)) % 165.30/165.06 [874]~E(x8741,x8742)+E(f392(x8741,x8743,x8744,x8745),f392(x8742,x8743,x8744,x8745)) % 165.30/165.06 [875]~E(x8751,x8752)+E(f392(x8753,x8751,x8754,x8755),f392(x8753,x8752,x8754,x8755)) % 165.30/165.06 [876]~E(x8761,x8762)+E(f392(x8763,x8764,x8761,x8765),f392(x8763,x8764,x8762,x8765)) % 165.30/165.06 [877]~E(x8771,x8772)+E(f392(x8773,x8774,x8775,x8771),f392(x8773,x8774,x8775,x8772)) % 165.30/165.06 [878]~E(x8781,x8782)+E(f258(x8781,x8783,x8784),f258(x8782,x8783,x8784)) % 165.30/165.06 [879]~E(x8791,x8792)+E(f258(x8793,x8791,x8794),f258(x8793,x8792,x8794)) % 165.30/165.06 [880]~E(x8801,x8802)+E(f258(x8803,x8804,x8801),f258(x8803,x8804,x8802)) % 165.30/165.06 [881]~E(x8811,x8812)+E(f405(x8811,x8813,x8814,x8815),f405(x8812,x8813,x8814,x8815)) % 165.30/165.06 [882]~E(x8821,x8822)+E(f405(x8823,x8821,x8824,x8825),f405(x8823,x8822,x8824,x8825)) % 165.30/165.06 [883]~E(x8831,x8832)+E(f405(x8833,x8834,x8831,x8835),f405(x8833,x8834,x8832,x8835)) % 165.30/165.06 [884]~E(x8841,x8842)+E(f405(x8843,x8844,x8845,x8841),f405(x8843,x8844,x8845,x8842)) % 165.30/165.06 [885]~E(x8851,x8852)+E(f238(x8851,x8853,x8854,x8855),f238(x8852,x8853,x8854,x8855)) % 165.30/165.06 [886]~E(x8861,x8862)+E(f238(x8863,x8861,x8864,x8865),f238(x8863,x8862,x8864,x8865)) % 165.30/165.06 [887]~E(x8871,x8872)+E(f238(x8873,x8874,x8871,x8875),f238(x8873,x8874,x8872,x8875)) % 165.30/165.06 [888]~E(x8881,x8882)+E(f238(x8883,x8884,x8885,x8881),f238(x8883,x8884,x8885,x8882)) % 165.30/165.06 [889]~E(x8891,x8892)+E(f584(x8891,x8893,x8894,x8895,x8896),f584(x8892,x8893,x8894,x8895,x8896)) % 165.30/165.06 [890]~E(x8901,x8902)+E(f584(x8903,x8901,x8904,x8905,x8906),f584(x8903,x8902,x8904,x8905,x8906)) % 165.30/165.06 [891]~E(x8911,x8912)+E(f584(x8913,x8914,x8911,x8915,x8916),f584(x8913,x8914,x8912,x8915,x8916)) % 165.30/165.06 [892]~E(x8921,x8922)+E(f584(x8923,x8924,x8925,x8921,x8926),f584(x8923,x8924,x8925,x8922,x8926)) % 165.30/165.06 [893]~E(x8931,x8932)+E(f584(x8933,x8934,x8935,x8936,x8931),f584(x8933,x8934,x8935,x8936,x8932)) % 165.30/165.06 [894]~E(x8941,x8942)+E(f220(x8941,x8943,x8944,x8945,x8946,x8947,x8948),f220(x8942,x8943,x8944,x8945,x8946,x8947,x8948)) % 165.30/165.06 [895]~E(x8951,x8952)+E(f220(x8953,x8951,x8954,x8955,x8956,x8957,x8958),f220(x8953,x8952,x8954,x8955,x8956,x8957,x8958)) % 165.30/165.06 [896]~E(x8961,x8962)+E(f220(x8963,x8964,x8961,x8965,x8966,x8967,x8968),f220(x8963,x8964,x8962,x8965,x8966,x8967,x8968)) % 165.30/165.06 [897]~E(x8971,x8972)+E(f220(x8973,x8974,x8975,x8971,x8976,x8977,x8978),f220(x8973,x8974,x8975,x8972,x8976,x8977,x8978)) % 165.30/165.06 [898]~E(x8981,x8982)+E(f220(x8983,x8984,x8985,x8986,x8981,x8987,x8988),f220(x8983,x8984,x8985,x8986,x8982,x8987,x8988)) % 165.30/165.06 [899]~E(x8991,x8992)+E(f220(x8993,x8994,x8995,x8996,x8997,x8991,x8998),f220(x8993,x8994,x8995,x8996,x8997,x8992,x8998)) % 165.30/165.06 [900]~E(x9001,x9002)+E(f220(x9003,x9004,x9005,x9006,x9007,x9008,x9001),f220(x9003,x9004,x9005,x9006,x9007,x9008,x9002)) % 165.30/165.06 [901]~E(x9011,x9012)+E(f742(x9011,x9013),f742(x9012,x9013)) % 165.30/165.06 [902]~E(x9021,x9022)+E(f742(x9023,x9021),f742(x9023,x9022)) % 165.30/165.06 [903]~E(x9031,x9032)+E(f188(x9031,x9033,x9034),f188(x9032,x9033,x9034)) % 165.30/165.06 [904]~E(x9041,x9042)+E(f188(x9043,x9041,x9044),f188(x9043,x9042,x9044)) % 165.30/165.06 [905]~E(x9051,x9052)+E(f188(x9053,x9054,x9051),f188(x9053,x9054,x9052)) % 165.30/165.06 [906]~E(x9061,x9062)+E(f767(x9061,x9063,x9064,x9065),f767(x9062,x9063,x9064,x9065)) % 165.30/165.06 [907]~E(x9071,x9072)+E(f767(x9073,x9071,x9074,x9075),f767(x9073,x9072,x9074,x9075)) % 165.30/165.06 [908]~E(x9081,x9082)+E(f767(x9083,x9084,x9081,x9085),f767(x9083,x9084,x9082,x9085)) % 165.30/165.06 [909]~E(x9091,x9092)+E(f767(x9093,x9094,x9095,x9091),f767(x9093,x9094,x9095,x9092)) % 165.30/165.06 [910]~E(x9101,x9102)+E(f539(x9101,x9103,x9104,x9105,x9106),f539(x9102,x9103,x9104,x9105,x9106)) % 165.30/165.06 [911]~E(x9111,x9112)+E(f539(x9113,x9111,x9114,x9115,x9116),f539(x9113,x9112,x9114,x9115,x9116)) % 165.30/165.06 [912]~E(x9121,x9122)+E(f539(x9123,x9124,x9121,x9125,x9126),f539(x9123,x9124,x9122,x9125,x9126)) % 165.30/165.06 [913]~E(x9131,x9132)+E(f539(x9133,x9134,x9135,x9131,x9136),f539(x9133,x9134,x9135,x9132,x9136)) % 165.30/165.06 [914]~E(x9141,x9142)+E(f539(x9143,x9144,x9145,x9146,x9141),f539(x9143,x9144,x9145,x9146,x9142)) % 165.30/165.06 [915]~E(x9151,x9152)+E(f756(x9151,x9153,x9154,x9155,x9156),f756(x9152,x9153,x9154,x9155,x9156)) % 165.30/165.06 [916]~E(x9161,x9162)+E(f756(x9163,x9161,x9164,x9165,x9166),f756(x9163,x9162,x9164,x9165,x9166)) % 165.30/165.06 [917]~E(x9171,x9172)+E(f756(x9173,x9174,x9171,x9175,x9176),f756(x9173,x9174,x9172,x9175,x9176)) % 165.30/165.06 [918]~E(x9181,x9182)+E(f756(x9183,x9184,x9185,x9181,x9186),f756(x9183,x9184,x9185,x9182,x9186)) % 165.30/165.06 [919]~E(x9191,x9192)+E(f756(x9193,x9194,x9195,x9196,x9191),f756(x9193,x9194,x9195,x9196,x9192)) % 165.30/165.06 [920]~E(x9201,x9202)+E(f260(x9201,x9203),f260(x9202,x9203)) % 165.30/165.06 [921]~E(x9211,x9212)+E(f260(x9213,x9211),f260(x9213,x9212)) % 165.30/165.06 [922]~E(x9221,x9222)+E(f507(x9221,x9223,x9224),f507(x9222,x9223,x9224)) % 165.30/165.06 [923]~E(x9231,x9232)+E(f507(x9233,x9231,x9234),f507(x9233,x9232,x9234)) % 165.30/165.06 [924]~E(x9241,x9242)+E(f507(x9243,x9244,x9241),f507(x9243,x9244,x9242)) % 165.30/165.06 [925]~E(x9251,x9252)+E(f681(x9251,x9253),f681(x9252,x9253)) % 165.30/165.06 [926]~E(x9261,x9262)+E(f681(x9263,x9261),f681(x9263,x9262)) % 165.30/165.06 [927]~E(x9271,x9272)+E(f607(x9271,x9273),f607(x9272,x9273)) % 165.30/165.06 [928]~E(x9281,x9282)+E(f607(x9283,x9281),f607(x9283,x9282)) % 165.30/165.06 [929]~E(x9291,x9292)+E(f200(x9291,x9293),f200(x9292,x9293)) % 165.30/165.06 [930]~E(x9301,x9302)+E(f200(x9303,x9301),f200(x9303,x9302)) % 165.30/165.06 [931]~E(x9311,x9312)+E(f317(x9311),f317(x9312)) % 165.30/165.06 [932]~E(x9321,x9322)+E(f122(x9321,x9323),f122(x9322,x9323)) % 165.30/165.06 [933]~E(x9331,x9332)+E(f122(x9333,x9331),f122(x9333,x9332)) % 165.30/165.06 [934]~E(x9341,x9342)+E(f839(x9341,x9343),f839(x9342,x9343)) % 165.30/165.06 [935]~E(x9351,x9352)+E(f839(x9353,x9351),f839(x9353,x9352)) % 165.30/165.06 [936]~E(x9361,x9362)+E(f371(x9361,x9363,x9364),f371(x9362,x9363,x9364)) % 165.30/165.06 [937]~E(x9371,x9372)+E(f371(x9373,x9371,x9374),f371(x9373,x9372,x9374)) % 165.30/165.06 [938]~E(x9381,x9382)+E(f371(x9383,x9384,x9381),f371(x9383,x9384,x9382)) % 165.30/165.06 [939]~E(x9391,x9392)+E(f313(x9391,x9393),f313(x9392,x9393)) % 165.30/165.06 [940]~E(x9401,x9402)+E(f313(x9403,x9401),f313(x9403,x9402)) % 165.30/165.06 [941]~E(x9411,x9412)+E(f202(x9411,x9413),f202(x9412,x9413)) % 165.30/165.06 [942]~E(x9421,x9422)+E(f202(x9423,x9421),f202(x9423,x9422)) % 165.30/165.06 [943]~E(x9431,x9432)+E(f464(x9431,x9433,x9434,x9435),f464(x9432,x9433,x9434,x9435)) % 165.30/165.06 [944]~E(x9441,x9442)+E(f464(x9443,x9441,x9444,x9445),f464(x9443,x9442,x9444,x9445)) % 165.30/165.06 [945]~E(x9451,x9452)+E(f464(x9453,x9454,x9451,x9455),f464(x9453,x9454,x9452,x9455)) % 165.30/165.06 [946]~E(x9461,x9462)+E(f464(x9463,x9464,x9465,x9461),f464(x9463,x9464,x9465,x9462)) % 165.30/165.06 [947]~E(x9471,x9472)+E(f582(x9471,x9473,x9474,x9475),f582(x9472,x9473,x9474,x9475)) % 165.30/165.06 [948]~E(x9481,x9482)+E(f582(x9483,x9481,x9484,x9485),f582(x9483,x9482,x9484,x9485)) % 165.30/165.06 [949]~E(x9491,x9492)+E(f582(x9493,x9494,x9491,x9495),f582(x9493,x9494,x9492,x9495)) % 165.30/165.06 [950]~E(x9501,x9502)+E(f582(x9503,x9504,x9505,x9501),f582(x9503,x9504,x9505,x9502)) % 165.30/165.06 [951]~E(x9511,x9512)+E(f458(x9511,x9513,x9514),f458(x9512,x9513,x9514)) % 165.30/165.06 [952]~E(x9521,x9522)+E(f458(x9523,x9521,x9524),f458(x9523,x9522,x9524)) % 165.30/165.06 [953]~E(x9531,x9532)+E(f458(x9533,x9534,x9531),f458(x9533,x9534,x9532)) % 165.30/165.06 [954]~E(x9541,x9542)+E(f377(x9541,x9543,x9544,x9545),f377(x9542,x9543,x9544,x9545)) % 165.30/165.06 [955]~E(x9551,x9552)+E(f377(x9553,x9551,x9554,x9555),f377(x9553,x9552,x9554,x9555)) % 165.30/165.06 [956]~E(x9561,x9562)+E(f377(x9563,x9564,x9561,x9565),f377(x9563,x9564,x9562,x9565)) % 165.30/165.06 [957]~E(x9571,x9572)+E(f377(x9573,x9574,x9575,x9571),f377(x9573,x9574,x9575,x9572)) % 165.30/165.06 [958]~E(x9581,x9582)+E(f589(x9581,x9583,x9584,x9585),f589(x9582,x9583,x9584,x9585)) % 165.30/165.06 [959]~E(x9591,x9592)+E(f589(x9593,x9591,x9594,x9595),f589(x9593,x9592,x9594,x9595)) % 165.30/165.06 [960]~E(x9601,x9602)+E(f589(x9603,x9604,x9601,x9605),f589(x9603,x9604,x9602,x9605)) % 165.30/165.06 [961]~E(x9611,x9612)+E(f589(x9613,x9614,x9615,x9611),f589(x9613,x9614,x9615,x9612)) % 165.30/165.06 [962]~E(x9621,x9622)+E(f430(x9621,x9623,x9624),f430(x9622,x9623,x9624)) % 165.30/165.06 [963]~E(x9631,x9632)+E(f430(x9633,x9631,x9634),f430(x9633,x9632,x9634)) % 165.30/165.06 [964]~E(x9641,x9642)+E(f430(x9643,x9644,x9641),f430(x9643,x9644,x9642)) % 165.30/165.06 [965]~E(x9651,x9652)+E(f849(x9651,x9653,x9654),f849(x9652,x9653,x9654)) % 165.30/165.06 [966]~E(x9661,x9662)+E(f849(x9663,x9661,x9664),f849(x9663,x9662,x9664)) % 165.30/165.06 [967]~E(x9671,x9672)+E(f849(x9673,x9674,x9671),f849(x9673,x9674,x9672)) % 165.30/165.06 [968]~E(x9681,x9682)+E(f564(x9681,x9683,x9684,x9685,x9686),f564(x9682,x9683,x9684,x9685,x9686)) % 165.30/165.06 [969]~E(x9691,x9692)+E(f564(x9693,x9691,x9694,x9695,x9696),f564(x9693,x9692,x9694,x9695,x9696)) % 165.30/165.06 [970]~E(x9701,x9702)+E(f564(x9703,x9704,x9701,x9705,x9706),f564(x9703,x9704,x9702,x9705,x9706)) % 165.30/165.06 [971]~E(x9711,x9712)+E(f564(x9713,x9714,x9715,x9711,x9716),f564(x9713,x9714,x9715,x9712,x9716)) % 165.30/165.06 [972]~E(x9721,x9722)+E(f564(x9723,x9724,x9725,x9726,x9721),f564(x9723,x9724,x9725,x9726,x9722)) % 165.30/165.06 [973]~E(x9731,x9732)+E(f799(x9731,x9733,x9734,x9735),f799(x9732,x9733,x9734,x9735)) % 165.30/165.06 [974]~E(x9741,x9742)+E(f799(x9743,x9741,x9744,x9745),f799(x9743,x9742,x9744,x9745)) % 165.30/165.06 [975]~E(x9751,x9752)+E(f799(x9753,x9754,x9751,x9755),f799(x9753,x9754,x9752,x9755)) % 165.30/165.06 [976]~E(x9761,x9762)+E(f799(x9763,x9764,x9765,x9761),f799(x9763,x9764,x9765,x9762)) % 165.30/165.06 [977]~E(x9771,x9772)+E(f676(x9771,x9773,x9774,x9775),f676(x9772,x9773,x9774,x9775)) % 165.30/165.06 [978]~E(x9781,x9782)+E(f676(x9783,x9781,x9784,x9785),f676(x9783,x9782,x9784,x9785)) % 165.30/165.06 [979]~E(x9791,x9792)+E(f676(x9793,x9794,x9791,x9795),f676(x9793,x9794,x9792,x9795)) % 165.30/165.06 [980]~E(x9801,x9802)+E(f676(x9803,x9804,x9805,x9801),f676(x9803,x9804,x9805,x9802)) % 165.30/165.06 [981]~E(x9811,x9812)+E(f833(x9811,x9813,x9814,x9815,x9816,x9817,x9818),f833(x9812,x9813,x9814,x9815,x9816,x9817,x9818)) % 165.30/165.06 [982]~E(x9821,x9822)+E(f833(x9823,x9821,x9824,x9825,x9826,x9827,x9828),f833(x9823,x9822,x9824,x9825,x9826,x9827,x9828)) % 165.30/165.06 [983]~E(x9831,x9832)+E(f833(x9833,x9834,x9831,x9835,x9836,x9837,x9838),f833(x9833,x9834,x9832,x9835,x9836,x9837,x9838)) % 165.30/165.06 [984]~E(x9841,x9842)+E(f833(x9843,x9844,x9845,x9841,x9846,x9847,x9848),f833(x9843,x9844,x9845,x9842,x9846,x9847,x9848)) % 165.30/165.06 [985]~E(x9851,x9852)+E(f833(x9853,x9854,x9855,x9856,x9851,x9857,x9858),f833(x9853,x9854,x9855,x9856,x9852,x9857,x9858)) % 165.30/165.06 [986]~E(x9861,x9862)+E(f833(x9863,x9864,x9865,x9866,x9867,x9861,x9868),f833(x9863,x9864,x9865,x9866,x9867,x9862,x9868)) % 165.30/165.06 [987]~E(x9871,x9872)+E(f833(x9873,x9874,x9875,x9876,x9877,x9878,x9871),f833(x9873,x9874,x9875,x9876,x9877,x9878,x9872)) % 165.30/165.06 [988]~E(x9881,x9882)+E(f380(x9881,x9883,x9884,x9885),f380(x9882,x9883,x9884,x9885)) % 165.30/165.06 [989]~E(x9891,x9892)+E(f380(x9893,x9891,x9894,x9895),f380(x9893,x9892,x9894,x9895)) % 165.30/165.06 [990]~E(x9901,x9902)+E(f380(x9903,x9904,x9901,x9905),f380(x9903,x9904,x9902,x9905)) % 165.30/165.06 [991]~E(x9911,x9912)+E(f380(x9913,x9914,x9915,x9911),f380(x9913,x9914,x9915,x9912)) % 165.30/165.06 [992]~E(x9921,x9922)+E(f346(x9921,x9923),f346(x9922,x9923)) % 165.30/165.06 [993]~E(x9931,x9932)+E(f346(x9933,x9931),f346(x9933,x9932)) % 165.30/165.06 [994]~E(x9941,x9942)+E(f817(x9941,x9943,x9944),f817(x9942,x9943,x9944)) % 165.30/165.06 [995]~E(x9951,x9952)+E(f817(x9953,x9951,x9954),f817(x9953,x9952,x9954)) % 165.30/165.06 [996]~E(x9961,x9962)+E(f817(x9963,x9964,x9961),f817(x9963,x9964,x9962)) % 165.30/165.06 [997]~E(x9971,x9972)+E(f369(x9971,x9973),f369(x9972,x9973)) % 165.30/165.06 [998]~E(x9981,x9982)+E(f369(x9983,x9981),f369(x9983,x9982)) % 165.30/165.06 [999]~E(x9991,x9992)+E(f60(x9991,x9993,x9994,x9995),f60(x9992,x9993,x9994,x9995)) % 165.30/165.06 [1000]~E(x10001,x10002)+E(f60(x10003,x10001,x10004,x10005),f60(x10003,x10002,x10004,x10005)) % 165.30/165.06 [1001]~E(x10011,x10012)+E(f60(x10013,x10014,x10011,x10015),f60(x10013,x10014,x10012,x10015)) % 165.30/165.06 [1002]~E(x10021,x10022)+E(f60(x10023,x10024,x10025,x10021),f60(x10023,x10024,x10025,x10022)) % 165.30/165.06 [1003]~E(x10031,x10032)+E(f860(x10031,x10033,x10034,x10035),f860(x10032,x10033,x10034,x10035)) % 165.30/165.06 [1004]~E(x10041,x10042)+E(f860(x10043,x10041,x10044,x10045),f860(x10043,x10042,x10044,x10045)) % 165.30/165.06 [1005]~E(x10051,x10052)+E(f860(x10053,x10054,x10051,x10055),f860(x10053,x10054,x10052,x10055)) % 165.30/165.06 [1006]~E(x10061,x10062)+E(f860(x10063,x10064,x10065,x10061),f860(x10063,x10064,x10065,x10062)) % 165.30/165.06 [1007]~E(x10071,x10072)+E(f299(x10071,x10073,x10074,x10075),f299(x10072,x10073,x10074,x10075)) % 165.30/165.06 [1008]~E(x10081,x10082)+E(f299(x10083,x10081,x10084,x10085),f299(x10083,x10082,x10084,x10085)) % 165.30/165.06 [1009]~E(x10091,x10092)+E(f299(x10093,x10094,x10091,x10095),f299(x10093,x10094,x10092,x10095)) % 165.30/165.06 [1010]~E(x10101,x10102)+E(f299(x10103,x10104,x10105,x10101),f299(x10103,x10104,x10105,x10102)) % 165.30/165.06 [1011]~E(x10111,x10112)+E(f388(x10111,x10113,x10114,x10115),f388(x10112,x10113,x10114,x10115)) % 165.30/165.06 [1012]~E(x10121,x10122)+E(f388(x10123,x10121,x10124,x10125),f388(x10123,x10122,x10124,x10125)) % 165.30/165.06 [1013]~E(x10131,x10132)+E(f388(x10133,x10134,x10131,x10135),f388(x10133,x10134,x10132,x10135)) % 165.30/165.06 [1014]~E(x10141,x10142)+E(f388(x10143,x10144,x10145,x10141),f388(x10143,x10144,x10145,x10142)) % 165.30/165.06 [1015]~E(x10151,x10152)+E(f679(x10151,x10153,x10154),f679(x10152,x10153,x10154)) % 165.30/165.06 [1016]~E(x10161,x10162)+E(f679(x10163,x10161,x10164),f679(x10163,x10162,x10164)) % 165.30/165.06 [1017]~E(x10171,x10172)+E(f679(x10173,x10174,x10171),f679(x10173,x10174,x10172)) % 165.30/165.06 [1018]~E(x10181,x10182)+E(f192(x10181,x10183,x10184),f192(x10182,x10183,x10184)) % 165.30/165.06 [1019]~E(x10191,x10192)+E(f192(x10193,x10191,x10194),f192(x10193,x10192,x10194)) % 165.30/165.06 [1020]~E(x10201,x10202)+E(f192(x10203,x10204,x10201),f192(x10203,x10204,x10202)) % 165.30/165.06 [1021]~E(x10211,x10212)+E(f49(x10211,x10213),f49(x10212,x10213)) % 165.30/165.06 [1022]~E(x10221,x10222)+E(f49(x10223,x10221),f49(x10223,x10222)) % 165.30/165.06 [1023]~E(x10231,x10232)+E(f586(x10231,x10233,x10234,x10235,x10236),f586(x10232,x10233,x10234,x10235,x10236)) % 165.30/165.06 [1024]~E(x10241,x10242)+E(f586(x10243,x10241,x10244,x10245,x10246),f586(x10243,x10242,x10244,x10245,x10246)) % 165.30/165.06 [1025]~E(x10251,x10252)+E(f586(x10253,x10254,x10251,x10255,x10256),f586(x10253,x10254,x10252,x10255,x10256)) % 165.30/165.06 [1026]~E(x10261,x10262)+E(f586(x10263,x10264,x10265,x10261,x10266),f586(x10263,x10264,x10265,x10262,x10266)) % 165.30/165.06 [1027]~E(x10271,x10272)+E(f586(x10273,x10274,x10275,x10276,x10271),f586(x10273,x10274,x10275,x10276,x10272)) % 165.30/165.06 [1028]~E(x10281,x10282)+E(f95(x10281,x10283,x10284),f95(x10282,x10283,x10284)) % 165.30/165.06 [1029]~E(x10291,x10292)+E(f95(x10293,x10291,x10294),f95(x10293,x10292,x10294)) % 165.30/165.06 [1030]~E(x10301,x10302)+E(f95(x10303,x10304,x10301),f95(x10303,x10304,x10302)) % 165.30/165.06 [1031]~E(x10311,x10312)+E(f456(x10311,x10313,x10314),f456(x10312,x10313,x10314)) % 165.30/165.06 [1032]~E(x10321,x10322)+E(f456(x10323,x10321,x10324),f456(x10323,x10322,x10324)) % 165.30/165.06 [1033]~E(x10331,x10332)+E(f456(x10333,x10334,x10331),f456(x10333,x10334,x10332)) % 165.30/165.06 [1034]~E(x10341,x10342)+E(f375(x10341,x10343,x10344),f375(x10342,x10343,x10344)) % 165.30/165.06 [1035]~E(x10351,x10352)+E(f375(x10353,x10351,x10354),f375(x10353,x10352,x10354)) % 165.30/165.06 [1036]~E(x10361,x10362)+E(f375(x10363,x10364,x10361),f375(x10363,x10364,x10362)) % 165.30/165.06 [1037]~E(x10371,x10372)+E(f856(x10371,x10373,x10374,x10375,x10376),f856(x10372,x10373,x10374,x10375,x10376)) % 165.30/165.06 [1038]~E(x10381,x10382)+E(f856(x10383,x10381,x10384,x10385,x10386),f856(x10383,x10382,x10384,x10385,x10386)) % 165.30/165.06 [1039]~E(x10391,x10392)+E(f856(x10393,x10394,x10391,x10395,x10396),f856(x10393,x10394,x10392,x10395,x10396)) % 165.30/165.06 [1040]~E(x10401,x10402)+E(f856(x10403,x10404,x10405,x10401,x10406),f856(x10403,x10404,x10405,x10402,x10406)) % 165.30/165.06 [1041]~E(x10411,x10412)+E(f856(x10413,x10414,x10415,x10416,x10411),f856(x10413,x10414,x10415,x10416,x10412)) % 165.30/165.06 [1042]~E(x10421,x10422)+E(f119(x10421,x10423,x10424),f119(x10422,x10423,x10424)) % 165.30/165.06 [1043]~E(x10431,x10432)+E(f119(x10433,x10431,x10434),f119(x10433,x10432,x10434)) % 165.30/165.06 [1044]~E(x10441,x10442)+E(f119(x10443,x10444,x10441),f119(x10443,x10444,x10442)) % 165.30/165.06 [1045]~E(x10451,x10452)+E(f531(x10451,x10453,x10454),f531(x10452,x10453,x10454)) % 165.30/165.06 [1046]~E(x10461,x10462)+E(f531(x10463,x10461,x10464),f531(x10463,x10462,x10464)) % 165.30/165.06 [1047]~E(x10471,x10472)+E(f531(x10473,x10474,x10471),f531(x10473,x10474,x10472)) % 165.30/165.06 [1048]~E(x10481,x10482)+E(f277(x10481),f277(x10482)) % 165.30/165.06 [1049]~E(x10491,x10492)+E(f500(x10491,x10493,x10494,x10495,x10496,x10497,x10498),f500(x10492,x10493,x10494,x10495,x10496,x10497,x10498)) % 165.30/165.06 [1050]~E(x10501,x10502)+E(f500(x10503,x10501,x10504,x10505,x10506,x10507,x10508),f500(x10503,x10502,x10504,x10505,x10506,x10507,x10508)) % 165.30/165.06 [1051]~E(x10511,x10512)+E(f500(x10513,x10514,x10511,x10515,x10516,x10517,x10518),f500(x10513,x10514,x10512,x10515,x10516,x10517,x10518)) % 165.30/165.06 [1052]~E(x10521,x10522)+E(f500(x10523,x10524,x10525,x10521,x10526,x10527,x10528),f500(x10523,x10524,x10525,x10522,x10526,x10527,x10528)) % 165.30/165.06 [1053]~E(x10531,x10532)+E(f500(x10533,x10534,x10535,x10536,x10531,x10537,x10538),f500(x10533,x10534,x10535,x10536,x10532,x10537,x10538)) % 165.30/165.06 [1054]~E(x10541,x10542)+E(f500(x10543,x10544,x10545,x10546,x10547,x10541,x10548),f500(x10543,x10544,x10545,x10546,x10547,x10542,x10548)) % 165.30/165.06 [1055]~E(x10551,x10552)+E(f500(x10553,x10554,x10555,x10556,x10557,x10558,x10551),f500(x10553,x10554,x10555,x10556,x10557,x10558,x10552)) % 165.30/165.06 [1056]~E(x10561,x10562)+E(f483(x10561,x10563,x10564,x10565),f483(x10562,x10563,x10564,x10565)) % 165.30/165.06 [1057]~E(x10571,x10572)+E(f483(x10573,x10571,x10574,x10575),f483(x10573,x10572,x10574,x10575)) % 165.30/165.06 [1058]~E(x10581,x10582)+E(f483(x10583,x10584,x10581,x10585),f483(x10583,x10584,x10582,x10585)) % 165.30/165.06 [1059]~E(x10591,x10592)+E(f483(x10593,x10594,x10595,x10591),f483(x10593,x10594,x10595,x10592)) % 165.30/165.06 [1060]~E(x10601,x10602)+E(f485(x10601,x10603,x10604),f485(x10602,x10603,x10604)) % 165.30/165.06 [1061]~E(x10611,x10612)+E(f485(x10613,x10611,x10614),f485(x10613,x10612,x10614)) % 165.30/165.06 [1062]~E(x10621,x10622)+E(f485(x10623,x10624,x10621),f485(x10623,x10624,x10622)) % 165.30/165.06 [1063]~E(x10631,x10632)+E(f600(x10631,x10633,x10634,x10635,x10636),f600(x10632,x10633,x10634,x10635,x10636)) % 165.30/165.06 [1064]~E(x10641,x10642)+E(f600(x10643,x10641,x10644,x10645,x10646),f600(x10643,x10642,x10644,x10645,x10646)) % 165.30/165.06 [1065]~E(x10651,x10652)+E(f600(x10653,x10654,x10651,x10655,x10656),f600(x10653,x10654,x10652,x10655,x10656)) % 165.30/165.06 [1066]~E(x10661,x10662)+E(f600(x10663,x10664,x10665,x10661,x10666),f600(x10663,x10664,x10665,x10662,x10666)) % 165.30/165.06 [1067]~E(x10671,x10672)+E(f600(x10673,x10674,x10675,x10676,x10671),f600(x10673,x10674,x10675,x10676,x10672)) % 165.30/165.06 [1068]~E(x10681,x10682)+E(f505(x10681,x10683,x10684),f505(x10682,x10683,x10684)) % 165.30/165.06 [1069]~E(x10691,x10692)+E(f505(x10693,x10691,x10694),f505(x10693,x10692,x10694)) % 165.30/165.06 [1070]~E(x10701,x10702)+E(f505(x10703,x10704,x10701),f505(x10703,x10704,x10702)) % 165.30/165.06 [1071]~E(x10711,x10712)+E(f476(x10711,x10713,x10714,x10715),f476(x10712,x10713,x10714,x10715)) % 165.30/165.06 [1072]~E(x10721,x10722)+E(f476(x10723,x10721,x10724,x10725),f476(x10723,x10722,x10724,x10725)) % 165.30/165.06 [1073]~E(x10731,x10732)+E(f476(x10733,x10734,x10731,x10735),f476(x10733,x10734,x10732,x10735)) % 165.30/165.06 [1074]~E(x10741,x10742)+E(f476(x10743,x10744,x10745,x10741),f476(x10743,x10744,x10745,x10742)) % 165.30/165.06 [1075]~E(x10751,x10752)+E(f510(x10751,x10753,x10754,x10755),f510(x10752,x10753,x10754,x10755)) % 165.30/165.06 [1076]~E(x10761,x10762)+E(f510(x10763,x10761,x10764,x10765),f510(x10763,x10762,x10764,x10765)) % 165.30/165.06 [1077]~E(x10771,x10772)+E(f510(x10773,x10774,x10771,x10775),f510(x10773,x10774,x10772,x10775)) % 165.30/165.06 [1078]~E(x10781,x10782)+E(f510(x10783,x10784,x10785,x10781),f510(x10783,x10784,x10785,x10782)) % 165.30/165.06 [1079]~E(x10791,x10792)+E(f472(x10791,x10793,x10794,x10795,x10796),f472(x10792,x10793,x10794,x10795,x10796)) % 165.30/165.06 [1080]~E(x10801,x10802)+E(f472(x10803,x10801,x10804,x10805,x10806),f472(x10803,x10802,x10804,x10805,x10806)) % 165.30/165.06 [1081]~E(x10811,x10812)+E(f472(x10813,x10814,x10811,x10815,x10816),f472(x10813,x10814,x10812,x10815,x10816)) % 165.30/165.06 [1082]~E(x10821,x10822)+E(f472(x10823,x10824,x10825,x10821,x10826),f472(x10823,x10824,x10825,x10822,x10826)) % 165.30/165.06 [1083]~E(x10831,x10832)+E(f472(x10833,x10834,x10835,x10836,x10831),f472(x10833,x10834,x10835,x10836,x10832)) % 165.30/165.06 [1084]~E(x10841,x10842)+E(f502(x10841,x10843),f502(x10842,x10843)) % 165.30/165.06 [1085]~E(x10851,x10852)+E(f502(x10853,x10851),f502(x10853,x10852)) % 165.30/165.06 [1086]~E(x10861,x10862)+E(f610(x10861,x10863),f610(x10862,x10863)) % 165.30/165.06 [1087]~E(x10871,x10872)+E(f610(x10873,x10871),f610(x10873,x10872)) % 165.30/165.06 [1088]~E(x10881,x10882)+E(f764(x10881,x10883,x10884),f764(x10882,x10883,x10884)) % 165.30/165.06 [1089]~E(x10891,x10892)+E(f764(x10893,x10891,x10894),f764(x10893,x10892,x10894)) % 165.30/165.06 [1090]~E(x10901,x10902)+E(f764(x10903,x10904,x10901),f764(x10903,x10904,x10902)) % 165.30/165.06 [1091]~E(x10911,x10912)+E(f497(x10911,x10913,x10914),f497(x10912,x10913,x10914)) % 165.30/165.06 [1092]~E(x10921,x10922)+E(f497(x10923,x10921,x10924),f497(x10923,x10922,x10924)) % 165.30/165.06 [1093]~E(x10931,x10932)+E(f497(x10933,x10934,x10931),f497(x10933,x10934,x10932)) % 165.30/165.06 [1094]~E(x10941,x10942)+E(f567(x10941,x10943,x10944,x10945,x10946,x10947,x10948,x10949),f567(x10942,x10943,x10944,x10945,x10946,x10947,x10948,x10949)) % 165.30/165.06 [1095]~E(x10951,x10952)+E(f567(x10953,x10951,x10954,x10955,x10956,x10957,x10958,x10959),f567(x10953,x10952,x10954,x10955,x10956,x10957,x10958,x10959)) % 165.30/165.06 [1096]~E(x10961,x10962)+E(f567(x10963,x10964,x10961,x10965,x10966,x10967,x10968,x10969),f567(x10963,x10964,x10962,x10965,x10966,x10967,x10968,x10969)) % 165.30/165.06 [1097]~E(x10971,x10972)+E(f567(x10973,x10974,x10975,x10971,x10976,x10977,x10978,x10979),f567(x10973,x10974,x10975,x10972,x10976,x10977,x10978,x10979)) % 165.30/165.06 [1098]~E(x10981,x10982)+E(f567(x10983,x10984,x10985,x10986,x10981,x10987,x10988,x10989),f567(x10983,x10984,x10985,x10986,x10982,x10987,x10988,x10989)) % 165.30/165.06 [1099]~E(x10991,x10992)+E(f567(x10993,x10994,x10995,x10996,x10997,x10991,x10998,x10999),f567(x10993,x10994,x10995,x10996,x10997,x10992,x10998,x10999)) % 165.30/165.06 [1100]~E(x11001,x11002)+E(f567(x11003,x11004,x11005,x11006,x11007,x11008,x11001,x11009),f567(x11003,x11004,x11005,x11006,x11007,x11008,x11002,x11009)) % 165.30/165.06 [1101]~E(x11011,x11012)+E(f567(x11013,x11014,x11015,x11016,x11017,x11018,x11019,x11011),f567(x11013,x11014,x11015,x11016,x11017,x11018,x11019,x11012)) % 165.30/165.06 [1102]~E(x11021,x11022)+E(f850(x11021,x11023,x11024,x11025),f850(x11022,x11023,x11024,x11025)) % 165.30/165.06 [1103]~E(x11031,x11032)+E(f850(x11033,x11031,x11034,x11035),f850(x11033,x11032,x11034,x11035)) % 165.30/165.06 [1104]~E(x11041,x11042)+E(f850(x11043,x11044,x11041,x11045),f850(x11043,x11044,x11042,x11045)) % 165.30/165.06 [1105]~E(x11051,x11052)+E(f850(x11053,x11054,x11055,x11051),f850(x11053,x11054,x11055,x11052)) % 165.30/165.06 [1106]~E(x11061,x11062)+E(f203(x11061,x11063,x11064,x11065),f203(x11062,x11063,x11064,x11065)) % 165.30/165.06 [1107]~E(x11071,x11072)+E(f203(x11073,x11071,x11074,x11075),f203(x11073,x11072,x11074,x11075)) % 165.30/165.06 [1108]~E(x11081,x11082)+E(f203(x11083,x11084,x11081,x11085),f203(x11083,x11084,x11082,x11085)) % 165.30/165.06 [1109]~E(x11091,x11092)+E(f203(x11093,x11094,x11095,x11091),f203(x11093,x11094,x11095,x11092)) % 165.30/165.06 [1110]~E(x11101,x11102)+E(f222(x11101,x11103,x11104,x11105),f222(x11102,x11103,x11104,x11105)) % 165.30/165.06 [1111]~E(x11111,x11112)+E(f222(x11113,x11111,x11114,x11115),f222(x11113,x11112,x11114,x11115)) % 165.30/165.06 [1112]~E(x11121,x11122)+E(f222(x11123,x11124,x11121,x11125),f222(x11123,x11124,x11122,x11125)) % 165.30/165.06 [1113]~E(x11131,x11132)+E(f222(x11133,x11134,x11135,x11131),f222(x11133,x11134,x11135,x11132)) % 165.30/165.06 [1114]~E(x11141,x11142)+E(f781(x11141,x11143,x11144),f781(x11142,x11143,x11144)) % 165.30/165.06 [1115]~E(x11151,x11152)+E(f781(x11153,x11151,x11154),f781(x11153,x11152,x11154)) % 165.30/165.06 [1116]~E(x11161,x11162)+E(f781(x11163,x11164,x11161),f781(x11163,x11164,x11162)) % 165.30/165.06 [1117]~E(x11171,x11172)+E(f714(x11171,x11173,x11174,x11175,x11176),f714(x11172,x11173,x11174,x11175,x11176)) % 165.30/165.06 [1118]~E(x11181,x11182)+E(f714(x11183,x11181,x11184,x11185,x11186),f714(x11183,x11182,x11184,x11185,x11186)) % 165.30/165.06 [1119]~E(x11191,x11192)+E(f714(x11193,x11194,x11191,x11195,x11196),f714(x11193,x11194,x11192,x11195,x11196)) % 165.30/165.06 [1120]~E(x11201,x11202)+E(f714(x11203,x11204,x11205,x11201,x11206),f714(x11203,x11204,x11205,x11202,x11206)) % 165.30/165.06 [1121]~E(x11211,x11212)+E(f714(x11213,x11214,x11215,x11216,x11211),f714(x11213,x11214,x11215,x11216,x11212)) % 165.30/165.06 [1122]~E(x11221,x11222)+E(f691(x11221,x11223,x11224),f691(x11222,x11223,x11224)) % 165.30/165.06 [1123]~E(x11231,x11232)+E(f691(x11233,x11231,x11234),f691(x11233,x11232,x11234)) % 165.30/165.06 [1124]~E(x11241,x11242)+E(f691(x11243,x11244,x11241),f691(x11243,x11244,x11242)) % 165.30/165.06 [1125]~E(x11251,x11252)+E(f89(x11251),f89(x11252)) % 165.30/165.06 [1126]~E(x11261,x11262)+E(f812(x11261,x11263,x11264),f812(x11262,x11263,x11264)) % 165.30/165.06 [1127]~E(x11271,x11272)+E(f812(x11273,x11271,x11274),f812(x11273,x11272,x11274)) % 165.30/165.06 [1128]~E(x11281,x11282)+E(f812(x11283,x11284,x11281),f812(x11283,x11284,x11282)) % 165.30/165.06 [1129]~E(x11291,x11292)+E(f454(x11291,x11293,x11294),f454(x11292,x11293,x11294)) % 165.30/165.06 [1130]~E(x11301,x11302)+E(f454(x11303,x11301,x11304),f454(x11303,x11302,x11304)) % 165.30/165.06 [1131]~E(x11311,x11312)+E(f454(x11313,x11314,x11311),f454(x11313,x11314,x11312)) % 165.30/165.06 [1132]~E(x11321,x11322)+E(f132(x11321,x11323,x11324,x11325),f132(x11322,x11323,x11324,x11325)) % 165.30/165.06 [1133]~E(x11331,x11332)+E(f132(x11333,x11331,x11334,x11335),f132(x11333,x11332,x11334,x11335)) % 165.30/165.06 [1134]~E(x11341,x11342)+E(f132(x11343,x11344,x11341,x11345),f132(x11343,x11344,x11342,x11345)) % 165.30/165.06 [1135]~E(x11351,x11352)+E(f132(x11353,x11354,x11355,x11351),f132(x11353,x11354,x11355,x11352)) % 165.30/165.06 [1136]~E(x11361,x11362)+E(f841(x11361,x11363,x11364,x11365,x11366),f841(x11362,x11363,x11364,x11365,x11366)) % 165.30/165.06 [1137]~E(x11371,x11372)+E(f841(x11373,x11371,x11374,x11375,x11376),f841(x11373,x11372,x11374,x11375,x11376)) % 165.30/165.06 [1138]~E(x11381,x11382)+E(f841(x11383,x11384,x11381,x11385,x11386),f841(x11383,x11384,x11382,x11385,x11386)) % 165.30/165.06 [1139]~E(x11391,x11392)+E(f841(x11393,x11394,x11395,x11391,x11396),f841(x11393,x11394,x11395,x11392,x11396)) % 165.30/165.06 [1140]~E(x11401,x11402)+E(f841(x11403,x11404,x11405,x11406,x11401),f841(x11403,x11404,x11405,x11406,x11402)) % 165.30/165.06 [1141]~E(x11411,x11412)+E(f809(x11411,x11413,x11414),f809(x11412,x11413,x11414)) % 165.30/165.06 [1142]~E(x11421,x11422)+E(f809(x11423,x11421,x11424),f809(x11423,x11422,x11424)) % 165.30/165.06 [1143]~E(x11431,x11432)+E(f809(x11433,x11434,x11431),f809(x11433,x11434,x11432)) % 165.30/165.06 [1144]~E(x11441,x11442)+E(f216(x11441),f216(x11442)) % 165.30/165.06 [1145]~E(x11451,x11452)+E(f844(x11451,x11453,x11454,x11455),f844(x11452,x11453,x11454,x11455)) % 165.30/165.06 [1146]~E(x11461,x11462)+E(f844(x11463,x11461,x11464,x11465),f844(x11463,x11462,x11464,x11465)) % 165.30/165.06 [1147]~E(x11471,x11472)+E(f844(x11473,x11474,x11471,x11475),f844(x11473,x11474,x11472,x11475)) % 165.30/165.06 [1148]~E(x11481,x11482)+E(f844(x11483,x11484,x11485,x11481),f844(x11483,x11484,x11485,x11482)) % 165.30/165.06 [1149]~E(x11491,x11492)+E(f215(x11491,x11493,x11494),f215(x11492,x11493,x11494)) % 165.30/165.06 [1150]~E(x11501,x11502)+E(f215(x11503,x11501,x11504),f215(x11503,x11502,x11504)) % 165.30/165.06 [1151]~E(x11511,x11512)+E(f215(x11513,x11514,x11511),f215(x11513,x11514,x11512)) % 165.30/165.06 [1152]~E(x11521,x11522)+E(f529(x11521,x11523,x11524,x11525,x11526,x11527,x11528,x11529),f529(x11522,x11523,x11524,x11525,x11526,x11527,x11528,x11529)) % 165.30/165.06 [1153]~E(x11531,x11532)+E(f529(x11533,x11531,x11534,x11535,x11536,x11537,x11538,x11539),f529(x11533,x11532,x11534,x11535,x11536,x11537,x11538,x11539)) % 165.30/165.06 [1154]~E(x11541,x11542)+E(f529(x11543,x11544,x11541,x11545,x11546,x11547,x11548,x11549),f529(x11543,x11544,x11542,x11545,x11546,x11547,x11548,x11549)) % 165.30/165.06 [1155]~E(x11551,x11552)+E(f529(x11553,x11554,x11555,x11551,x11556,x11557,x11558,x11559),f529(x11553,x11554,x11555,x11552,x11556,x11557,x11558,x11559)) % 165.30/165.06 [1156]~E(x11561,x11562)+E(f529(x11563,x11564,x11565,x11566,x11561,x11567,x11568,x11569),f529(x11563,x11564,x11565,x11566,x11562,x11567,x11568,x11569)) % 165.30/165.06 [1157]~E(x11571,x11572)+E(f529(x11573,x11574,x11575,x11576,x11577,x11571,x11578,x11579),f529(x11573,x11574,x11575,x11576,x11577,x11572,x11578,x11579)) % 165.30/165.06 [1158]~E(x11581,x11582)+E(f529(x11583,x11584,x11585,x11586,x11587,x11588,x11581,x11589),f529(x11583,x11584,x11585,x11586,x11587,x11588,x11582,x11589)) % 165.30/165.06 [1159]~E(x11591,x11592)+E(f529(x11593,x11594,x11595,x11596,x11597,x11598,x11599,x11591),f529(x11593,x11594,x11595,x11596,x11597,x11598,x11599,x11592)) % 165.30/165.06 [1160]~E(x11601,x11602)+E(f218(x11601,x11603,x11604,x11605),f218(x11602,x11603,x11604,x11605)) % 165.30/165.06 [1161]~E(x11611,x11612)+E(f218(x11613,x11611,x11614,x11615),f218(x11613,x11612,x11614,x11615)) % 165.30/165.06 [1162]~E(x11621,x11622)+E(f218(x11623,x11624,x11621,x11625),f218(x11623,x11624,x11622,x11625)) % 165.30/165.06 [1163]~E(x11631,x11632)+E(f218(x11633,x11634,x11635,x11631),f218(x11633,x11634,x11635,x11632)) % 165.30/165.06 [1164]~E(x11641,x11642)+E(f217(x11641),f217(x11642)) % 165.30/165.06 [1165]~E(x11651,x11652)+E(f498(x11651,x11653,x11654),f498(x11652,x11653,x11654)) % 165.30/165.06 [1166]~E(x11661,x11662)+E(f498(x11663,x11661,x11664),f498(x11663,x11662,x11664)) % 165.30/165.06 [1167]~E(x11671,x11672)+E(f498(x11673,x11674,x11671),f498(x11673,x11674,x11672)) % 165.30/165.06 [1168]~E(x11681,x11682)+E(f351(x11681,x11683),f351(x11682,x11683)) % 165.30/165.06 [1169]~E(x11691,x11692)+E(f351(x11693,x11691),f351(x11693,x11692)) % 165.30/165.06 [1170]~E(x11701,x11702)+E(f826(x11701,x11703,x11704,x11705),f826(x11702,x11703,x11704,x11705)) % 165.30/165.06 [1171]~E(x11711,x11712)+E(f826(x11713,x11711,x11714,x11715),f826(x11713,x11712,x11714,x11715)) % 165.30/165.06 [1172]~E(x11721,x11722)+E(f826(x11723,x11724,x11721,x11725),f826(x11723,x11724,x11722,x11725)) % 165.30/165.06 [1173]~E(x11731,x11732)+E(f826(x11733,x11734,x11735,x11731),f826(x11733,x11734,x11735,x11732)) % 165.30/165.06 [1174]~E(x11741,x11742)+E(f78(x11741,x11743,x11744,x11745),f78(x11742,x11743,x11744,x11745)) % 165.30/165.06 [1175]~E(x11751,x11752)+E(f78(x11753,x11751,x11754,x11755),f78(x11753,x11752,x11754,x11755)) % 165.30/165.06 [1176]~E(x11761,x11762)+E(f78(x11763,x11764,x11761,x11765),f78(x11763,x11764,x11762,x11765)) % 165.30/165.06 [1177]~E(x11771,x11772)+E(f78(x11773,x11774,x11775,x11771),f78(x11773,x11774,x11775,x11772)) % 165.30/165.06 [1178]~E(x11781,x11782)+E(f762(x11781,x11783),f762(x11782,x11783)) % 165.30/165.06 [1179]~E(x11791,x11792)+E(f762(x11793,x11791),f762(x11793,x11792)) % 165.30/165.06 [1180]~E(x11801,x11802)+E(f775(x11801,x11803,x11804,x11805,x11806),f775(x11802,x11803,x11804,x11805,x11806)) % 165.30/165.06 [1181]~E(x11811,x11812)+E(f775(x11813,x11811,x11814,x11815,x11816),f775(x11813,x11812,x11814,x11815,x11816)) % 165.30/165.06 [1182]~E(x11821,x11822)+E(f775(x11823,x11824,x11821,x11825,x11826),f775(x11823,x11824,x11822,x11825,x11826)) % 165.30/165.06 [1183]~E(x11831,x11832)+E(f775(x11833,x11834,x11835,x11831,x11836),f775(x11833,x11834,x11835,x11832,x11836)) % 165.30/165.06 [1184]~E(x11841,x11842)+E(f775(x11843,x11844,x11845,x11846,x11841),f775(x11843,x11844,x11845,x11846,x11842)) % 165.30/165.06 [1185]~E(x11851,x11852)+E(f151(x11851,x11853,x11854,x11855),f151(x11852,x11853,x11854,x11855)) % 165.30/165.06 [1186]~E(x11861,x11862)+E(f151(x11863,x11861,x11864,x11865),f151(x11863,x11862,x11864,x11865)) % 165.30/165.06 [1187]~E(x11871,x11872)+E(f151(x11873,x11874,x11871,x11875),f151(x11873,x11874,x11872,x11875)) % 165.30/165.06 [1188]~E(x11881,x11882)+E(f151(x11883,x11884,x11885,x11881),f151(x11883,x11884,x11885,x11882)) % 165.30/165.06 [1189]~E(x11891,x11892)+E(f391(x11891,x11893,x11894,x11895),f391(x11892,x11893,x11894,x11895)) % 165.30/165.06 [1190]~E(x11901,x11902)+E(f391(x11903,x11901,x11904,x11905),f391(x11903,x11902,x11904,x11905)) % 165.30/165.06 [1191]~E(x11911,x11912)+E(f391(x11913,x11914,x11911,x11915),f391(x11913,x11914,x11912,x11915)) % 165.30/165.06 [1192]~E(x11921,x11922)+E(f391(x11923,x11924,x11925,x11921),f391(x11923,x11924,x11925,x11922)) % 165.30/165.06 [1193]~E(x11931,x11932)+E(f364(x11931,x11933,x11934),f364(x11932,x11933,x11934)) % 165.30/165.06 [1194]~E(x11941,x11942)+E(f364(x11943,x11941,x11944),f364(x11943,x11942,x11944)) % 165.30/165.06 [1195]~E(x11951,x11952)+E(f364(x11953,x11954,x11951),f364(x11953,x11954,x11952)) % 165.30/165.06 [1196]~E(x11961,x11962)+E(f778(x11961,x11963,x11964,x11965,x11966,x11967),f778(x11962,x11963,x11964,x11965,x11966,x11967)) % 165.30/165.06 [1197]~E(x11971,x11972)+E(f778(x11973,x11971,x11974,x11975,x11976,x11977),f778(x11973,x11972,x11974,x11975,x11976,x11977)) % 165.30/165.06 [1198]~E(x11981,x11982)+E(f778(x11983,x11984,x11981,x11985,x11986,x11987),f778(x11983,x11984,x11982,x11985,x11986,x11987)) % 165.30/165.06 [1199]~E(x11991,x11992)+E(f778(x11993,x11994,x11995,x11991,x11996,x11997),f778(x11993,x11994,x11995,x11992,x11996,x11997)) % 165.30/165.06 [1200]~E(x12001,x12002)+E(f778(x12003,x12004,x12005,x12006,x12001,x12007),f778(x12003,x12004,x12005,x12006,x12002,x12007)) % 165.30/165.06 [1201]~E(x12011,x12012)+E(f778(x12013,x12014,x12015,x12016,x12017,x12011),f778(x12013,x12014,x12015,x12016,x12017,x12012)) % 165.30/165.06 [1202]~E(x12021,x12022)+E(f603(x12021,x12023,x12024,x12025,x12026),f603(x12022,x12023,x12024,x12025,x12026)) % 165.30/165.06 [1203]~E(x12031,x12032)+E(f603(x12033,x12031,x12034,x12035,x12036),f603(x12033,x12032,x12034,x12035,x12036)) % 165.30/165.06 [1204]~E(x12041,x12042)+E(f603(x12043,x12044,x12041,x12045,x12046),f603(x12043,x12044,x12042,x12045,x12046)) % 165.30/165.06 [1205]~E(x12051,x12052)+E(f603(x12053,x12054,x12055,x12051,x12056),f603(x12053,x12054,x12055,x12052,x12056)) % 165.30/165.06 [1206]~E(x12061,x12062)+E(f603(x12063,x12064,x12065,x12066,x12061),f603(x12063,x12064,x12065,x12066,x12062)) % 165.30/165.06 [1207]~E(x12071,x12072)+E(f204(x12071,x12073,x12074,x12075),f204(x12072,x12073,x12074,x12075)) % 165.30/165.06 [1208]~E(x12081,x12082)+E(f204(x12083,x12081,x12084,x12085),f204(x12083,x12082,x12084,x12085)) % 165.30/165.06 [1209]~E(x12091,x12092)+E(f204(x12093,x12094,x12091,x12095),f204(x12093,x12094,x12092,x12095)) % 165.30/165.06 [1210]~E(x12101,x12102)+E(f204(x12103,x12104,x12105,x12101),f204(x12103,x12104,x12105,x12102)) % 165.30/165.06 [1211]~E(x12111,x12112)+E(f466(x12111,x12113,x12114,x12115),f466(x12112,x12113,x12114,x12115)) % 165.30/165.06 [1212]~E(x12121,x12122)+E(f466(x12123,x12121,x12124,x12125),f466(x12123,x12122,x12124,x12125)) % 165.30/165.06 [1213]~E(x12131,x12132)+E(f466(x12133,x12134,x12131,x12135),f466(x12133,x12134,x12132,x12135)) % 165.30/165.06 [1214]~E(x12141,x12142)+E(f466(x12143,x12144,x12145,x12141),f466(x12143,x12144,x12145,x12142)) % 165.30/165.06 [1215]~E(x12151,x12152)+E(f469(x12151,x12153,x12154,x12155,x12156),f469(x12152,x12153,x12154,x12155,x12156)) % 165.30/165.06 [1216]~E(x12161,x12162)+E(f469(x12163,x12161,x12164,x12165,x12166),f469(x12163,x12162,x12164,x12165,x12166)) % 165.30/165.06 [1217]~E(x12171,x12172)+E(f469(x12173,x12174,x12171,x12175,x12176),f469(x12173,x12174,x12172,x12175,x12176)) % 165.30/165.06 [1218]~E(x12181,x12182)+E(f469(x12183,x12184,x12185,x12181,x12186),f469(x12183,x12184,x12185,x12182,x12186)) % 165.30/165.06 [1219]~E(x12191,x12192)+E(f469(x12193,x12194,x12195,x12196,x12191),f469(x12193,x12194,x12195,x12196,x12192)) % 165.30/165.06 [1220]~E(x12201,x12202)+E(f504(x12201,x12203,x12204),f504(x12202,x12203,x12204)) % 165.30/165.06 [1221]~E(x12211,x12212)+E(f504(x12213,x12211,x12214),f504(x12213,x12212,x12214)) % 165.30/165.06 [1222]~E(x12221,x12222)+E(f504(x12223,x12224,x12221),f504(x12223,x12224,x12222)) % 165.30/165.06 [1223]~E(x12231,x12232)+E(f486(x12231,x12233,x12234),f486(x12232,x12233,x12234)) % 165.30/165.06 [1224]~E(x12241,x12242)+E(f486(x12243,x12241,x12244),f486(x12243,x12242,x12244)) % 165.30/165.06 [1225]~E(x12251,x12252)+E(f486(x12253,x12254,x12251),f486(x12253,x12254,x12252)) % 165.30/165.06 [1226]~E(x12261,x12262)+E(f673(x12261,x12263),f673(x12262,x12263)) % 165.30/165.06 [1227]~E(x12271,x12272)+E(f673(x12273,x12271),f673(x12273,x12272)) % 165.30/165.06 [1228]~E(x12281,x12282)+E(f384(x12281,x12283,x12284,x12285),f384(x12282,x12283,x12284,x12285)) % 165.30/165.06 [1229]~E(x12291,x12292)+E(f384(x12293,x12291,x12294,x12295),f384(x12293,x12292,x12294,x12295)) % 165.30/165.06 [1230]~E(x12301,x12302)+E(f384(x12303,x12304,x12301,x12305),f384(x12303,x12304,x12302,x12305)) % 165.30/165.06 [1231]~E(x12311,x12312)+E(f384(x12313,x12314,x12315,x12311),f384(x12313,x12314,x12315,x12312)) % 165.30/165.06 [1232]~E(x12321,x12322)+E(f403(x12321,x12323),f403(x12322,x12323)) % 165.30/165.06 [1233]~E(x12331,x12332)+E(f403(x12333,x12331),f403(x12333,x12332)) % 165.30/165.06 [1234]~E(x12341,x12342)+E(f280(x12341,x12343),f280(x12342,x12343)) % 165.30/165.06 [1235]~E(x12351,x12352)+E(f280(x12353,x12351),f280(x12353,x12352)) % 165.30/165.06 [1236]~E(x12361,x12362)+E(f417(x12361,x12363,x12364,x12365,x12366),f417(x12362,x12363,x12364,x12365,x12366)) % 165.30/165.06 [1237]~E(x12371,x12372)+E(f417(x12373,x12371,x12374,x12375,x12376),f417(x12373,x12372,x12374,x12375,x12376)) % 165.30/165.06 [1238]~E(x12381,x12382)+E(f417(x12383,x12384,x12381,x12385,x12386),f417(x12383,x12384,x12382,x12385,x12386)) % 165.30/165.06 [1239]~E(x12391,x12392)+E(f417(x12393,x12394,x12395,x12391,x12396),f417(x12393,x12394,x12395,x12392,x12396)) % 165.30/165.06 [1240]~E(x12401,x12402)+E(f417(x12403,x12404,x12405,x12406,x12401),f417(x12403,x12404,x12405,x12406,x12402)) % 165.30/165.06 [1241]~E(x12411,x12412)+E(f675(x12411,x12413,x12414,x12415),f675(x12412,x12413,x12414,x12415)) % 165.30/165.06 [1242]~E(x12421,x12422)+E(f675(x12423,x12421,x12424,x12425),f675(x12423,x12422,x12424,x12425)) % 165.30/165.06 [1243]~E(x12431,x12432)+E(f675(x12433,x12434,x12431,x12435),f675(x12433,x12434,x12432,x12435)) % 165.30/165.06 [1244]~E(x12441,x12442)+E(f675(x12443,x12444,x12445,x12441),f675(x12443,x12444,x12445,x12442)) % 165.30/165.06 [1245]~E(x12451,x12452)+E(f536(x12451,x12453,x12454),f536(x12452,x12453,x12454)) % 165.30/165.06 [1246]~E(x12461,x12462)+E(f536(x12463,x12461,x12464),f536(x12463,x12462,x12464)) % 165.30/165.06 [1247]~E(x12471,x12472)+E(f536(x12473,x12474,x12471),f536(x12473,x12474,x12472)) % 165.30/165.06 [1248]~E(x12481,x12482)+E(f587(x12481,x12483,x12484,x12485),f587(x12482,x12483,x12484,x12485)) % 165.30/165.06 [1249]~E(x12491,x12492)+E(f587(x12493,x12491,x12494,x12495),f587(x12493,x12492,x12494,x12495)) % 165.30/165.06 [1250]~E(x12501,x12502)+E(f587(x12503,x12504,x12501,x12505),f587(x12503,x12504,x12502,x12505)) % 165.30/165.06 [1251]~E(x12511,x12512)+E(f587(x12513,x12514,x12515,x12511),f587(x12513,x12514,x12515,x12512)) % 165.30/165.06 [1252]~E(x12521,x12522)+E(f530(x12521,x12523,x12524),f530(x12522,x12523,x12524)) % 165.30/165.06 [1253]~E(x12531,x12532)+E(f530(x12533,x12531,x12534),f530(x12533,x12532,x12534)) % 165.30/165.06 [1254]~E(x12541,x12542)+E(f530(x12543,x12544,x12541),f530(x12543,x12544,x12542)) % 165.30/165.06 [1255]~E(x12551,x12552)+E(f284(x12551,x12553,x12554,x12555),f284(x12552,x12553,x12554,x12555)) % 165.30/165.06 [1256]~E(x12561,x12562)+E(f284(x12563,x12561,x12564,x12565),f284(x12563,x12562,x12564,x12565)) % 165.30/165.06 [1257]~E(x12571,x12572)+E(f284(x12573,x12574,x12571,x12575),f284(x12573,x12574,x12572,x12575)) % 165.30/165.06 [1258]~E(x12581,x12582)+E(f284(x12583,x12584,x12585,x12581),f284(x12583,x12584,x12585,x12582)) % 165.30/165.06 [1259]~E(x12591,x12592)+E(f211(x12591,x12593),f211(x12592,x12593)) % 165.30/165.06 [1260]~E(x12601,x12602)+E(f211(x12603,x12601),f211(x12603,x12602)) % 165.30/165.06 [1261]~E(x12611,x12612)+E(f413(x12611,x12613,x12614),f413(x12612,x12613,x12614)) % 165.30/165.06 [1262]~E(x12621,x12622)+E(f413(x12623,x12621,x12624),f413(x12623,x12622,x12624)) % 165.30/165.06 [1263]~E(x12631,x12632)+E(f413(x12633,x12634,x12631),f413(x12633,x12634,x12632)) % 165.30/165.06 [1264]~E(x12641,x12642)+E(f275(x12641,x12643,x12644,x12645,x12646),f275(x12642,x12643,x12644,x12645,x12646)) % 165.30/165.06 [1265]~E(x12651,x12652)+E(f275(x12653,x12651,x12654,x12655,x12656),f275(x12653,x12652,x12654,x12655,x12656)) % 165.30/165.06 [1266]~E(x12661,x12662)+E(f275(x12663,x12664,x12661,x12665,x12666),f275(x12663,x12664,x12662,x12665,x12666)) % 165.30/165.06 [1267]~E(x12671,x12672)+E(f275(x12673,x12674,x12675,x12671,x12676),f275(x12673,x12674,x12675,x12672,x12676)) % 165.30/165.06 [1268]~E(x12681,x12682)+E(f275(x12683,x12684,x12685,x12686,x12681),f275(x12683,x12684,x12685,x12686,x12682)) % 165.30/165.06 [1269]~E(x12691,x12692)+E(f401(x12691,x12693,x12694,x12695),f401(x12692,x12693,x12694,x12695)) % 165.30/165.06 [1270]~E(x12701,x12702)+E(f401(x12703,x12701,x12704,x12705),f401(x12703,x12702,x12704,x12705)) % 165.30/165.06 [1271]~E(x12711,x12712)+E(f401(x12713,x12714,x12711,x12715),f401(x12713,x12714,x12712,x12715)) % 165.30/165.06 [1272]~E(x12721,x12722)+E(f401(x12723,x12724,x12725,x12721),f401(x12723,x12724,x12725,x12722)) % 165.30/165.06 [1273]~E(x12731,x12732)+E(f474(x12731,x12733,x12734,x12735,x12736),f474(x12732,x12733,x12734,x12735,x12736)) % 165.30/165.06 [1274]~E(x12741,x12742)+E(f474(x12743,x12741,x12744,x12745,x12746),f474(x12743,x12742,x12744,x12745,x12746)) % 165.30/165.06 [1275]~E(x12751,x12752)+E(f474(x12753,x12754,x12751,x12755,x12756),f474(x12753,x12754,x12752,x12755,x12756)) % 165.30/165.06 [1276]~E(x12761,x12762)+E(f474(x12763,x12764,x12765,x12761,x12766),f474(x12763,x12764,x12765,x12762,x12766)) % 165.30/165.06 [1277]~E(x12771,x12772)+E(f474(x12773,x12774,x12775,x12776,x12771),f474(x12773,x12774,x12775,x12776,x12772)) % 165.30/165.06 [1278]~E(x12781,x12782)+E(f214(x12781,x12783),f214(x12782,x12783)) % 165.30/165.06 [1279]~E(x12791,x12792)+E(f214(x12793,x12791),f214(x12793,x12792)) % 165.30/165.06 [1280]~E(x12801,x12802)+E(f53(x12801,x12803),f53(x12802,x12803)) % 165.30/165.06 [1281]~E(x12811,x12812)+E(f53(x12813,x12811),f53(x12813,x12812)) % 165.30/165.06 [1282]~E(x12821,x12822)+E(f136(x12821),f136(x12822)) % 165.30/165.06 [1283]~E(x12831,x12832)+E(f475(x12831,x12833,x12834,x12835),f475(x12832,x12833,x12834,x12835)) % 165.30/165.06 [1284]~E(x12841,x12842)+E(f475(x12843,x12841,x12844,x12845),f475(x12843,x12842,x12844,x12845)) % 165.30/165.06 [1285]~E(x12851,x12852)+E(f475(x12853,x12854,x12851,x12855),f475(x12853,x12854,x12852,x12855)) % 165.30/165.06 [1286]~E(x12861,x12862)+E(f475(x12863,x12864,x12865,x12861),f475(x12863,x12864,x12865,x12862)) % 165.30/165.06 [1287]~E(x12871,x12872)+E(f836(x12871,x12873),f836(x12872,x12873)) % 165.30/165.06 [1288]~E(x12881,x12882)+E(f836(x12883,x12881),f836(x12883,x12882)) % 165.30/165.06 [1289]~E(x12891,x12892)+E(f455(x12891,x12893,x12894),f455(x12892,x12893,x12894)) % 165.30/165.06 [1290]~E(x12901,x12902)+E(f455(x12903,x12901,x12904),f455(x12903,x12902,x12904)) % 165.30/165.06 [1291]~E(x12911,x12912)+E(f455(x12913,x12914,x12911),f455(x12913,x12914,x12912)) % 165.30/165.06 [1292]~E(x12921,x12922)+E(f434(x12921,x12923,x12924,x12925,x12926,x12927),f434(x12922,x12923,x12924,x12925,x12926,x12927)) % 165.30/165.06 [1293]~E(x12931,x12932)+E(f434(x12933,x12931,x12934,x12935,x12936,x12937),f434(x12933,x12932,x12934,x12935,x12936,x12937)) % 165.30/165.06 [1294]~E(x12941,x12942)+E(f434(x12943,x12944,x12941,x12945,x12946,x12947),f434(x12943,x12944,x12942,x12945,x12946,x12947)) % 165.30/165.06 [1295]~E(x12951,x12952)+E(f434(x12953,x12954,x12955,x12951,x12956,x12957),f434(x12953,x12954,x12955,x12952,x12956,x12957)) % 165.30/165.06 [1296]~E(x12961,x12962)+E(f434(x12963,x12964,x12965,x12966,x12961,x12967),f434(x12963,x12964,x12965,x12966,x12962,x12967)) % 165.30/165.06 [1297]~E(x12971,x12972)+E(f434(x12973,x12974,x12975,x12976,x12977,x12971),f434(x12973,x12974,x12975,x12976,x12977,x12972)) % 165.30/165.06 [1298]~E(x12981,x12982)+E(f744(x12981,x12983,x12984,x12985,x12986),f744(x12982,x12983,x12984,x12985,x12986)) % 165.30/165.06 [1299]~E(x12991,x12992)+E(f744(x12993,x12991,x12994,x12995,x12996),f744(x12993,x12992,x12994,x12995,x12996)) % 165.30/165.06 [1300]~E(x13001,x13002)+E(f744(x13003,x13004,x13001,x13005,x13006),f744(x13003,x13004,x13002,x13005,x13006)) % 165.30/165.06 [1301]~E(x13011,x13012)+E(f744(x13013,x13014,x13015,x13011,x13016),f744(x13013,x13014,x13015,x13012,x13016)) % 165.30/165.06 [1302]~E(x13021,x13022)+E(f744(x13023,x13024,x13025,x13026,x13021),f744(x13023,x13024,x13025,x13026,x13022)) % 165.30/165.06 [1303]~E(x13031,x13032)+E(f487(x13031,x13033,x13034),f487(x13032,x13033,x13034)) % 165.30/165.06 [1304]~E(x13041,x13042)+E(f487(x13043,x13041,x13044),f487(x13043,x13042,x13044)) % 165.30/165.06 [1305]~E(x13051,x13052)+E(f487(x13053,x13054,x13051),f487(x13053,x13054,x13052)) % 165.30/165.06 [1306]~E(x13061,x13062)+E(f232(x13061,x13063),f232(x13062,x13063)) % 165.30/165.06 [1307]~E(x13071,x13072)+E(f232(x13073,x13071),f232(x13073,x13072)) % 165.30/165.06 [1308]~E(x13081,x13082)+E(f449(x13081),f449(x13082)) % 165.30/165.06 [1309]~E(x13091,x13092)+E(f642(x13091,x13093,x13094),f642(x13092,x13093,x13094)) % 165.30/165.06 [1310]~E(x13101,x13102)+E(f642(x13103,x13101,x13104),f642(x13103,x13102,x13104)) % 165.30/165.06 [1311]~E(x13111,x13112)+E(f642(x13113,x13114,x13111),f642(x13113,x13114,x13112)) % 165.30/165.06 [1312]~E(x13121,x13122)+E(f731(x13121,x13123,x13124,x13125,x13126),f731(x13122,x13123,x13124,x13125,x13126)) % 165.30/165.06 [1313]~E(x13131,x13132)+E(f731(x13133,x13131,x13134,x13135,x13136),f731(x13133,x13132,x13134,x13135,x13136)) % 165.30/165.06 [1314]~E(x13141,x13142)+E(f731(x13143,x13144,x13141,x13145,x13146),f731(x13143,x13144,x13142,x13145,x13146)) % 165.30/165.06 [1315]~E(x13151,x13152)+E(f731(x13153,x13154,x13155,x13151,x13156),f731(x13153,x13154,x13155,x13152,x13156)) % 165.30/165.06 [1316]~E(x13161,x13162)+E(f731(x13163,x13164,x13165,x13166,x13161),f731(x13163,x13164,x13165,x13166,x13162)) % 165.30/165.06 [1317]~E(x13171,x13172)+E(f516(x13171),f516(x13172)) % 165.30/165.06 [1318]~E(x13181,x13182)+E(f689(x13181,x13183),f689(x13182,x13183)) % 165.30/165.06 [1319]~E(x13191,x13192)+E(f689(x13193,x13191),f689(x13193,x13192)) % 165.30/165.06 [1320]~E(x13201,x13202)+E(f414(x13201,x13203,x13204,x13205,x13206),f414(x13202,x13203,x13204,x13205,x13206)) % 165.30/165.06 [1321]~E(x13211,x13212)+E(f414(x13213,x13211,x13214,x13215,x13216),f414(x13213,x13212,x13214,x13215,x13216)) % 165.30/165.06 [1322]~E(x13221,x13222)+E(f414(x13223,x13224,x13221,x13225,x13226),f414(x13223,x13224,x13222,x13225,x13226)) % 165.30/165.06 [1323]~E(x13231,x13232)+E(f414(x13233,x13234,x13235,x13231,x13236),f414(x13233,x13234,x13235,x13232,x13236)) % 165.30/165.06 [1324]~E(x13241,x13242)+E(f414(x13243,x13244,x13245,x13246,x13241),f414(x13243,x13244,x13245,x13246,x13242)) % 165.30/165.06 [1325]~E(x13251,x13252)+E(f829(x13251,x13253,x13254,x13255,x13256),f829(x13252,x13253,x13254,x13255,x13256)) % 165.30/165.06 [1326]~E(x13261,x13262)+E(f829(x13263,x13261,x13264,x13265,x13266),f829(x13263,x13262,x13264,x13265,x13266)) % 165.30/165.06 [1327]~E(x13271,x13272)+E(f829(x13273,x13274,x13271,x13275,x13276),f829(x13273,x13274,x13272,x13275,x13276)) % 165.30/165.06 [1328]~E(x13281,x13282)+E(f829(x13283,x13284,x13285,x13281,x13286),f829(x13283,x13284,x13285,x13282,x13286)) % 165.30/165.06 [1329]~E(x13291,x13292)+E(f829(x13293,x13294,x13295,x13296,x13291),f829(x13293,x13294,x13295,x13296,x13292)) % 165.30/165.06 [1330]~E(x13301,x13302)+E(f17(x13301,x13303,x13304,x13305),f17(x13302,x13303,x13304,x13305)) % 165.30/165.06 [1331]~E(x13311,x13312)+E(f17(x13313,x13311,x13314,x13315),f17(x13313,x13312,x13314,x13315)) % 165.30/165.06 [1332]~E(x13321,x13322)+E(f17(x13323,x13324,x13321,x13325),f17(x13323,x13324,x13322,x13325)) % 165.30/165.06 [1333]~E(x13331,x13332)+E(f17(x13333,x13334,x13335,x13331),f17(x13333,x13334,x13335,x13332)) % 165.30/165.06 [1334]~E(x13341,x13342)+E(f645(x13341,x13343,x13344,x13345),f645(x13342,x13343,x13344,x13345)) % 165.30/165.06 [1335]~E(x13351,x13352)+E(f645(x13353,x13351,x13354,x13355),f645(x13353,x13352,x13354,x13355)) % 165.30/165.06 [1336]~E(x13361,x13362)+E(f645(x13363,x13364,x13361,x13365),f645(x13363,x13364,x13362,x13365)) % 165.30/165.06 [1337]~E(x13371,x13372)+E(f645(x13373,x13374,x13375,x13371),f645(x13373,x13374,x13375,x13372)) % 165.30/165.06 [1338]~E(x13381,x13382)+E(f658(x13381,x13383,x13384,x13385,x13386),f658(x13382,x13383,x13384,x13385,x13386)) % 165.30/165.06 [1339]~E(x13391,x13392)+E(f658(x13393,x13391,x13394,x13395,x13396),f658(x13393,x13392,x13394,x13395,x13396)) % 165.30/165.06 [1340]~E(x13401,x13402)+E(f658(x13403,x13404,x13401,x13405,x13406),f658(x13403,x13404,x13402,x13405,x13406)) % 165.30/165.06 [1341]~E(x13411,x13412)+E(f658(x13413,x13414,x13415,x13411,x13416),f658(x13413,x13414,x13415,x13412,x13416)) % 165.30/165.06 [1342]~E(x13421,x13422)+E(f658(x13423,x13424,x13425,x13426,x13421),f658(x13423,x13424,x13425,x13426,x13422)) % 165.30/165.06 [1343]~E(x13431,x13432)+E(f422(x13431,x13433,x13434),f422(x13432,x13433,x13434)) % 165.30/165.06 [1344]~E(x13441,x13442)+E(f422(x13443,x13441,x13444),f422(x13443,x13442,x13444)) % 165.30/165.06 [1345]~E(x13451,x13452)+E(f422(x13453,x13454,x13451),f422(x13453,x13454,x13452)) % 165.30/165.06 [1346]~E(x13461,x13462)+E(f557(x13461,x13463,x13464),f557(x13462,x13463,x13464)) % 165.30/165.06 [1347]~E(x13471,x13472)+E(f557(x13473,x13471,x13474),f557(x13473,x13472,x13474)) % 165.30/165.06 [1348]~E(x13481,x13482)+E(f557(x13483,x13484,x13481),f557(x13483,x13484,x13482)) % 165.30/165.06 [1349]~E(x13491,x13492)+E(f439(x13491,x13493,x13494,x13495,x13496,x13497,x13498,x13499,x134910),f439(x13492,x13493,x13494,x13495,x13496,x13497,x13498,x13499,x134910)) % 165.30/165.06 [1350]~E(x13501,x13502)+E(f439(x13503,x13501,x13504,x13505,x13506,x13507,x13508,x13509,x135010),f439(x13503,x13502,x13504,x13505,x13506,x13507,x13508,x13509,x135010)) % 165.30/165.06 [1351]~E(x13511,x13512)+E(f439(x13513,x13514,x13511,x13515,x13516,x13517,x13518,x13519,x135110),f439(x13513,x13514,x13512,x13515,x13516,x13517,x13518,x13519,x135110)) % 165.30/165.06 [1352]~E(x13521,x13522)+E(f439(x13523,x13524,x13525,x13521,x13526,x13527,x13528,x13529,x135210),f439(x13523,x13524,x13525,x13522,x13526,x13527,x13528,x13529,x135210)) % 165.30/165.06 [1353]~E(x13531,x13532)+E(f439(x13533,x13534,x13535,x13536,x13531,x13537,x13538,x13539,x135310),f439(x13533,x13534,x13535,x13536,x13532,x13537,x13538,x13539,x135310)) % 165.30/165.06 [1354]~E(x13541,x13542)+E(f439(x13543,x13544,x13545,x13546,x13547,x13541,x13548,x13549,x135410),f439(x13543,x13544,x13545,x13546,x13547,x13542,x13548,x13549,x135410)) % 165.30/165.06 [1355]~E(x13551,x13552)+E(f439(x13553,x13554,x13555,x13556,x13557,x13558,x13551,x13559,x135510),f439(x13553,x13554,x13555,x13556,x13557,x13558,x13552,x13559,x135510)) % 165.30/165.06 [1356]~E(x13561,x13562)+E(f439(x13563,x13564,x13565,x13566,x13567,x13568,x13569,x13561,x135610),f439(x13563,x13564,x13565,x13566,x13567,x13568,x13569,x13562,x135610)) % 165.30/165.06 [1357]~E(x13571,x13572)+E(f439(x13573,x13574,x13575,x13576,x13577,x13578,x13579,x135710,x13571),f439(x13573,x13574,x13575,x13576,x13577,x13578,x13579,x135710,x13572)) % 165.30/165.06 [1358]~E(x13581,x13582)+E(f553(x13581,x13583,x13584,x13585),f553(x13582,x13583,x13584,x13585)) % 165.30/165.06 [1359]~E(x13591,x13592)+E(f553(x13593,x13591,x13594,x13595),f553(x13593,x13592,x13594,x13595)) % 165.30/165.06 [1360]~E(x13601,x13602)+E(f553(x13603,x13604,x13601,x13605),f553(x13603,x13604,x13602,x13605)) % 165.30/165.06 [1361]~E(x13611,x13612)+E(f553(x13613,x13614,x13615,x13611),f553(x13613,x13614,x13615,x13612)) % 165.30/165.06 [1362]~E(x13621,x13622)+E(f609(x13621,x13623),f609(x13622,x13623)) % 165.30/165.06 [1363]~E(x13631,x13632)+E(f609(x13633,x13631),f609(x13633,x13632)) % 165.30/165.06 [1364]~E(x13641,x13642)+E(f213(x13641),f213(x13642)) % 165.30/165.06 [1365]~E(x13651,x13652)+E(f355(x13651,x13653,x13654),f355(x13652,x13653,x13654)) % 165.30/165.06 [1366]~E(x13661,x13662)+E(f355(x13663,x13661,x13664),f355(x13663,x13662,x13664)) % 165.30/165.06 [1367]~E(x13671,x13672)+E(f355(x13673,x13674,x13671),f355(x13673,x13674,x13672)) % 165.30/165.06 [1368]~E(x13681,x13682)+E(f686(x13681,x13683),f686(x13682,x13683)) % 165.30/165.06 [1369]~E(x13691,x13692)+E(f686(x13693,x13691),f686(x13693,x13692)) % 165.30/165.06 [1370]~E(x13701,x13702)+E(f360(x13701),f360(x13702)) % 165.30/165.06 [1371]~E(x13711,x13712)+E(f297(x13711,x13713,x13714,x13715,x13716),f297(x13712,x13713,x13714,x13715,x13716)) % 165.30/165.06 [1372]~E(x13721,x13722)+E(f297(x13723,x13721,x13724,x13725,x13726),f297(x13723,x13722,x13724,x13725,x13726)) % 165.30/165.06 [1373]~E(x13731,x13732)+E(f297(x13733,x13734,x13731,x13735,x13736),f297(x13733,x13734,x13732,x13735,x13736)) % 165.30/165.06 [1374]~E(x13741,x13742)+E(f297(x13743,x13744,x13745,x13741,x13746),f297(x13743,x13744,x13745,x13742,x13746)) % 165.30/165.06 [1375]~E(x13751,x13752)+E(f297(x13753,x13754,x13755,x13756,x13751),f297(x13753,x13754,x13755,x13756,x13752)) % 165.30/165.06 [1376]~E(x13761,x13762)+E(f424(x13761,x13763,x13764,x13765,x13766),f424(x13762,x13763,x13764,x13765,x13766)) % 165.30/165.06 [1377]~E(x13771,x13772)+E(f424(x13773,x13771,x13774,x13775,x13776),f424(x13773,x13772,x13774,x13775,x13776)) % 165.30/165.06 [1378]~E(x13781,x13782)+E(f424(x13783,x13784,x13781,x13785,x13786),f424(x13783,x13784,x13782,x13785,x13786)) % 165.30/165.06 [1379]~E(x13791,x13792)+E(f424(x13793,x13794,x13795,x13791,x13796),f424(x13793,x13794,x13795,x13792,x13796)) % 165.30/165.06 [1380]~E(x13801,x13802)+E(f424(x13803,x13804,x13805,x13806,x13801),f424(x13803,x13804,x13805,x13806,x13802)) % 165.30/165.06 [1381]~E(x13811,x13812)+E(f316(x13811,x13813,x13814),f316(x13812,x13813,x13814)) % 165.30/165.06 [1382]~E(x13821,x13822)+E(f316(x13823,x13821,x13824),f316(x13823,x13822,x13824)) % 165.30/165.06 [1383]~E(x13831,x13832)+E(f316(x13833,x13834,x13831),f316(x13833,x13834,x13832)) % 165.30/165.06 [1384]~E(x13841,x13842)+E(f54(x13841,x13843),f54(x13842,x13843)) % 165.30/165.06 [1385]~E(x13851,x13852)+E(f54(x13853,x13851),f54(x13853,x13852)) % 165.30/165.06 [1386]~E(x13861,x13862)+E(f491(x13861,x13863,x13864,x13865,x13866),f491(x13862,x13863,x13864,x13865,x13866)) % 165.30/165.06 [1387]~E(x13871,x13872)+E(f491(x13873,x13871,x13874,x13875,x13876),f491(x13873,x13872,x13874,x13875,x13876)) % 165.30/165.06 [1388]~E(x13881,x13882)+E(f491(x13883,x13884,x13881,x13885,x13886),f491(x13883,x13884,x13882,x13885,x13886)) % 165.30/165.06 [1389]~E(x13891,x13892)+E(f491(x13893,x13894,x13895,x13891,x13896),f491(x13893,x13894,x13895,x13892,x13896)) % 165.30/165.06 [1390]~E(x13901,x13902)+E(f491(x13903,x13904,x13905,x13906,x13901),f491(x13903,x13904,x13905,x13906,x13902)) % 165.30/165.06 [1391]~E(x13911,x13912)+E(f352(x13911,x13913,x13914,x13915),f352(x13912,x13913,x13914,x13915)) % 165.30/165.06 [1392]~E(x13921,x13922)+E(f352(x13923,x13921,x13924,x13925),f352(x13923,x13922,x13924,x13925)) % 165.30/165.06 [1393]~E(x13931,x13932)+E(f352(x13933,x13934,x13931,x13935),f352(x13933,x13934,x13932,x13935)) % 165.30/165.06 [1394]~E(x13941,x13942)+E(f352(x13943,x13944,x13945,x13941),f352(x13943,x13944,x13945,x13942)) % 165.30/165.06 [1395]~E(x13951,x13952)+E(f492(x13951,x13953,x13954,x13955,x13956,x13957,x13958),f492(x13952,x13953,x13954,x13955,x13956,x13957,x13958)) % 165.30/165.06 [1396]~E(x13961,x13962)+E(f492(x13963,x13961,x13964,x13965,x13966,x13967,x13968),f492(x13963,x13962,x13964,x13965,x13966,x13967,x13968)) % 165.30/165.06 [1397]~E(x13971,x13972)+E(f492(x13973,x13974,x13971,x13975,x13976,x13977,x13978),f492(x13973,x13974,x13972,x13975,x13976,x13977,x13978)) % 165.30/165.06 [1398]~E(x13981,x13982)+E(f492(x13983,x13984,x13985,x13981,x13986,x13987,x13988),f492(x13983,x13984,x13985,x13982,x13986,x13987,x13988)) % 165.30/165.06 [1399]~E(x13991,x13992)+E(f492(x13993,x13994,x13995,x13996,x13991,x13997,x13998),f492(x13993,x13994,x13995,x13996,x13992,x13997,x13998)) % 165.30/165.06 [1400]~E(x14001,x14002)+E(f492(x14003,x14004,x14005,x14006,x14007,x14001,x14008),f492(x14003,x14004,x14005,x14006,x14007,x14002,x14008)) % 165.30/165.06 [1401]~E(x14011,x14012)+E(f492(x14013,x14014,x14015,x14016,x14017,x14018,x14011),f492(x14013,x14014,x14015,x14016,x14017,x14018,x14012)) % 165.30/165.06 [1402]~E(x14021,x14022)+E(f124(x14021,x14023),f124(x14022,x14023)) % 165.30/165.06 [1403]~E(x14031,x14032)+E(f124(x14033,x14031),f124(x14033,x14032)) % 165.30/165.06 [1404]~E(x14041,x14042)+E(f207(x14041,x14043,x14044,x14045),f207(x14042,x14043,x14044,x14045)) % 165.30/165.06 [1405]~E(x14051,x14052)+E(f207(x14053,x14051,x14054,x14055),f207(x14053,x14052,x14054,x14055)) % 165.30/165.06 [1406]~E(x14061,x14062)+E(f207(x14063,x14064,x14061,x14065),f207(x14063,x14064,x14062,x14065)) % 165.30/165.06 [1407]~E(x14071,x14072)+E(f207(x14073,x14074,x14075,x14071),f207(x14073,x14074,x14075,x14072)) % 165.30/165.06 [1408]~E(x14081,x14082)+E(f779(x14081,x14083,x14084,x14085,x14086,x14087,x14088),f779(x14082,x14083,x14084,x14085,x14086,x14087,x14088)) % 165.30/165.06 [1409]~E(x14091,x14092)+E(f779(x14093,x14091,x14094,x14095,x14096,x14097,x14098),f779(x14093,x14092,x14094,x14095,x14096,x14097,x14098)) % 165.30/165.06 [1410]~E(x14101,x14102)+E(f779(x14103,x14104,x14101,x14105,x14106,x14107,x14108),f779(x14103,x14104,x14102,x14105,x14106,x14107,x14108)) % 165.30/165.06 [1411]~E(x14111,x14112)+E(f779(x14113,x14114,x14115,x14111,x14116,x14117,x14118),f779(x14113,x14114,x14115,x14112,x14116,x14117,x14118)) % 165.30/165.06 [1412]~E(x14121,x14122)+E(f779(x14123,x14124,x14125,x14126,x14121,x14127,x14128),f779(x14123,x14124,x14125,x14126,x14122,x14127,x14128)) % 165.30/165.06 [1413]~E(x14131,x14132)+E(f779(x14133,x14134,x14135,x14136,x14137,x14131,x14138),f779(x14133,x14134,x14135,x14136,x14137,x14132,x14138)) % 165.30/165.06 [1414]~E(x14141,x14142)+E(f779(x14143,x14144,x14145,x14146,x14147,x14148,x14141),f779(x14143,x14144,x14145,x14146,x14147,x14148,x14142)) % 165.30/165.06 [1415]~E(x14151,x14152)+E(f571(x14151,x14153),f571(x14152,x14153)) % 165.30/165.06 [1416]~E(x14161,x14162)+E(f571(x14163,x14161),f571(x14163,x14162)) % 165.30/165.06 [1417]~E(x14171,x14172)+E(f97(x14171,x14173,x14174,x14175),f97(x14172,x14173,x14174,x14175)) % 165.30/165.06 [1418]~E(x14181,x14182)+E(f97(x14183,x14181,x14184,x14185),f97(x14183,x14182,x14184,x14185)) % 165.30/165.06 [1419]~E(x14191,x14192)+E(f97(x14193,x14194,x14191,x14195),f97(x14193,x14194,x14192,x14195)) % 165.30/165.06 [1420]~E(x14201,x14202)+E(f97(x14203,x14204,x14205,x14201),f97(x14203,x14204,x14205,x14202)) % 165.30/165.06 [1421]~E(x14211,x14212)+E(f558(x14211,x14213,x14214,x14215,x14216),f558(x14212,x14213,x14214,x14215,x14216)) % 165.30/165.06 [1422]~E(x14221,x14222)+E(f558(x14223,x14221,x14224,x14225,x14226),f558(x14223,x14222,x14224,x14225,x14226)) % 165.30/165.06 [1423]~E(x14231,x14232)+E(f558(x14233,x14234,x14231,x14235,x14236),f558(x14233,x14234,x14232,x14235,x14236)) % 165.30/165.06 [1424]~E(x14241,x14242)+E(f558(x14243,x14244,x14245,x14241,x14246),f558(x14243,x14244,x14245,x14242,x14246)) % 165.30/165.06 [1425]~E(x14251,x14252)+E(f558(x14253,x14254,x14255,x14256,x14251),f558(x14253,x14254,x14255,x14256,x14252)) % 165.30/165.06 [1426]~E(x14261,x14262)+E(f370(x14261,x14263,x14264),f370(x14262,x14263,x14264)) % 165.30/165.06 [1427]~E(x14271,x14272)+E(f370(x14273,x14271,x14274),f370(x14273,x14272,x14274)) % 165.30/165.06 [1428]~E(x14281,x14282)+E(f370(x14283,x14284,x14281),f370(x14283,x14284,x14282)) % 165.30/165.06 [1429]~E(x14291,x14292)+E(f774(x14291,x14293),f774(x14292,x14293)) % 165.30/165.06 [1430]~E(x14301,x14302)+E(f774(x14303,x14301),f774(x14303,x14302)) % 165.30/165.06 [1431]~E(x14311,x14312)+E(f233(x14311,x14313,x14314),f233(x14312,x14313,x14314)) % 165.30/165.06 [1432]~E(x14321,x14322)+E(f233(x14323,x14321,x14324),f233(x14323,x14322,x14324)) % 165.30/165.06 [1433]~E(x14331,x14332)+E(f233(x14333,x14334,x14331),f233(x14333,x14334,x14332)) % 165.30/165.06 [1434]~E(x14341,x14342)+E(f227(x14341,x14343),f227(x14342,x14343)) % 165.30/165.06 [1435]~E(x14351,x14352)+E(f227(x14353,x14351),f227(x14353,x14352)) % 165.30/165.06 [1436]~E(x14361,x14362)+E(f617(x14361,x14363,x14364),f617(x14362,x14363,x14364)) % 165.30/165.06 [1437]~E(x14371,x14372)+E(f617(x14373,x14371,x14374),f617(x14373,x14372,x14374)) % 165.30/165.06 [1438]~E(x14381,x14382)+E(f617(x14383,x14384,x14381),f617(x14383,x14384,x14382)) % 165.30/165.06 [1439]~E(x14391,x14392)+E(f602(x14391,x14393,x14394,x14395,x14396),f602(x14392,x14393,x14394,x14395,x14396)) % 165.30/165.06 [1440]~E(x14401,x14402)+E(f602(x14403,x14401,x14404,x14405,x14406),f602(x14403,x14402,x14404,x14405,x14406)) % 165.30/165.06 [1441]~E(x14411,x14412)+E(f602(x14413,x14414,x14411,x14415,x14416),f602(x14413,x14414,x14412,x14415,x14416)) % 165.30/165.06 [1442]~E(x14421,x14422)+E(f602(x14423,x14424,x14425,x14421,x14426),f602(x14423,x14424,x14425,x14422,x14426)) % 165.30/165.06 [1443]~E(x14431,x14432)+E(f602(x14433,x14434,x14435,x14436,x14431),f602(x14433,x14434,x14435,x14436,x14432)) % 165.30/165.06 [1444]~E(x14441,x14442)+E(f776(x14441,x14443,x14444,x14445),f776(x14442,x14443,x14444,x14445)) % 165.30/165.06 [1445]~E(x14451,x14452)+E(f776(x14453,x14451,x14454,x14455),f776(x14453,x14452,x14454,x14455)) % 165.30/165.06 [1446]~E(x14461,x14462)+E(f776(x14463,x14464,x14461,x14465),f776(x14463,x14464,x14462,x14465)) % 165.30/165.06 [1447]~E(x14471,x14472)+E(f776(x14473,x14474,x14475,x14471),f776(x14473,x14474,x14475,x14472)) % 165.30/165.06 [1448]~E(x14481,x14482)+E(f359(x14481),f359(x14482)) % 165.30/165.06 [1449]~E(x14491,x14492)+E(f452(x14491,x14493,x14494,x14495),f452(x14492,x14493,x14494,x14495)) % 165.30/165.06 [1450]~E(x14501,x14502)+E(f452(x14503,x14501,x14504,x14505),f452(x14503,x14502,x14504,x14505)) % 165.30/165.06 [1451]~E(x14511,x14512)+E(f452(x14513,x14514,x14511,x14515),f452(x14513,x14514,x14512,x14515)) % 165.30/165.06 [1452]~E(x14521,x14522)+E(f452(x14523,x14524,x14525,x14521),f452(x14523,x14524,x14525,x14522)) % 165.30/165.06 [1453]~E(x14531,x14532)+E(f562(x14531,x14533,x14534,x14535,x14536),f562(x14532,x14533,x14534,x14535,x14536)) % 165.30/165.06 [1454]~E(x14541,x14542)+E(f562(x14543,x14541,x14544,x14545,x14546),f562(x14543,x14542,x14544,x14545,x14546)) % 165.30/165.06 [1455]~E(x14551,x14552)+E(f562(x14553,x14554,x14551,x14555,x14556),f562(x14553,x14554,x14552,x14555,x14556)) % 165.30/165.06 [1456]~E(x14561,x14562)+E(f562(x14563,x14564,x14565,x14561,x14566),f562(x14563,x14564,x14565,x14562,x14566)) % 165.30/165.06 [1457]~E(x14571,x14572)+E(f562(x14573,x14574,x14575,x14576,x14571),f562(x14573,x14574,x14575,x14576,x14572)) % 165.30/165.06 [1458]~E(x14581,x14582)+E(f792(x14581,x14583),f792(x14582,x14583)) % 165.30/165.06 [1459]~E(x14591,x14592)+E(f792(x14593,x14591),f792(x14593,x14592)) % 165.30/165.06 [1460]~E(x14601,x14602)+E(f674(x14601,x14603,x14604,x14605),f674(x14602,x14603,x14604,x14605)) % 165.30/165.06 [1461]~E(x14611,x14612)+E(f674(x14613,x14611,x14614,x14615),f674(x14613,x14612,x14614,x14615)) % 165.30/165.06 [1462]~E(x14621,x14622)+E(f674(x14623,x14624,x14621,x14625),f674(x14623,x14624,x14622,x14625)) % 165.30/165.06 [1463]~E(x14631,x14632)+E(f674(x14633,x14634,x14635,x14631),f674(x14633,x14634,x14635,x14632)) % 165.30/165.06 [1464]~E(x14641,x14642)+E(f583(x14641,x14643,x14644,x14645,x14646),f583(x14642,x14643,x14644,x14645,x14646)) % 165.30/165.06 [1465]~E(x14651,x14652)+E(f583(x14653,x14651,x14654,x14655,x14656),f583(x14653,x14652,x14654,x14655,x14656)) % 165.30/165.06 [1466]~E(x14661,x14662)+E(f583(x14663,x14664,x14661,x14665,x14666),f583(x14663,x14664,x14662,x14665,x14666)) % 165.30/165.06 [1467]~E(x14671,x14672)+E(f583(x14673,x14674,x14675,x14671,x14676),f583(x14673,x14674,x14675,x14672,x14676)) % 165.30/165.06 [1468]~E(x14681,x14682)+E(f583(x14683,x14684,x14685,x14686,x14681),f583(x14683,x14684,x14685,x14686,x14682)) % 165.30/165.06 [1469]~E(x14691,x14692)+E(f147(x14691,x14693),f147(x14692,x14693)) % 165.30/165.06 [1470]~E(x14701,x14702)+E(f147(x14703,x14701),f147(x14703,x14702)) % 165.30/165.06 [1471]~E(x14711,x14712)+E(f279(x14711,x14713),f279(x14712,x14713)) % 165.30/165.06 [1472]~E(x14721,x14722)+E(f279(x14723,x14721),f279(x14723,x14722)) % 165.30/165.06 [1473]~E(x14731,x14732)+E(f480(x14731,x14733,x14734,x14735),f480(x14732,x14733,x14734,x14735)) % 165.30/165.06 [1474]~E(x14741,x14742)+E(f480(x14743,x14741,x14744,x14745),f480(x14743,x14742,x14744,x14745)) % 165.30/165.06 [1475]~E(x14751,x14752)+E(f480(x14753,x14754,x14751,x14755),f480(x14753,x14754,x14752,x14755)) % 165.30/165.06 [1476]~E(x14761,x14762)+E(f480(x14763,x14764,x14765,x14761),f480(x14763,x14764,x14765,x14762)) % 165.30/165.06 [1477]~E(x14771,x14772)+E(f240(x14771,x14773,x14774),f240(x14772,x14773,x14774)) % 165.30/165.06 [1478]~E(x14781,x14782)+E(f240(x14783,x14781,x14784),f240(x14783,x14782,x14784)) % 165.30/165.06 [1479]~E(x14791,x14792)+E(f240(x14793,x14794,x14791),f240(x14793,x14794,x14792)) % 165.30/165.06 [1480]~E(x14801,x14802)+E(f588(x14801,x14803,x14804,x14805),f588(x14802,x14803,x14804,x14805)) % 165.30/165.06 [1481]~E(x14811,x14812)+E(f588(x14813,x14811,x14814,x14815),f588(x14813,x14812,x14814,x14815)) % 165.30/165.06 [1482]~E(x14821,x14822)+E(f588(x14823,x14824,x14821,x14825),f588(x14823,x14824,x14822,x14825)) % 165.30/165.06 [1483]~E(x14831,x14832)+E(f588(x14833,x14834,x14835,x14831),f588(x14833,x14834,x14835,x14832)) % 165.30/165.06 [1484]~E(x14841,x14842)+E(f784(x14841,x14843,x14844,x14845),f784(x14842,x14843,x14844,x14845)) % 165.30/165.06 [1485]~E(x14851,x14852)+E(f784(x14853,x14851,x14854,x14855),f784(x14853,x14852,x14854,x14855)) % 165.30/165.06 [1486]~E(x14861,x14862)+E(f784(x14863,x14864,x14861,x14865),f784(x14863,x14864,x14862,x14865)) % 165.30/165.06 [1487]~E(x14871,x14872)+E(f784(x14873,x14874,x14875,x14871),f784(x14873,x14874,x14875,x14872)) % 165.30/165.06 [1488]~E(x14881,x14882)+E(f590(x14881,x14883,x14884,x14885),f590(x14882,x14883,x14884,x14885)) % 165.30/165.06 [1489]~E(x14891,x14892)+E(f590(x14893,x14891,x14894,x14895),f590(x14893,x14892,x14894,x14895)) % 165.30/165.06 [1490]~E(x14901,x14902)+E(f590(x14903,x14904,x14901,x14905),f590(x14903,x14904,x14902,x14905)) % 165.30/165.06 [1491]~E(x14911,x14912)+E(f590(x14913,x14914,x14915,x14911),f590(x14913,x14914,x14915,x14912)) % 165.30/165.06 [1492]~E(x14921,x14922)+E(f800(x14921,x14923,x14924,x14925),f800(x14922,x14923,x14924,x14925)) % 165.30/165.06 [1493]~E(x14931,x14932)+E(f800(x14933,x14931,x14934,x14935),f800(x14933,x14932,x14934,x14935)) % 165.30/165.06 [1494]~E(x14941,x14942)+E(f800(x14943,x14944,x14941,x14945),f800(x14943,x14944,x14942,x14945)) % 165.30/165.06 [1495]~E(x14951,x14952)+E(f800(x14953,x14954,x14955,x14951),f800(x14953,x14954,x14955,x14952)) % 165.30/165.06 [1496]~E(x14961,x14962)+E(f123(x14961,x14963,x14964,x14965),f123(x14962,x14963,x14964,x14965)) % 165.30/165.06 [1497]~E(x14971,x14972)+E(f123(x14973,x14971,x14974,x14975),f123(x14973,x14972,x14974,x14975)) % 165.30/165.06 [1498]~E(x14981,x14982)+E(f123(x14983,x14984,x14981,x14985),f123(x14983,x14984,x14982,x14985)) % 165.30/165.06 [1499]~E(x14991,x14992)+E(f123(x14993,x14994,x14995,x14991),f123(x14993,x14994,x14995,x14992)) % 165.30/165.06 [1500]~E(x15001,x15002)+E(f121(x15001,x15003,x15004),f121(x15002,x15003,x15004)) % 165.30/165.06 [1501]~E(x15011,x15012)+E(f121(x15013,x15011,x15014),f121(x15013,x15012,x15014)) % 165.30/165.06 [1502]~E(x15021,x15022)+E(f121(x15023,x15024,x15021),f121(x15023,x15024,x15022)) % 165.30/165.06 [1503]~E(x15031,x15032)+E(f601(x15031,x15033,x15034,x15035,x15036),f601(x15032,x15033,x15034,x15035,x15036)) % 165.30/165.06 [1504]~E(x15041,x15042)+E(f601(x15043,x15041,x15044,x15045,x15046),f601(x15043,x15042,x15044,x15045,x15046)) % 165.30/165.06 [1505]~E(x15051,x15052)+E(f601(x15053,x15054,x15051,x15055,x15056),f601(x15053,x15054,x15052,x15055,x15056)) % 165.30/165.06 [1506]~E(x15061,x15062)+E(f601(x15063,x15064,x15065,x15061,x15066),f601(x15063,x15064,x15065,x15062,x15066)) % 165.30/165.06 [1507]~E(x15071,x15072)+E(f601(x15073,x15074,x15075,x15076,x15071),f601(x15073,x15074,x15075,x15076,x15072)) % 165.30/165.06 [1508]~E(x15081,x15082)+E(f534(x15081,x15083,x15084),f534(x15082,x15083,x15084)) % 165.30/165.06 [1509]~E(x15091,x15092)+E(f534(x15093,x15091,x15094),f534(x15093,x15092,x15094)) % 165.30/165.06 [1510]~E(x15101,x15102)+E(f534(x15103,x15104,x15101),f534(x15103,x15104,x15102)) % 165.30/165.06 [1511]~E(x15111,x15112)+E(f463(x15111,x15113,x15114),f463(x15112,x15113,x15114)) % 165.30/165.06 [1512]~E(x15121,x15122)+E(f463(x15123,x15121,x15124),f463(x15123,x15122,x15124)) % 165.30/165.06 [1513]~E(x15131,x15132)+E(f463(x15133,x15134,x15131),f463(x15133,x15134,x15132)) % 165.30/165.06 [1514]~E(x15141,x15142)+E(f444(x15141,x15143),f444(x15142,x15143)) % 165.30/165.06 [1515]~E(x15151,x15152)+E(f444(x15153,x15151),f444(x15153,x15152)) % 165.30/165.06 [1516]~E(x15161,x15162)+E(f647(x15161,x15163,x15164,x15165,x15166,x15167),f647(x15162,x15163,x15164,x15165,x15166,x15167)) % 165.30/165.06 [1517]~E(x15171,x15172)+E(f647(x15173,x15171,x15174,x15175,x15176,x15177),f647(x15173,x15172,x15174,x15175,x15176,x15177)) % 165.30/165.06 [1518]~E(x15181,x15182)+E(f647(x15183,x15184,x15181,x15185,x15186,x15187),f647(x15183,x15184,x15182,x15185,x15186,x15187)) % 165.30/165.06 [1519]~E(x15191,x15192)+E(f647(x15193,x15194,x15195,x15191,x15196,x15197),f647(x15193,x15194,x15195,x15192,x15196,x15197)) % 165.30/165.06 [1520]~E(x15201,x15202)+E(f647(x15203,x15204,x15205,x15206,x15201,x15207),f647(x15203,x15204,x15205,x15206,x15202,x15207)) % 165.30/165.06 [1521]~E(x15211,x15212)+E(f647(x15213,x15214,x15215,x15216,x15217,x15211),f647(x15213,x15214,x15215,x15216,x15217,x15212)) % 165.30/165.06 [1522]~E(x15221,x15222)+E(f44(x15221),f44(x15222)) % 165.30/165.06 [1523]~E(x15231,x15232)+E(f769(x15231,x15233,x15234,x15235,x15236,x15237,x15238),f769(x15232,x15233,x15234,x15235,x15236,x15237,x15238)) % 165.30/165.06 [1524]~E(x15241,x15242)+E(f769(x15243,x15241,x15244,x15245,x15246,x15247,x15248),f769(x15243,x15242,x15244,x15245,x15246,x15247,x15248)) % 165.30/165.06 [1525]~E(x15251,x15252)+E(f769(x15253,x15254,x15251,x15255,x15256,x15257,x15258),f769(x15253,x15254,x15252,x15255,x15256,x15257,x15258)) % 165.30/165.06 [1526]~E(x15261,x15262)+E(f769(x15263,x15264,x15265,x15261,x15266,x15267,x15268),f769(x15263,x15264,x15265,x15262,x15266,x15267,x15268)) % 165.30/165.06 [1527]~E(x15271,x15272)+E(f769(x15273,x15274,x15275,x15276,x15271,x15277,x15278),f769(x15273,x15274,x15275,x15276,x15272,x15277,x15278)) % 165.30/165.06 [1528]~E(x15281,x15282)+E(f769(x15283,x15284,x15285,x15286,x15287,x15281,x15288),f769(x15283,x15284,x15285,x15286,x15287,x15282,x15288)) % 165.30/165.06 [1529]~E(x15291,x15292)+E(f769(x15293,x15294,x15295,x15296,x15297,x15298,x15291),f769(x15293,x15294,x15295,x15296,x15297,x15298,x15292)) % 165.30/165.06 [1530]~E(x15301,x15302)+E(f482(x15301,x15303,x15304,x15305,x15306,x15307,x15308),f482(x15302,x15303,x15304,x15305,x15306,x15307,x15308)) % 165.30/165.06 [1531]~E(x15311,x15312)+E(f482(x15313,x15311,x15314,x15315,x15316,x15317,x15318),f482(x15313,x15312,x15314,x15315,x15316,x15317,x15318)) % 165.30/165.06 [1532]~E(x15321,x15322)+E(f482(x15323,x15324,x15321,x15325,x15326,x15327,x15328),f482(x15323,x15324,x15322,x15325,x15326,x15327,x15328)) % 165.30/165.06 [1533]~E(x15331,x15332)+E(f482(x15333,x15334,x15335,x15331,x15336,x15337,x15338),f482(x15333,x15334,x15335,x15332,x15336,x15337,x15338)) % 165.30/165.06 [1534]~E(x15341,x15342)+E(f482(x15343,x15344,x15345,x15346,x15341,x15347,x15348),f482(x15343,x15344,x15345,x15346,x15342,x15347,x15348)) % 165.30/165.06 [1535]~E(x15351,x15352)+E(f482(x15353,x15354,x15355,x15356,x15357,x15351,x15358),f482(x15353,x15354,x15355,x15356,x15357,x15352,x15358)) % 165.30/165.06 [1536]~E(x15361,x15362)+E(f482(x15363,x15364,x15365,x15366,x15367,x15368,x15361),f482(x15363,x15364,x15365,x15366,x15367,x15368,x15362)) % 165.30/165.06 [1537]~E(x15371,x15372)+E(f788(x15371,x15373,x15374),f788(x15372,x15373,x15374)) % 165.30/165.06 [1538]~E(x15381,x15382)+E(f788(x15383,x15381,x15384),f788(x15383,x15382,x15384)) % 165.30/165.06 [1539]~E(x15391,x15392)+E(f788(x15393,x15394,x15391),f788(x15393,x15394,x15392)) % 165.30/165.06 [1540]~E(x15401,x15402)+E(f578(x15401,x15403,x15404,x15405,x15406,x15407),f578(x15402,x15403,x15404,x15405,x15406,x15407)) % 165.30/165.06 [1541]~E(x15411,x15412)+E(f578(x15413,x15411,x15414,x15415,x15416,x15417),f578(x15413,x15412,x15414,x15415,x15416,x15417)) % 165.30/165.06 [1542]~E(x15421,x15422)+E(f578(x15423,x15424,x15421,x15425,x15426,x15427),f578(x15423,x15424,x15422,x15425,x15426,x15427)) % 165.30/165.06 [1543]~E(x15431,x15432)+E(f578(x15433,x15434,x15435,x15431,x15436,x15437),f578(x15433,x15434,x15435,x15432,x15436,x15437)) % 165.30/165.06 [1544]~E(x15441,x15442)+E(f578(x15443,x15444,x15445,x15446,x15441,x15447),f578(x15443,x15444,x15445,x15446,x15442,x15447)) % 165.30/165.06 [1545]~E(x15451,x15452)+E(f578(x15453,x15454,x15455,x15456,x15457,x15451),f578(x15453,x15454,x15455,x15456,x15457,x15452)) % 165.30/165.06 [1546]~E(x15461,x15462)+E(f342(x15461),f342(x15462)) % 165.30/165.06 [1547]~E(x15471,x15472)+E(f852(x15471,x15473,x15474,x15475),f852(x15472,x15473,x15474,x15475)) % 165.30/165.06 [1548]~E(x15481,x15482)+E(f852(x15483,x15481,x15484,x15485),f852(x15483,x15482,x15484,x15485)) % 165.30/165.06 [1549]~E(x15491,x15492)+E(f852(x15493,x15494,x15491,x15495),f852(x15493,x15494,x15492,x15495)) % 165.30/165.06 [1550]~E(x15501,x15502)+E(f852(x15503,x15504,x15505,x15501),f852(x15503,x15504,x15505,x15502)) % 165.30/165.06 [1551]~E(x15511,x15512)+E(f715(x15511,x15513,x15514,x15515,x15516),f715(x15512,x15513,x15514,x15515,x15516)) % 165.30/165.06 [1552]~E(x15521,x15522)+E(f715(x15523,x15521,x15524,x15525,x15526),f715(x15523,x15522,x15524,x15525,x15526)) % 165.30/165.06 [1553]~E(x15531,x15532)+E(f715(x15533,x15534,x15531,x15535,x15536),f715(x15533,x15534,x15532,x15535,x15536)) % 165.30/165.06 [1554]~E(x15541,x15542)+E(f715(x15543,x15544,x15545,x15541,x15546),f715(x15543,x15544,x15545,x15542,x15546)) % 165.30/165.06 [1555]~E(x15551,x15552)+E(f715(x15553,x15554,x15555,x15556,x15551),f715(x15553,x15554,x15555,x15556,x15552)) % 165.30/165.06 [1556]~E(x15561,x15562)+E(f524(x15561,x15563,x15564,x15565,x15566),f524(x15562,x15563,x15564,x15565,x15566)) % 165.30/165.06 [1557]~E(x15571,x15572)+E(f524(x15573,x15571,x15574,x15575,x15576),f524(x15573,x15572,x15574,x15575,x15576)) % 165.30/165.06 [1558]~E(x15581,x15582)+E(f524(x15583,x15584,x15581,x15585,x15586),f524(x15583,x15584,x15582,x15585,x15586)) % 165.30/165.06 [1559]~E(x15591,x15592)+E(f524(x15593,x15594,x15595,x15591,x15596),f524(x15593,x15594,x15595,x15592,x15596)) % 165.30/165.06 [1560]~E(x15601,x15602)+E(f524(x15603,x15604,x15605,x15606,x15601),f524(x15603,x15604,x15605,x15606,x15602)) % 165.30/165.06 [1561]~E(x15611,x15612)+E(f754(x15611,x15613,x15614,x15615),f754(x15612,x15613,x15614,x15615)) % 165.30/165.06 [1562]~E(x15621,x15622)+E(f754(x15623,x15621,x15624,x15625),f754(x15623,x15622,x15624,x15625)) % 165.30/165.06 [1563]~E(x15631,x15632)+E(f754(x15633,x15634,x15631,x15635),f754(x15633,x15634,x15632,x15635)) % 165.30/165.06 [1564]~E(x15641,x15642)+E(f754(x15643,x15644,x15645,x15641),f754(x15643,x15644,x15645,x15642)) % 165.30/165.06 [1565]~E(x15651,x15652)+E(f593(x15651,x15653,x15654),f593(x15652,x15653,x15654)) % 165.30/165.06 [1566]~E(x15661,x15662)+E(f593(x15663,x15661,x15664),f593(x15663,x15662,x15664)) % 165.30/165.06 [1567]~E(x15671,x15672)+E(f593(x15673,x15674,x15671),f593(x15673,x15674,x15672)) % 165.30/165.06 [1568]~E(x15681,x15682)+E(f597(x15681,x15683,x15684,x15685),f597(x15682,x15683,x15684,x15685)) % 165.30/165.06 [1569]~E(x15691,x15692)+E(f597(x15693,x15691,x15694,x15695),f597(x15693,x15692,x15694,x15695)) % 165.30/165.06 [1570]~E(x15701,x15702)+E(f597(x15703,x15704,x15701,x15705),f597(x15703,x15704,x15702,x15705)) % 165.30/165.06 [1571]~E(x15711,x15712)+E(f597(x15713,x15714,x15715,x15711),f597(x15713,x15714,x15715,x15712)) % 165.30/165.06 [1572]~E(x15721,x15722)+E(f237(x15721,x15723,x15724),f237(x15722,x15723,x15724)) % 165.30/165.06 [1573]~E(x15731,x15732)+E(f237(x15733,x15731,x15734),f237(x15733,x15732,x15734)) % 165.30/165.06 [1574]~E(x15741,x15742)+E(f237(x15743,x15744,x15741),f237(x15743,x15744,x15742)) % 165.30/165.06 [1575]~E(x15751,x15752)+E(f629(x15751,x15753),f629(x15752,x15753)) % 165.30/165.06 [1576]~E(x15761,x15762)+E(f629(x15763,x15761),f629(x15763,x15762)) % 165.30/165.06 [1577]~E(x15771,x15772)+E(f854(x15771,x15773,x15774),f854(x15772,x15773,x15774)) % 165.30/165.06 [1578]~E(x15781,x15782)+E(f854(x15783,x15781,x15784),f854(x15783,x15782,x15784)) % 165.30/165.06 [1579]~E(x15791,x15792)+E(f854(x15793,x15794,x15791),f854(x15793,x15794,x15792)) % 165.30/165.06 [1580]~E(x15801,x15802)+E(f838(x15801,x15803),f838(x15802,x15803)) % 165.30/165.06 [1581]~E(x15811,x15812)+E(f838(x15813,x15811),f838(x15813,x15812)) % 165.30/165.06 [1582]~E(x15821,x15822)+E(f720(x15821,x15823,x15824,x15825),f720(x15822,x15823,x15824,x15825)) % 165.30/165.06 [1583]~E(x15831,x15832)+E(f720(x15833,x15831,x15834,x15835),f720(x15833,x15832,x15834,x15835)) % 165.30/165.06 [1584]~E(x15841,x15842)+E(f720(x15843,x15844,x15841,x15845),f720(x15843,x15844,x15842,x15845)) % 165.30/165.06 [1585]~E(x15851,x15852)+E(f720(x15853,x15854,x15855,x15851),f720(x15853,x15854,x15855,x15852)) % 165.30/165.06 [1586]~E(x15861,x15862)+E(f551(x15861,x15863,x15864,x15865),f551(x15862,x15863,x15864,x15865)) % 165.30/165.06 [1587]~E(x15871,x15872)+E(f551(x15873,x15871,x15874,x15875),f551(x15873,x15872,x15874,x15875)) % 165.30/165.06 [1588]~E(x15881,x15882)+E(f551(x15883,x15884,x15881,x15885),f551(x15883,x15884,x15882,x15885)) % 165.30/165.06 [1589]~E(x15891,x15892)+E(f551(x15893,x15894,x15895,x15891),f551(x15893,x15894,x15895,x15892)) % 165.30/165.06 [1590]~E(x15901,x15902)+E(f540(x15901,x15903,x15904,x15905,x15906,x15907),f540(x15902,x15903,x15904,x15905,x15906,x15907)) % 165.30/165.06 [1591]~E(x15911,x15912)+E(f540(x15913,x15911,x15914,x15915,x15916,x15917),f540(x15913,x15912,x15914,x15915,x15916,x15917)) % 165.30/165.06 [1592]~E(x15921,x15922)+E(f540(x15923,x15924,x15921,x15925,x15926,x15927),f540(x15923,x15924,x15922,x15925,x15926,x15927)) % 165.30/165.06 [1593]~E(x15931,x15932)+E(f540(x15933,x15934,x15935,x15931,x15936,x15937),f540(x15933,x15934,x15935,x15932,x15936,x15937)) % 165.30/165.06 [1594]~E(x15941,x15942)+E(f540(x15943,x15944,x15945,x15946,x15941,x15947),f540(x15943,x15944,x15945,x15946,x15942,x15947)) % 165.30/165.06 [1595]~E(x15951,x15952)+E(f540(x15953,x15954,x15955,x15956,x15957,x15951),f540(x15953,x15954,x15955,x15956,x15957,x15952)) % 165.30/165.06 [1596]~E(x15961,x15962)+E(f701(x15961,x15963,x15964,x15965),f701(x15962,x15963,x15964,x15965)) % 165.30/165.06 [1597]~E(x15971,x15972)+E(f701(x15973,x15971,x15974,x15975),f701(x15973,x15972,x15974,x15975)) % 165.30/165.06 [1598]~E(x15981,x15982)+E(f701(x15983,x15984,x15981,x15985),f701(x15983,x15984,x15982,x15985)) % 165.30/165.06 [1599]~E(x15991,x15992)+E(f701(x15993,x15994,x15995,x15991),f701(x15993,x15994,x15995,x15992)) % 165.30/165.06 [1600]~E(x16001,x16002)+E(f785(x16001,x16003,x16004,x16005,x16006,x16007),f785(x16002,x16003,x16004,x16005,x16006,x16007)) % 165.30/165.06 [1601]~E(x16011,x16012)+E(f785(x16013,x16011,x16014,x16015,x16016,x16017),f785(x16013,x16012,x16014,x16015,x16016,x16017)) % 165.30/165.06 [1602]~E(x16021,x16022)+E(f785(x16023,x16024,x16021,x16025,x16026,x16027),f785(x16023,x16024,x16022,x16025,x16026,x16027)) % 165.30/165.06 [1603]~E(x16031,x16032)+E(f785(x16033,x16034,x16035,x16031,x16036,x16037),f785(x16033,x16034,x16035,x16032,x16036,x16037)) % 165.30/165.06 [1604]~E(x16041,x16042)+E(f785(x16043,x16044,x16045,x16046,x16041,x16047),f785(x16043,x16044,x16045,x16046,x16042,x16047)) % 165.30/165.06 [1605]~E(x16051,x16052)+E(f785(x16053,x16054,x16055,x16056,x16057,x16051),f785(x16053,x16054,x16055,x16056,x16057,x16052)) % 165.30/165.06 [1606]~E(x16061,x16062)+E(f120(x16061,x16063,x16064),f120(x16062,x16063,x16064)) % 165.30/165.06 [1607]~E(x16071,x16072)+E(f120(x16073,x16071,x16074),f120(x16073,x16072,x16074)) % 165.30/165.06 [1608]~E(x16081,x16082)+E(f120(x16083,x16084,x16081),f120(x16083,x16084,x16082)) % 165.30/165.06 [1609]~E(x16091,x16092)+E(f576(x16091,x16093,x16094,x16095,x16096,x16097),f576(x16092,x16093,x16094,x16095,x16096,x16097)) % 165.30/165.06 [1610]~E(x16101,x16102)+E(f576(x16103,x16101,x16104,x16105,x16106,x16107),f576(x16103,x16102,x16104,x16105,x16106,x16107)) % 165.30/165.06 [1611]~E(x16111,x16112)+E(f576(x16113,x16114,x16111,x16115,x16116,x16117),f576(x16113,x16114,x16112,x16115,x16116,x16117)) % 165.30/165.06 [1612]~E(x16121,x16122)+E(f576(x16123,x16124,x16125,x16121,x16126,x16127),f576(x16123,x16124,x16125,x16122,x16126,x16127)) % 165.30/165.06 [1613]~E(x16131,x16132)+E(f576(x16133,x16134,x16135,x16136,x16131,x16137),f576(x16133,x16134,x16135,x16136,x16132,x16137)) % 165.30/165.06 [1614]~E(x16141,x16142)+E(f576(x16143,x16144,x16145,x16146,x16147,x16141),f576(x16143,x16144,x16145,x16146,x16147,x16142)) % 165.30/165.06 [1615]~E(x16151,x16152)+E(f733(x16151,x16153,x16154),f733(x16152,x16153,x16154)) % 165.30/165.06 [1616]~E(x16161,x16162)+E(f733(x16163,x16161,x16164),f733(x16163,x16162,x16164)) % 165.30/165.06 [1617]~E(x16171,x16172)+E(f733(x16173,x16174,x16171),f733(x16173,x16174,x16172)) % 165.30/165.06 [1618]~E(x16181,x16182)+E(f858(x16181,x16183,x16184,x16185,x16186),f858(x16182,x16183,x16184,x16185,x16186)) % 165.30/165.06 [1619]~E(x16191,x16192)+E(f858(x16193,x16191,x16194,x16195,x16196),f858(x16193,x16192,x16194,x16195,x16196)) % 165.30/165.06 [1620]~E(x16201,x16202)+E(f858(x16203,x16204,x16201,x16205,x16206),f858(x16203,x16204,x16202,x16205,x16206)) % 165.30/165.06 [1621]~E(x16211,x16212)+E(f858(x16213,x16214,x16215,x16211,x16216),f858(x16213,x16214,x16215,x16212,x16216)) % 165.30/165.06 [1622]~E(x16221,x16222)+E(f858(x16223,x16224,x16225,x16226,x16221),f858(x16223,x16224,x16225,x16226,x16222)) % 165.30/165.06 [1623]~E(x16231,x16232)+E(f386(x16231,x16233,x16234,x16235),f386(x16232,x16233,x16234,x16235)) % 165.30/165.06 [1624]~E(x16241,x16242)+E(f386(x16243,x16241,x16244,x16245),f386(x16243,x16242,x16244,x16245)) % 165.30/165.06 [1625]~E(x16251,x16252)+E(f386(x16253,x16254,x16251,x16255),f386(x16253,x16254,x16252,x16255)) % 165.30/165.06 [1626]~E(x16261,x16262)+E(f386(x16263,x16264,x16265,x16261),f386(x16263,x16264,x16265,x16262)) % 165.30/165.06 [1627]~E(x16271,x16272)+E(f451(x16271,x16273,x16274),f451(x16272,x16273,x16274)) % 165.30/165.06 [1628]~E(x16281,x16282)+E(f451(x16283,x16281,x16284),f451(x16283,x16282,x16284)) % 165.30/165.06 [1629]~E(x16291,x16292)+E(f451(x16293,x16294,x16291),f451(x16293,x16294,x16292)) % 165.30/165.06 [1630]~E(x16301,x16302)+E(f703(x16301,x16303,x16304,x16305,x16306),f703(x16302,x16303,x16304,x16305,x16306)) % 165.30/165.06 [1631]~E(x16311,x16312)+E(f703(x16313,x16311,x16314,x16315,x16316),f703(x16313,x16312,x16314,x16315,x16316)) % 165.30/165.06 [1632]~E(x16321,x16322)+E(f703(x16323,x16324,x16321,x16325,x16326),f703(x16323,x16324,x16322,x16325,x16326)) % 165.30/165.06 [1633]~E(x16331,x16332)+E(f703(x16333,x16334,x16335,x16331,x16336),f703(x16333,x16334,x16335,x16332,x16336)) % 165.30/165.06 [1634]~E(x16341,x16342)+E(f703(x16343,x16344,x16345,x16346,x16341),f703(x16343,x16344,x16345,x16346,x16342)) % 165.30/165.06 [1635]~E(x16351,x16352)+E(f825(x16351,x16353,x16354),f825(x16352,x16353,x16354)) % 165.30/165.06 [1636]~E(x16361,x16362)+E(f825(x16363,x16361,x16364),f825(x16363,x16362,x16364)) % 165.30/165.06 [1637]~E(x16371,x16372)+E(f825(x16373,x16374,x16371),f825(x16373,x16374,x16372)) % 165.30/165.06 [1638]~E(x16381,x16382)+E(f684(x16381,x16383),f684(x16382,x16383)) % 165.30/165.06 [1639]~E(x16391,x16392)+E(f684(x16393,x16391),f684(x16393,x16392)) % 165.30/165.06 [1640]~E(x16401,x16402)+E(f372(x16401,x16403,x16404),f372(x16402,x16403,x16404)) % 165.30/165.06 [1641]~E(x16411,x16412)+E(f372(x16413,x16411,x16414),f372(x16413,x16412,x16414)) % 165.30/165.06 [1642]~E(x16421,x16422)+E(f372(x16423,x16424,x16421),f372(x16423,x16424,x16422)) % 165.30/165.06 [1643]~E(x16431,x16432)+E(f433(x16431,x16433,x16434,x16435),f433(x16432,x16433,x16434,x16435)) % 165.30/165.06 [1644]~E(x16441,x16442)+E(f433(x16443,x16441,x16444,x16445),f433(x16443,x16442,x16444,x16445)) % 165.30/165.06 [1645]~E(x16451,x16452)+E(f433(x16453,x16454,x16451,x16455),f433(x16453,x16454,x16452,x16455)) % 165.30/165.06 [1646]~E(x16461,x16462)+E(f433(x16463,x16464,x16465,x16461),f433(x16463,x16464,x16465,x16462)) % 165.30/165.06 [1647]~E(x16471,x16472)+E(f627(x16471,x16473,x16474),f627(x16472,x16473,x16474)) % 165.30/165.06 [1648]~E(x16481,x16482)+E(f627(x16483,x16481,x16484),f627(x16483,x16482,x16484)) % 165.30/165.06 [1649]~E(x16491,x16492)+E(f627(x16493,x16494,x16491),f627(x16493,x16494,x16492)) % 165.30/165.06 [1650]~E(x16501,x16502)+E(f63(x16501,x16503,x16504),f63(x16502,x16503,x16504)) % 165.30/165.06 [1651]~E(x16511,x16512)+E(f63(x16513,x16511,x16514),f63(x16513,x16512,x16514)) % 165.30/165.06 [1652]~E(x16521,x16522)+E(f63(x16523,x16524,x16521),f63(x16523,x16524,x16522)) % 165.30/165.06 [1653]~E(x16531,x16532)+E(f378(x16531,x16533,x16534,x16535),f378(x16532,x16533,x16534,x16535)) % 165.30/165.06 [1654]~E(x16541,x16542)+E(f378(x16543,x16541,x16544,x16545),f378(x16543,x16542,x16544,x16545)) % 165.30/165.06 [1655]~E(x16551,x16552)+E(f378(x16553,x16554,x16551,x16555),f378(x16553,x16554,x16552,x16555)) % 165.30/165.06 [1656]~E(x16561,x16562)+E(f378(x16563,x16564,x16565,x16561),f378(x16563,x16564,x16565,x16562)) % 165.30/165.06 [1657]~E(x16571,x16572)+E(f525(x16571,x16573,x16574,x16575,x16576),f525(x16572,x16573,x16574,x16575,x16576)) % 165.30/165.06 [1658]~E(x16581,x16582)+E(f525(x16583,x16581,x16584,x16585,x16586),f525(x16583,x16582,x16584,x16585,x16586)) % 165.30/165.06 [1659]~E(x16591,x16592)+E(f525(x16593,x16594,x16591,x16595,x16596),f525(x16593,x16594,x16592,x16595,x16596)) % 165.30/165.06 [1660]~E(x16601,x16602)+E(f525(x16603,x16604,x16605,x16601,x16606),f525(x16603,x16604,x16605,x16602,x16606)) % 165.30/165.06 [1661]~E(x16611,x16612)+E(f525(x16613,x16614,x16615,x16616,x16611),f525(x16613,x16614,x16615,x16616,x16612)) % 165.30/165.06 [1662]~E(x16621,x16622)+E(f55(x16621,x16623,x16624),f55(x16622,x16623,x16624)) % 165.30/165.06 [1663]~E(x16631,x16632)+E(f55(x16633,x16631,x16634),f55(x16633,x16632,x16634)) % 165.30/165.06 [1664]~E(x16641,x16642)+E(f55(x16643,x16644,x16641),f55(x16643,x16644,x16642)) % 165.30/165.06 [1665]~E(x16651,x16652)+E(f773(x16651,x16653,x16654),f773(x16652,x16653,x16654)) % 165.30/165.06 [1666]~E(x16661,x16662)+E(f773(x16663,x16661,x16664),f773(x16663,x16662,x16664)) % 165.30/165.06 [1667]~E(x16671,x16672)+E(f773(x16673,x16674,x16671),f773(x16673,x16674,x16672)) % 165.30/165.06 [1668]~E(x16681,x16682)+E(f648(x16681,x16683),f648(x16682,x16683)) % 165.30/165.06 [1669]~E(x16691,x16692)+E(f648(x16693,x16691),f648(x16693,x16692)) % 165.30/165.06 [1670]~E(x16701,x16702)+E(f631(x16701,x16703),f631(x16702,x16703)) % 165.30/165.06 [1671]~E(x16711,x16712)+E(f631(x16713,x16711),f631(x16713,x16712)) % 165.30/165.06 [1672]~E(x16721,x16722)+E(f446(x16721,x16723),f446(x16722,x16723)) % 165.30/165.06 [1673]~E(x16731,x16732)+E(f446(x16733,x16731),f446(x16733,x16732)) % 165.30/165.06 [1674]~E(x16741,x16742)+E(f408(x16741,x16743),f408(x16742,x16743)) % 165.30/165.06 [1675]~E(x16751,x16752)+E(f408(x16753,x16751),f408(x16753,x16752)) % 165.30/165.06 [1676]~E(x16761,x16762)+E(f428(x16761,x16763,x16764),f428(x16762,x16763,x16764)) % 165.30/165.06 [1677]~E(x16771,x16772)+E(f428(x16773,x16771,x16774),f428(x16773,x16772,x16774)) % 165.30/165.06 [1678]~E(x16781,x16782)+E(f428(x16783,x16784,x16781),f428(x16783,x16784,x16782)) % 165.30/165.06 [1679]~E(x16791,x16792)+E(f96(x16791,x16793,x16794),f96(x16792,x16793,x16794)) % 165.30/165.06 [1680]~E(x16801,x16802)+E(f96(x16803,x16801,x16804),f96(x16803,x16802,x16804)) % 165.30/165.06 [1681]~E(x16811,x16812)+E(f96(x16813,x16814,x16811),f96(x16813,x16814,x16812)) % 165.30/165.06 [1682]~E(x16821,x16822)+E(f636(x16821,x16823,x16824),f636(x16822,x16823,x16824)) % 165.30/165.06 [1683]~E(x16831,x16832)+E(f636(x16833,x16831,x16834),f636(x16833,x16832,x16834)) % 165.30/165.06 [1684]~E(x16841,x16842)+E(f636(x16843,x16844,x16841),f636(x16843,x16844,x16842)) % 165.30/165.06 [1685]~E(x16851,x16852)+E(f735(x16851,x16853,x16854),f735(x16852,x16853,x16854)) % 165.30/165.06 [1686]~E(x16861,x16862)+E(f735(x16863,x16861,x16864),f735(x16863,x16862,x16864)) % 165.30/165.06 [1687]~E(x16871,x16872)+E(f735(x16873,x16874,x16871),f735(x16873,x16874,x16872)) % 165.30/165.06 [1688]~E(x16881,x16882)+E(f749(x16881,x16883,x16884,x16885,x16886),f749(x16882,x16883,x16884,x16885,x16886)) % 165.30/165.06 [1689]~E(x16891,x16892)+E(f749(x16893,x16891,x16894,x16895,x16896),f749(x16893,x16892,x16894,x16895,x16896)) % 165.30/165.06 [1690]~E(x16901,x16902)+E(f749(x16903,x16904,x16901,x16905,x16906),f749(x16903,x16904,x16902,x16905,x16906)) % 165.30/165.06 [1691]~E(x16911,x16912)+E(f749(x16913,x16914,x16915,x16911,x16916),f749(x16913,x16914,x16915,x16912,x16916)) % 165.30/165.06 [1692]~E(x16921,x16922)+E(f749(x16923,x16924,x16925,x16926,x16921),f749(x16923,x16924,x16925,x16926,x16922)) % 165.30/165.06 [1693]~E(x16931,x16932)+E(f488(x16931,x16933,x16934,x16935,x16936,x16937),f488(x16932,x16933,x16934,x16935,x16936,x16937)) % 165.30/165.06 [1694]~E(x16941,x16942)+E(f488(x16943,x16941,x16944,x16945,x16946,x16947),f488(x16943,x16942,x16944,x16945,x16946,x16947)) % 165.30/165.06 [1695]~E(x16951,x16952)+E(f488(x16953,x16954,x16951,x16955,x16956,x16957),f488(x16953,x16954,x16952,x16955,x16956,x16957)) % 165.30/165.06 [1696]~E(x16961,x16962)+E(f488(x16963,x16964,x16965,x16961,x16966,x16967),f488(x16963,x16964,x16965,x16962,x16966,x16967)) % 165.30/165.06 [1697]~E(x16971,x16972)+E(f488(x16973,x16974,x16975,x16976,x16971,x16977),f488(x16973,x16974,x16975,x16976,x16972,x16977)) % 165.30/165.06 [1698]~E(x16981,x16982)+E(f488(x16983,x16984,x16985,x16986,x16987,x16981),f488(x16983,x16984,x16985,x16986,x16987,x16982)) % 165.30/165.06 [1699]~E(x16991,x16992)+E(f425(x16991),f425(x16992)) % 165.30/165.06 [1700]~E(x17001,x17002)+E(f626(x17001,x17003,x17004),f626(x17002,x17003,x17004)) % 165.30/165.06 [1701]~E(x17011,x17012)+E(f626(x17013,x17011,x17014),f626(x17013,x17012,x17014)) % 165.30/165.06 [1702]~E(x17021,x17022)+E(f626(x17023,x17024,x17021),f626(x17023,x17024,x17022)) % 165.30/165.06 [1703]~E(x17031,x17032)+E(f581(x17031,x17033,x17034),f581(x17032,x17033,x17034)) % 165.30/165.06 [1704]~E(x17041,x17042)+E(f581(x17043,x17041,x17044),f581(x17043,x17042,x17044)) % 165.30/165.06 [1705]~E(x17051,x17052)+E(f581(x17053,x17054,x17051),f581(x17053,x17054,x17052)) % 165.30/165.06 [1706]~E(x17061,x17062)+E(f426(x17061,x17063,x17064,x17065),f426(x17062,x17063,x17064,x17065)) % 165.30/165.06 [1707]~E(x17071,x17072)+E(f426(x17073,x17071,x17074,x17075),f426(x17073,x17072,x17074,x17075)) % 165.30/165.06 [1708]~E(x17081,x17082)+E(f426(x17083,x17084,x17081,x17085),f426(x17083,x17084,x17082,x17085)) % 165.30/165.06 [1709]~E(x17091,x17092)+E(f426(x17093,x17094,x17095,x17091),f426(x17093,x17094,x17095,x17092)) % 165.30/165.06 [1710]~E(x17101,x17102)+E(f212(x17101),f212(x17102)) % 165.30/165.06 [1711]~E(x17111,x17112)+E(f687(x17111,x17113,x17114,x17115),f687(x17112,x17113,x17114,x17115)) % 165.30/165.06 [1712]~E(x17121,x17122)+E(f687(x17123,x17121,x17124,x17125),f687(x17123,x17122,x17124,x17125)) % 165.30/165.06 [1713]~E(x17131,x17132)+E(f687(x17133,x17134,x17131,x17135),f687(x17133,x17134,x17132,x17135)) % 165.30/165.06 [1714]~E(x17141,x17142)+E(f687(x17143,x17144,x17145,x17141),f687(x17143,x17144,x17145,x17142)) % 165.30/165.06 [1715]~E(x17151,x17152)+E(f183(x17151),f183(x17152)) % 165.30/165.06 [1716]~E(x17161,x17162)+E(f580(x17161,x17163,x17164),f580(x17162,x17163,x17164)) % 165.30/165.06 [1717]~E(x17171,x17172)+E(f580(x17173,x17171,x17174),f580(x17173,x17172,x17174)) % 165.30/165.06 [1718]~E(x17181,x17182)+E(f580(x17183,x17184,x17181),f580(x17183,x17184,x17182)) % 165.30/165.06 [1719]~E(x17191,x17192)+E(f339(x17191),f339(x17192)) % 165.30/165.06 [1720]~E(x17201,x17202)+E(f522(x17201,x17203,x17204),f522(x17202,x17203,x17204)) % 165.30/165.06 [1721]~E(x17211,x17212)+E(f522(x17213,x17211,x17214),f522(x17213,x17212,x17214)) % 165.30/165.06 [1722]~E(x17221,x17222)+E(f522(x17223,x17224,x17221),f522(x17223,x17224,x17222)) % 165.30/165.06 [1723]~E(x17231,x17232)+E(f278(x17231,x17233),f278(x17232,x17233)) % 165.30/165.06 [1724]~E(x17241,x17242)+E(f278(x17243,x17241),f278(x17243,x17242)) % 165.30/165.06 [1725]~E(x17251,x17252)+E(f292(x17251,x17253),f292(x17252,x17253)) % 165.30/165.06 [1726]~E(x17261,x17262)+E(f292(x17263,x17261),f292(x17263,x17262)) % 165.30/165.06 [1727]~E(x17271,x17272)+E(f820(x17271,x17273,x17274),f820(x17272,x17273,x17274)) % 165.30/165.06 [1728]~E(x17281,x17282)+E(f820(x17283,x17281,x17284),f820(x17283,x17282,x17284)) % 165.30/165.06 [1729]~E(x17291,x17292)+E(f820(x17293,x17294,x17291),f820(x17293,x17294,x17292)) % 165.30/165.06 [1730]~E(x17301,x17302)+E(f750(x17301,x17303,x17304,x17305,x17306),f750(x17302,x17303,x17304,x17305,x17306)) % 165.30/165.06 [1731]~E(x17311,x17312)+E(f750(x17313,x17311,x17314,x17315,x17316),f750(x17313,x17312,x17314,x17315,x17316)) % 165.30/165.06 [1732]~E(x17321,x17322)+E(f750(x17323,x17324,x17321,x17325,x17326),f750(x17323,x17324,x17322,x17325,x17326)) % 165.30/165.06 [1733]~E(x17331,x17332)+E(f750(x17333,x17334,x17335,x17331,x17336),f750(x17333,x17334,x17335,x17332,x17336)) % 165.30/165.06 [1734]~E(x17341,x17342)+E(f750(x17343,x17344,x17345,x17346,x17341),f750(x17343,x17344,x17345,x17346,x17342)) % 165.30/165.06 [1735]~E(x17351,x17352)+E(f503(x17351,x17353,x17354),f503(x17352,x17353,x17354)) % 165.30/165.06 [1736]~E(x17361,x17362)+E(f503(x17363,x17361,x17364),f503(x17363,x17362,x17364)) % 165.30/165.06 [1737]~E(x17371,x17372)+E(f503(x17373,x17374,x17371),f503(x17373,x17374,x17372)) % 165.30/165.06 [1738]~E(x17381,x17382)+E(f663(x17381,x17383),f663(x17382,x17383)) % 165.30/165.06 [1739]~E(x17391,x17392)+E(f663(x17393,x17391),f663(x17393,x17392)) % 165.30/165.06 [1740]~E(x17401,x17402)+E(f706(x17401,x17403,x17404),f706(x17402,x17403,x17404)) % 165.30/165.06 [1741]~E(x17411,x17412)+E(f706(x17413,x17411,x17414),f706(x17413,x17412,x17414)) % 165.30/165.06 [1742]~E(x17421,x17422)+E(f706(x17423,x17424,x17421),f706(x17423,x17424,x17422)) % 165.30/165.06 [1743]~E(x17431,x17432)+E(f400(x17431,x17433,x17434,x17435),f400(x17432,x17433,x17434,x17435)) % 165.30/165.06 [1744]~E(x17441,x17442)+E(f400(x17443,x17441,x17444,x17445),f400(x17443,x17442,x17444,x17445)) % 165.30/165.06 [1745]~E(x17451,x17452)+E(f400(x17453,x17454,x17451,x17455),f400(x17453,x17454,x17452,x17455)) % 165.30/165.06 [1746]~E(x17461,x17462)+E(f400(x17463,x17464,x17465,x17461),f400(x17463,x17464,x17465,x17462)) % 165.30/165.06 [1747]~E(x17471,x17472)+E(f692(x17471,x17473,x17474),f692(x17472,x17473,x17474)) % 165.30/165.06 [1748]~E(x17481,x17482)+E(f692(x17483,x17481,x17484),f692(x17483,x17482,x17484)) % 165.30/165.06 [1749]~E(x17491,x17492)+E(f692(x17493,x17494,x17491),f692(x17493,x17494,x17492)) % 165.30/165.06 [1750]~E(x17501,x17502)+E(f471(x17501,x17503,x17504,x17505,x17506),f471(x17502,x17503,x17504,x17505,x17506)) % 165.30/165.06 [1751]~E(x17511,x17512)+E(f471(x17513,x17511,x17514,x17515,x17516),f471(x17513,x17512,x17514,x17515,x17516)) % 165.30/165.06 [1752]~E(x17521,x17522)+E(f471(x17523,x17524,x17521,x17525,x17526),f471(x17523,x17524,x17522,x17525,x17526)) % 165.30/165.06 [1753]~E(x17531,x17532)+E(f471(x17533,x17534,x17535,x17531,x17536),f471(x17533,x17534,x17535,x17532,x17536)) % 165.30/165.06 [1754]~E(x17541,x17542)+E(f471(x17543,x17544,x17545,x17546,x17541),f471(x17543,x17544,x17545,x17546,x17542)) % 165.30/165.06 [1755]~E(x17551,x17552)+E(f837(x17551,x17553,x17554),f837(x17552,x17553,x17554)) % 165.30/165.06 [1756]~E(x17561,x17562)+E(f837(x17563,x17561,x17564),f837(x17563,x17562,x17564)) % 165.30/165.06 [1757]~E(x17571,x17572)+E(f837(x17573,x17574,x17571),f837(x17573,x17574,x17572)) % 165.30/165.06 [1758]~E(x17581,x17582)+E(f725(x17581,x17583,x17584),f725(x17582,x17583,x17584)) % 165.30/165.06 [1759]~E(x17591,x17592)+E(f725(x17593,x17591,x17594),f725(x17593,x17592,x17594)) % 165.30/165.06 [1760]~E(x17601,x17602)+E(f725(x17603,x17604,x17601),f725(x17603,x17604,x17602)) % 165.30/165.06 [1761]~E(x17611,x17612)+E(f336(x17611,x17613,x17614,x17615),f336(x17612,x17613,x17614,x17615)) % 165.30/165.06 [1762]~E(x17621,x17622)+E(f336(x17623,x17621,x17624,x17625),f336(x17623,x17622,x17624,x17625)) % 165.30/165.06 [1763]~E(x17631,x17632)+E(f336(x17633,x17634,x17631,x17635),f336(x17633,x17634,x17632,x17635)) % 165.30/165.06 [1764]~E(x17641,x17642)+E(f336(x17643,x17644,x17645,x17641),f336(x17643,x17644,x17645,x17642)) % 165.30/165.06 [1765]~E(x17651,x17652)+E(f206(x17651,x17653,x17654,x17655),f206(x17652,x17653,x17654,x17655)) % 165.30/165.06 [1766]~E(x17661,x17662)+E(f206(x17663,x17661,x17664,x17665),f206(x17663,x17662,x17664,x17665)) % 165.30/165.06 [1767]~E(x17671,x17672)+E(f206(x17673,x17674,x17671,x17675),f206(x17673,x17674,x17672,x17675)) % 165.30/165.06 [1768]~E(x17681,x17682)+E(f206(x17683,x17684,x17685,x17681),f206(x17683,x17684,x17685,x17682)) % 165.30/165.06 [1769]~E(x17691,x17692)+E(f789(x17691,x17693,x17694,x17695),f789(x17692,x17693,x17694,x17695)) % 165.30/165.06 [1770]~E(x17701,x17702)+E(f789(x17703,x17701,x17704,x17705),f789(x17703,x17702,x17704,x17705)) % 165.30/165.06 [1771]~E(x17711,x17712)+E(f789(x17713,x17714,x17711,x17715),f789(x17713,x17714,x17712,x17715)) % 165.30/165.06 [1772]~E(x17721,x17722)+E(f789(x17723,x17724,x17725,x17721),f789(x17723,x17724,x17725,x17722)) % 165.30/165.06 [1773]~E(x17731,x17732)+E(f281(x17731,x17733,x17734,x17735),f281(x17732,x17733,x17734,x17735)) % 165.30/165.06 [1774]~E(x17741,x17742)+E(f281(x17743,x17741,x17744,x17745),f281(x17743,x17742,x17744,x17745)) % 165.30/165.06 [1775]~E(x17751,x17752)+E(f281(x17753,x17754,x17751,x17755),f281(x17753,x17754,x17752,x17755)) % 165.30/165.06 [1776]~E(x17761,x17762)+E(f281(x17763,x17764,x17765,x17761),f281(x17763,x17764,x17765,x17762)) % 165.30/165.06 [1777]~E(x17771,x17772)+E(f283(x17771,x17773),f283(x17772,x17773)) % 165.30/165.06 [1778]~E(x17781,x17782)+E(f283(x17783,x17781),f283(x17783,x17782)) % 165.30/165.06 [1779]~E(x17791,x17792)+E(f604(x17791,x17793,x17794,x17795,x17796,x17797,x17798),f604(x17792,x17793,x17794,x17795,x17796,x17797,x17798)) % 165.30/165.06 [1780]~E(x17801,x17802)+E(f604(x17803,x17801,x17804,x17805,x17806,x17807,x17808),f604(x17803,x17802,x17804,x17805,x17806,x17807,x17808)) % 165.30/165.06 [1781]~E(x17811,x17812)+E(f604(x17813,x17814,x17811,x17815,x17816,x17817,x17818),f604(x17813,x17814,x17812,x17815,x17816,x17817,x17818)) % 165.30/165.06 [1782]~E(x17821,x17822)+E(f604(x17823,x17824,x17825,x17821,x17826,x17827,x17828),f604(x17823,x17824,x17825,x17822,x17826,x17827,x17828)) % 165.30/165.06 [1783]~E(x17831,x17832)+E(f604(x17833,x17834,x17835,x17836,x17831,x17837,x17838),f604(x17833,x17834,x17835,x17836,x17832,x17837,x17838)) % 165.30/165.06 [1784]~E(x17841,x17842)+E(f604(x17843,x17844,x17845,x17846,x17847,x17841,x17848),f604(x17843,x17844,x17845,x17846,x17847,x17842,x17848)) % 165.30/165.06 [1785]~E(x17851,x17852)+E(f604(x17853,x17854,x17855,x17856,x17857,x17858,x17851),f604(x17853,x17854,x17855,x17856,x17857,x17858,x17852)) % 165.30/165.06 [1786]~E(x17861,x17862)+E(f835(x17861,x17863,x17864,x17865,x17866),f835(x17862,x17863,x17864,x17865,x17866)) % 165.30/165.06 [1787]~E(x17871,x17872)+E(f835(x17873,x17871,x17874,x17875,x17876),f835(x17873,x17872,x17874,x17875,x17876)) % 165.30/165.06 [1788]~E(x17881,x17882)+E(f835(x17883,x17884,x17881,x17885,x17886),f835(x17883,x17884,x17882,x17885,x17886)) % 165.30/165.06 [1789]~E(x17891,x17892)+E(f835(x17893,x17894,x17895,x17891,x17896),f835(x17893,x17894,x17895,x17892,x17896)) % 165.30/165.06 [1790]~E(x17901,x17902)+E(f835(x17903,x17904,x17905,x17906,x17901),f835(x17903,x17904,x17905,x17906,x17902)) % 165.30/165.06 [1791]~E(x17911,x17912)+E(f699(x17911,x17913,x17914,x17915,x17916,x17917),f699(x17912,x17913,x17914,x17915,x17916,x17917)) % 165.30/165.06 [1792]~E(x17921,x17922)+E(f699(x17923,x17921,x17924,x17925,x17926,x17927),f699(x17923,x17922,x17924,x17925,x17926,x17927)) % 165.30/165.06 [1793]~E(x17931,x17932)+E(f699(x17933,x17934,x17931,x17935,x17936,x17937),f699(x17933,x17934,x17932,x17935,x17936,x17937)) % 165.30/165.06 [1794]~E(x17941,x17942)+E(f699(x17943,x17944,x17945,x17941,x17946,x17947),f699(x17943,x17944,x17945,x17942,x17946,x17947)) % 165.30/165.06 [1795]~E(x17951,x17952)+E(f699(x17953,x17954,x17955,x17956,x17951,x17957),f699(x17953,x17954,x17955,x17956,x17952,x17957)) % 165.30/165.06 [1796]~E(x17961,x17962)+E(f699(x17963,x17964,x17965,x17966,x17967,x17961),f699(x17963,x17964,x17965,x17966,x17967,x17962)) % 165.30/165.06 [1797]~E(x17971,x17972)+E(f807(x17971,x17973,x17974),f807(x17972,x17973,x17974)) % 165.30/165.06 [1798]~E(x17981,x17982)+E(f807(x17983,x17981,x17984),f807(x17983,x17982,x17984)) % 165.30/165.06 [1799]~E(x17991,x17992)+E(f807(x17993,x17994,x17991),f807(x17993,x17994,x17992)) % 165.30/165.06 [1800]~E(x18001,x18002)+E(f845(x18001,x18003,x18004),f845(x18002,x18003,x18004)) % 165.30/165.06 [1801]~E(x18011,x18012)+E(f845(x18013,x18011,x18014),f845(x18013,x18012,x18014)) % 165.30/165.06 [1802]~E(x18021,x18022)+E(f845(x18023,x18024,x18021),f845(x18023,x18024,x18022)) % 165.30/165.06 [1803]~E(x18031,x18032)+E(f819(x18031,x18033),f819(x18032,x18033)) % 165.30/165.06 [1804]~E(x18041,x18042)+E(f819(x18043,x18041),f819(x18043,x18042)) % 165.30/165.06 [1805]~E(x18051,x18052)+E(f418(x18051,x18053,x18054),f418(x18052,x18053,x18054)) % 165.30/165.06 [1806]~E(x18061,x18062)+E(f418(x18063,x18061,x18064),f418(x18063,x18062,x18064)) % 165.30/165.06 [1807]~E(x18071,x18072)+E(f418(x18073,x18074,x18071),f418(x18073,x18074,x18072)) % 165.30/165.06 [1808]~E(x18081,x18082)+E(f324(x18081,x18083,x18084,x18085),f324(x18082,x18083,x18084,x18085)) % 165.30/165.06 [1809]~E(x18091,x18092)+E(f324(x18093,x18091,x18094,x18095),f324(x18093,x18092,x18094,x18095)) % 165.30/165.06 [1810]~E(x18101,x18102)+E(f324(x18103,x18104,x18101,x18105),f324(x18103,x18104,x18102,x18105)) % 165.30/165.06 [1811]~E(x18111,x18112)+E(f324(x18113,x18114,x18115,x18111),f324(x18113,x18114,x18115,x18112)) % 165.30/165.06 [1812]~E(x18121,x18122)+E(f465(x18121,x18123,x18124,x18125),f465(x18122,x18123,x18124,x18125)) % 165.30/165.06 [1813]~E(x18131,x18132)+E(f465(x18133,x18131,x18134,x18135),f465(x18133,x18132,x18134,x18135)) % 165.30/165.06 [1814]~E(x18141,x18142)+E(f465(x18143,x18144,x18141,x18145),f465(x18143,x18144,x18142,x18145)) % 165.30/165.06 [1815]~E(x18151,x18152)+E(f465(x18153,x18154,x18155,x18151),f465(x18153,x18154,x18155,x18152)) % 165.30/165.06 [1816]~E(x18161,x18162)+E(f141(x18161,x18163,x18164),f141(x18162,x18163,x18164)) % 165.30/165.06 [1817]~E(x18171,x18172)+E(f141(x18173,x18171,x18174),f141(x18173,x18172,x18174)) % 165.30/165.06 [1818]~E(x18181,x18182)+E(f141(x18183,x18184,x18181),f141(x18183,x18184,x18182)) % 165.30/165.06 [1819]~E(x18191,x18192)+E(f595(x18191,x18193,x18194),f595(x18192,x18193,x18194)) % 165.30/165.06 [1820]~E(x18201,x18202)+E(f595(x18203,x18201,x18204),f595(x18203,x18202,x18204)) % 165.30/165.06 [1821]~E(x18211,x18212)+E(f595(x18213,x18214,x18211),f595(x18213,x18214,x18212)) % 165.30/165.06 [1822]~E(x18221,x18222)+E(f818(x18221,x18223),f818(x18222,x18223)) % 165.30/165.06 [1823]~E(x18231,x18232)+E(f818(x18233,x18231),f818(x18233,x18232)) % 165.30/165.06 [1824]~E(x18241,x18242)+E(f842(x18241,x18243,x18244,x18245),f842(x18242,x18243,x18244,x18245)) % 165.30/165.06 [1825]~E(x18251,x18252)+E(f842(x18253,x18251,x18254,x18255),f842(x18253,x18252,x18254,x18255)) % 165.30/165.06 [1826]~E(x18261,x18262)+E(f842(x18263,x18264,x18261,x18265),f842(x18263,x18264,x18262,x18265)) % 165.30/165.06 [1827]~E(x18271,x18272)+E(f842(x18273,x18274,x18275,x18271),f842(x18273,x18274,x18275,x18272)) % 165.30/165.06 [1828]~E(x18281,x18282)+E(f473(x18281,x18283,x18284,x18285,x18286),f473(x18282,x18283,x18284,x18285,x18286)) % 165.30/165.06 [1829]~E(x18291,x18292)+E(f473(x18293,x18291,x18294,x18295,x18296),f473(x18293,x18292,x18294,x18295,x18296)) % 165.30/165.06 [1830]~E(x18301,x18302)+E(f473(x18303,x18304,x18301,x18305,x18306),f473(x18303,x18304,x18302,x18305,x18306)) % 165.30/165.06 [1831]~E(x18311,x18312)+E(f473(x18313,x18314,x18315,x18311,x18316),f473(x18313,x18314,x18315,x18312,x18316)) % 165.30/165.06 [1832]~E(x18321,x18322)+E(f473(x18323,x18324,x18325,x18326,x18321),f473(x18323,x18324,x18325,x18326,x18322)) % 165.30/165.06 [1833]~E(x18331,x18332)+E(f362(x18331,x18333,x18334,x18335),f362(x18332,x18333,x18334,x18335)) % 165.30/165.06 [1834]~E(x18341,x18342)+E(f362(x18343,x18341,x18344,x18345),f362(x18343,x18342,x18344,x18345)) % 165.30/165.06 [1835]~E(x18351,x18352)+E(f362(x18353,x18354,x18351,x18355),f362(x18353,x18354,x18352,x18355)) % 165.30/165.06 [1836]~E(x18361,x18362)+E(f362(x18363,x18364,x18365,x18361),f362(x18363,x18364,x18365,x18362)) % 165.30/165.06 [1837]~E(x18371,x18372)+E(f440(x18371,x18373,x18374,x18375),f440(x18372,x18373,x18374,x18375)) % 165.30/165.06 [1838]~E(x18381,x18382)+E(f440(x18383,x18381,x18384,x18385),f440(x18383,x18382,x18384,x18385)) % 165.30/165.06 [1839]~E(x18391,x18392)+E(f440(x18393,x18394,x18391,x18395),f440(x18393,x18394,x18392,x18395)) % 165.30/165.06 [1840]~E(x18401,x18402)+E(f440(x18403,x18404,x18405,x18401),f440(x18403,x18404,x18405,x18402)) % 165.30/165.06 [1841]~E(x18411,x18412)+E(f293(x18411,x18413,x18414),f293(x18412,x18413,x18414)) % 165.30/165.06 [1842]~E(x18421,x18422)+E(f293(x18423,x18421,x18424),f293(x18423,x18422,x18424)) % 165.30/165.06 [1843]~E(x18431,x18432)+E(f293(x18433,x18434,x18431),f293(x18433,x18434,x18432)) % 165.30/165.06 [1844]~E(x18441,x18442)+E(f235(x18441,x18443,x18444),f235(x18442,x18443,x18444)) % 165.30/165.06 [1845]~E(x18451,x18452)+E(f235(x18453,x18451,x18454),f235(x18453,x18452,x18454)) % 165.30/165.06 [1846]~E(x18461,x18462)+E(f235(x18463,x18464,x18461),f235(x18463,x18464,x18462)) % 165.30/165.06 [1847]~E(x18471,x18472)+E(f479(x18471,x18473,x18474,x18475),f479(x18472,x18473,x18474,x18475)) % 165.30/165.06 [1848]~E(x18481,x18482)+E(f479(x18483,x18481,x18484,x18485),f479(x18483,x18482,x18484,x18485)) % 165.30/165.06 [1849]~E(x18491,x18492)+E(f479(x18493,x18494,x18491,x18495),f479(x18493,x18494,x18492,x18495)) % 165.30/165.06 [1850]~E(x18501,x18502)+E(f479(x18503,x18504,x18505,x18501),f479(x18503,x18504,x18505,x18502)) % 165.30/165.06 [1851]~E(x18511,x18512)+E(f410(x18511,x18513,x18514,x18515,x18516),f410(x18512,x18513,x18514,x18515,x18516)) % 165.30/165.06 [1852]~E(x18521,x18522)+E(f410(x18523,x18521,x18524,x18525,x18526),f410(x18523,x18522,x18524,x18525,x18526)) % 165.30/165.06 [1853]~E(x18531,x18532)+E(f410(x18533,x18534,x18531,x18535,x18536),f410(x18533,x18534,x18532,x18535,x18536)) % 165.30/165.06 [1854]~E(x18541,x18542)+E(f410(x18543,x18544,x18545,x18541,x18546),f410(x18543,x18544,x18545,x18542,x18546)) % 165.30/165.06 [1855]~E(x18551,x18552)+E(f410(x18553,x18554,x18555,x18556,x18551),f410(x18553,x18554,x18555,x18556,x18552)) % 165.30/165.06 [1856]~E(x18561,x18562)+E(f437(x18561,x18563,x18564),f437(x18562,x18563,x18564)) % 165.30/165.06 [1857]~E(x18571,x18572)+E(f437(x18573,x18571,x18574),f437(x18573,x18572,x18574)) % 165.30/165.06 [1858]~E(x18581,x18582)+E(f437(x18583,x18584,x18581),f437(x18583,x18584,x18582)) % 165.30/165.06 [1859]~E(x18591,x18592)+E(f560(x18591,x18593,x18594,x18595),f560(x18592,x18593,x18594,x18595)) % 165.30/165.06 [1860]~E(x18601,x18602)+E(f560(x18603,x18601,x18604,x18605),f560(x18603,x18602,x18604,x18605)) % 165.30/165.06 [1861]~E(x18611,x18612)+E(f560(x18613,x18614,x18611,x18615),f560(x18613,x18614,x18612,x18615)) % 165.30/165.06 [1862]~E(x18621,x18622)+E(f560(x18623,x18624,x18625,x18621),f560(x18623,x18624,x18625,x18622)) % 165.30/165.06 [1863]~E(x18631,x18632)+E(f416(x18631,x18633,x18634),f416(x18632,x18633,x18634)) % 165.30/165.06 [1864]~E(x18641,x18642)+E(f416(x18643,x18641,x18644),f416(x18643,x18642,x18644)) % 165.30/165.06 [1865]~E(x18651,x18652)+E(f416(x18653,x18654,x18651),f416(x18653,x18654,x18652)) % 165.30/165.06 [1866]~E(x18661,x18662)+E(f402(x18661,x18663),f402(x18662,x18663)) % 165.30/165.06 [1867]~E(x18671,x18672)+E(f402(x18673,x18671),f402(x18673,x18672)) % 165.30/165.06 [1868]~E(x18681,x18682)+E(f565(x18681,x18683,x18684,x18685,x18686),f565(x18682,x18683,x18684,x18685,x18686)) % 165.30/165.06 [1869]~E(x18691,x18692)+E(f565(x18693,x18691,x18694,x18695,x18696),f565(x18693,x18692,x18694,x18695,x18696)) % 165.30/165.06 [1870]~E(x18701,x18702)+E(f565(x18703,x18704,x18701,x18705,x18706),f565(x18703,x18704,x18702,x18705,x18706)) % 165.30/165.06 [1871]~E(x18711,x18712)+E(f565(x18713,x18714,x18715,x18711,x18716),f565(x18713,x18714,x18715,x18712,x18716)) % 165.30/165.06 [1872]~E(x18721,x18722)+E(f565(x18723,x18724,x18725,x18726,x18721),f565(x18723,x18724,x18725,x18726,x18722)) % 165.30/165.06 [1873]~E(x18731,x18732)+E(f462(x18731,x18733,x18734),f462(x18732,x18733,x18734)) % 165.30/165.06 [1874]~E(x18741,x18742)+E(f462(x18743,x18741,x18744),f462(x18743,x18742,x18744)) % 165.30/165.06 [1875]~E(x18751,x18752)+E(f462(x18753,x18754,x18751),f462(x18753,x18754,x18752)) % 165.30/165.06 [1876]~E(x18761,x18762)+E(f358(x18761,x18763,x18764,x18765,x18766,x18767),f358(x18762,x18763,x18764,x18765,x18766,x18767)) % 165.30/165.06 [1877]~E(x18771,x18772)+E(f358(x18773,x18771,x18774,x18775,x18776,x18777),f358(x18773,x18772,x18774,x18775,x18776,x18777)) % 165.30/165.06 [1878]~E(x18781,x18782)+E(f358(x18783,x18784,x18781,x18785,x18786,x18787),f358(x18783,x18784,x18782,x18785,x18786,x18787)) % 165.30/165.06 [1879]~E(x18791,x18792)+E(f358(x18793,x18794,x18795,x18791,x18796,x18797),f358(x18793,x18794,x18795,x18792,x18796,x18797)) % 165.30/165.06 [1880]~E(x18801,x18802)+E(f358(x18803,x18804,x18805,x18806,x18801,x18807),f358(x18803,x18804,x18805,x18806,x18802,x18807)) % 165.30/165.06 [1881]~E(x18811,x18812)+E(f358(x18813,x18814,x18815,x18816,x18817,x18811),f358(x18813,x18814,x18815,x18816,x18817,x18812)) % 165.30/165.06 [1882]~E(x18821,x18822)+E(f547(x18821,x18823,x18824),f547(x18822,x18823,x18824)) % 165.30/165.06 [1883]~E(x18831,x18832)+E(f547(x18833,x18831,x18834),f547(x18833,x18832,x18834)) % 165.30/165.06 [1884]~E(x18841,x18842)+E(f547(x18843,x18844,x18841),f547(x18843,x18844,x18842)) % 165.30/165.06 [1885]~E(x18851,x18852)+E(f859(x18851,x18853,x18854,x18855,x18856),f859(x18852,x18853,x18854,x18855,x18856)) % 165.30/165.06 [1886]~E(x18861,x18862)+E(f859(x18863,x18861,x18864,x18865,x18866),f859(x18863,x18862,x18864,x18865,x18866)) % 165.30/165.06 [1887]~E(x18871,x18872)+E(f859(x18873,x18874,x18871,x18875,x18876),f859(x18873,x18874,x18872,x18875,x18876)) % 165.30/165.06 [1888]~E(x18881,x18882)+E(f859(x18883,x18884,x18885,x18881,x18886),f859(x18883,x18884,x18885,x18882,x18886)) % 165.30/165.06 [1889]~E(x18891,x18892)+E(f859(x18893,x18894,x18895,x18896,x18891),f859(x18893,x18894,x18895,x18896,x18892)) % 165.30/165.06 [1890]~E(x18901,x18902)+E(f614(x18901,x18903,x18904),f614(x18902,x18903,x18904)) % 165.30/165.06 [1891]~E(x18911,x18912)+E(f614(x18913,x18911,x18914),f614(x18913,x18912,x18914)) % 165.30/165.06 [1892]~E(x18921,x18922)+E(f614(x18923,x18924,x18921),f614(x18923,x18924,x18922)) % 165.30/165.06 [1893]~E(x18931,x18932)+E(f790(x18931),f790(x18932)) % 165.30/165.06 [1894]~E(x18941,x18942)+E(f650(x18941,x18943,x18944),f650(x18942,x18943,x18944)) % 165.30/165.06 [1895]~E(x18951,x18952)+E(f650(x18953,x18951,x18954),f650(x18953,x18952,x18954)) % 165.30/165.06 [1896]~E(x18961,x18962)+E(f650(x18963,x18964,x18961),f650(x18963,x18964,x18962)) % 165.30/165.06 [1897]~E(x18971,x18972)+E(f399(x18971,x18973,x18974,x18975),f399(x18972,x18973,x18974,x18975)) % 165.30/165.06 [1898]~E(x18981,x18982)+E(f399(x18983,x18981,x18984,x18985),f399(x18983,x18982,x18984,x18985)) % 165.30/165.06 [1899]~E(x18991,x18992)+E(f399(x18993,x18994,x18991,x18995),f399(x18993,x18994,x18992,x18995)) % 165.30/165.06 [1900]~E(x19001,x19002)+E(f399(x19003,x19004,x19005,x19001),f399(x19003,x19004,x19005,x19002)) % 165.30/165.06 [1901]~E(x19011,x19012)+E(f734(x19011,x19013,x19014),f734(x19012,x19013,x19014)) % 165.30/165.06 [1902]~E(x19021,x19022)+E(f734(x19023,x19021,x19024),f734(x19023,x19022,x19024)) % 165.30/165.06 [1903]~E(x19031,x19032)+E(f734(x19033,x19034,x19031),f734(x19033,x19034,x19032)) % 165.30/165.06 [1904]~E(x19041,x19042)+E(f163(x19041,x19043),f163(x19042,x19043)) % 165.30/165.06 [1905]~E(x19051,x19052)+E(f163(x19053,x19051),f163(x19053,x19052)) % 165.30/165.06 [1906]~E(x19061,x19062)+E(f262(x19061,x19063,x19064),f262(x19062,x19063,x19064)) % 165.30/165.06 [1907]~E(x19071,x19072)+E(f262(x19073,x19071,x19074),f262(x19073,x19072,x19074)) % 165.30/165.06 [1908]~E(x19081,x19082)+E(f262(x19083,x19084,x19081),f262(x19083,x19084,x19082)) % 165.30/165.06 [1909]~E(x19091,x19092)+E(f794(x19091,x19093,x19094),f794(x19092,x19093,x19094)) % 165.30/165.06 [1910]~E(x19101,x19102)+E(f794(x19103,x19101,x19104),f794(x19103,x19102,x19104)) % 165.30/165.06 [1911]~E(x19111,x19112)+E(f794(x19113,x19114,x19111),f794(x19113,x19114,x19112)) % 165.30/165.06 [1912]~E(x19121,x19122)+E(f752(x19121,x19123,x19124,x19125,x19126),f752(x19122,x19123,x19124,x19125,x19126)) % 165.30/165.06 [1913]~E(x19131,x19132)+E(f752(x19133,x19131,x19134,x19135,x19136),f752(x19133,x19132,x19134,x19135,x19136)) % 165.30/165.06 [1914]~E(x19141,x19142)+E(f752(x19143,x19144,x19141,x19145,x19146),f752(x19143,x19144,x19142,x19145,x19146)) % 165.30/165.06 [1915]~E(x19151,x19152)+E(f752(x19153,x19154,x19155,x19151,x19156),f752(x19153,x19154,x19155,x19152,x19156)) % 165.30/165.06 [1916]~E(x19161,x19162)+E(f752(x19163,x19164,x19165,x19166,x19161),f752(x19163,x19164,x19165,x19166,x19162)) % 165.30/165.06 [1917]~E(x19171,x19172)+E(f341(x19171),f341(x19172)) % 165.30/165.06 [1918]~E(x19181,x19182)+E(f713(x19181,x19183,x19184,x19185,x19186),f713(x19182,x19183,x19184,x19185,x19186)) % 165.30/165.06 [1919]~E(x19191,x19192)+E(f713(x19193,x19191,x19194,x19195,x19196),f713(x19193,x19192,x19194,x19195,x19196)) % 165.30/165.06 [1920]~E(x19201,x19202)+E(f713(x19203,x19204,x19201,x19205,x19206),f713(x19203,x19204,x19202,x19205,x19206)) % 165.30/165.06 [1921]~E(x19211,x19212)+E(f713(x19213,x19214,x19215,x19211,x19216),f713(x19213,x19214,x19215,x19212,x19216)) % 165.30/165.06 [1922]~E(x19221,x19222)+E(f713(x19223,x19224,x19225,x19226,x19221),f713(x19223,x19224,x19225,x19226,x19222)) % 165.30/165.06 [1923]~E(x19231,x19232)+E(f667(x19231,x19233),f667(x19232,x19233)) % 165.30/165.06 [1924]~E(x19241,x19242)+E(f667(x19243,x19241),f667(x19243,x19242)) % 165.30/165.06 [1925]~E(x19251,x19252)+E(f848(x19251,x19253,x19254),f848(x19252,x19253,x19254)) % 165.30/165.06 [1926]~E(x19261,x19262)+E(f848(x19263,x19261,x19264),f848(x19263,x19262,x19264)) % 165.30/165.06 [1927]~E(x19271,x19272)+E(f848(x19273,x19274,x19271),f848(x19273,x19274,x19272)) % 165.30/165.06 [1928]~E(x19281,x19282)+E(f448(x19281,x19283),f448(x19282,x19283)) % 165.30/165.06 [1929]~E(x19291,x19292)+E(f448(x19293,x19291),f448(x19293,x19292)) % 165.30/165.06 [1930]~E(x19301,x19302)+E(f248(x19301,x19303),f248(x19302,x19303)) % 165.30/165.06 [1931]~E(x19311,x19312)+E(f248(x19313,x19311),f248(x19313,x19312)) % 165.30/165.06 [1932]~E(x19321,x19322)+E(f741(x19321,x19323,x19324),f741(x19322,x19323,x19324)) % 165.30/165.06 [1933]~E(x19331,x19332)+E(f741(x19333,x19331,x19334),f741(x19333,x19332,x19334)) % 165.30/165.06 [1934]~E(x19341,x19342)+E(f741(x19343,x19344,x19341),f741(x19343,x19344,x19342)) % 165.30/165.06 [1935]~E(x19351,x19352)+E(f611(x19351,x19353,x19354),f611(x19352,x19353,x19354)) % 165.30/165.06 [1936]~E(x19361,x19362)+E(f611(x19363,x19361,x19364),f611(x19363,x19362,x19364)) % 165.30/165.06 [1937]~E(x19371,x19372)+E(f611(x19373,x19374,x19371),f611(x19373,x19374,x19372)) % 165.30/165.06 [1938]~E(x19381,x19382)+E(f575(x19381,x19383,x19384,x19385,x19386),f575(x19382,x19383,x19384,x19385,x19386)) % 165.30/165.06 [1939]~E(x19391,x19392)+E(f575(x19393,x19391,x19394,x19395,x19396),f575(x19393,x19392,x19394,x19395,x19396)) % 165.30/165.06 [1940]~E(x19401,x19402)+E(f575(x19403,x19404,x19401,x19405,x19406),f575(x19403,x19404,x19402,x19405,x19406)) % 165.30/165.06 [1941]~E(x19411,x19412)+E(f575(x19413,x19414,x19415,x19411,x19416),f575(x19413,x19414,x19415,x19412,x19416)) % 165.30/165.06 [1942]~E(x19421,x19422)+E(f575(x19423,x19424,x19425,x19426,x19421),f575(x19423,x19424,x19425,x19426,x19422)) % 165.30/165.06 [1943]~E(x19431,x19432)+E(f295(x19431,x19433,x19434),f295(x19432,x19433,x19434)) % 165.30/165.06 [1944]~E(x19441,x19442)+E(f295(x19443,x19441,x19444),f295(x19443,x19442,x19444)) % 165.30/165.06 [1945]~E(x19451,x19452)+E(f295(x19453,x19454,x19451),f295(x19453,x19454,x19452)) % 165.30/165.06 [1946]~E(x19461,x19462)+E(f712(x19461,x19463,x19464,x19465,x19466),f712(x19462,x19463,x19464,x19465,x19466)) % 165.30/165.06 [1947]~E(x19471,x19472)+E(f712(x19473,x19471,x19474,x19475,x19476),f712(x19473,x19472,x19474,x19475,x19476)) % 165.30/165.06 [1948]~E(x19481,x19482)+E(f712(x19483,x19484,x19481,x19485,x19486),f712(x19483,x19484,x19482,x19485,x19486)) % 165.30/165.06 [1949]~E(x19491,x19492)+E(f712(x19493,x19494,x19495,x19491,x19496),f712(x19493,x19494,x19495,x19492,x19496)) % 165.30/165.06 [1950]~E(x19501,x19502)+E(f712(x19503,x19504,x19505,x19506,x19501),f712(x19503,x19504,x19505,x19506,x19502)) % 165.30/165.06 [1951]~E(x19511,x19512)+E(f461(x19511,x19513,x19514),f461(x19512,x19513,x19514)) % 165.30/165.06 [1952]~E(x19521,x19522)+E(f461(x19523,x19521,x19524),f461(x19523,x19522,x19524)) % 165.30/165.06 [1953]~E(x19531,x19532)+E(f461(x19533,x19534,x19531),f461(x19533,x19534,x19532)) % 165.30/165.06 [1954]~E(x19541,x19542)+E(f700(x19541,x19543,x19544,x19545,x19546,x19547),f700(x19542,x19543,x19544,x19545,x19546,x19547)) % 165.30/165.06 [1955]~E(x19551,x19552)+E(f700(x19553,x19551,x19554,x19555,x19556,x19557),f700(x19553,x19552,x19554,x19555,x19556,x19557)) % 165.30/165.06 [1956]~E(x19561,x19562)+E(f700(x19563,x19564,x19561,x19565,x19566,x19567),f700(x19563,x19564,x19562,x19565,x19566,x19567)) % 165.30/165.06 [1957]~E(x19571,x19572)+E(f700(x19573,x19574,x19575,x19571,x19576,x19577),f700(x19573,x19574,x19575,x19572,x19576,x19577)) % 165.30/165.06 [1958]~E(x19581,x19582)+E(f700(x19583,x19584,x19585,x19586,x19581,x19587),f700(x19583,x19584,x19585,x19586,x19582,x19587)) % 165.30/165.06 [1959]~E(x19591,x19592)+E(f700(x19593,x19594,x19595,x19596,x19597,x19591),f700(x19593,x19594,x19595,x19596,x19597,x19592)) % 165.30/165.06 [1960]~E(x19601,x19602)+E(f545(x19601,x19603,x19604),f545(x19602,x19603,x19604)) % 165.30/165.06 [1961]~E(x19611,x19612)+E(f545(x19613,x19611,x19614),f545(x19613,x19612,x19614)) % 165.30/165.06 [1962]~E(x19621,x19622)+E(f545(x19623,x19624,x19621),f545(x19623,x19624,x19622)) % 165.30/165.06 [1963]~E(x19631,x19632)+E(f787(x19631,x19633,x19634),f787(x19632,x19633,x19634)) % 165.30/165.06 [1964]~E(x19641,x19642)+E(f787(x19643,x19641,x19644),f787(x19643,x19642,x19644)) % 165.30/165.06 [1965]~E(x19651,x19652)+E(f787(x19653,x19654,x19651),f787(x19653,x19654,x19652)) % 165.30/165.06 [1966]~E(x19661,x19662)+E(f797(x19661,x19663,x19664,x19665),f797(x19662,x19663,x19664,x19665)) % 165.30/165.06 [1967]~E(x19671,x19672)+E(f797(x19673,x19671,x19674,x19675),f797(x19673,x19672,x19674,x19675)) % 165.30/165.06 [1968]~E(x19681,x19682)+E(f797(x19683,x19684,x19681,x19685),f797(x19683,x19684,x19682,x19685)) % 165.30/165.06 [1969]~E(x19691,x19692)+E(f797(x19693,x19694,x19695,x19691),f797(x19693,x19694,x19695,x19692)) % 165.30/165.06 [1970]~E(x19701,x19702)+E(f591(x19701,x19703,x19704,x19705,x19706),f591(x19702,x19703,x19704,x19705,x19706)) % 165.30/165.06 [1971]~E(x19711,x19712)+E(f591(x19713,x19711,x19714,x19715,x19716),f591(x19713,x19712,x19714,x19715,x19716)) % 165.30/165.06 [1972]~E(x19721,x19722)+E(f591(x19723,x19724,x19721,x19725,x19726),f591(x19723,x19724,x19722,x19725,x19726)) % 165.30/165.06 [1973]~E(x19731,x19732)+E(f591(x19733,x19734,x19735,x19731,x19736),f591(x19733,x19734,x19735,x19732,x19736)) % 165.30/165.06 [1974]~E(x19741,x19742)+E(f591(x19743,x19744,x19745,x19746,x19741),f591(x19743,x19744,x19745,x19746,x19742)) % 165.30/165.06 [1975]~E(x19751,x19752)+E(f791(x19751,x19753),f791(x19752,x19753)) % 165.30/165.06 [1976]~E(x19761,x19762)+E(f791(x19763,x19761),f791(x19763,x19762)) % 165.30/165.06 [1977]~E(x19771,x19772)+E(f831(x19771,x19773,x19774,x19775,x19776),f831(x19772,x19773,x19774,x19775,x19776)) % 165.30/165.06 [1978]~E(x19781,x19782)+E(f831(x19783,x19781,x19784,x19785,x19786),f831(x19783,x19782,x19784,x19785,x19786)) % 165.30/165.06 [1979]~E(x19791,x19792)+E(f831(x19793,x19794,x19791,x19795,x19796),f831(x19793,x19794,x19792,x19795,x19796)) % 165.30/165.06 [1980]~E(x19801,x19802)+E(f831(x19803,x19804,x19805,x19801,x19806),f831(x19803,x19804,x19805,x19802,x19806)) % 165.30/165.06 [1981]~E(x19811,x19812)+E(f831(x19813,x19814,x19815,x19816,x19811),f831(x19813,x19814,x19815,x19816,x19812)) % 165.30/165.06 [1982]~E(x19821,x19822)+E(f815(x19821),f815(x19822)) % 165.30/165.06 [1983]~E(x19831,x19832)+E(f514(x19831,x19833,x19834),f514(x19832,x19833,x19834)) % 165.30/165.06 [1984]~E(x19841,x19842)+E(f514(x19843,x19841,x19844),f514(x19843,x19842,x19844)) % 165.30/165.06 [1985]~E(x19851,x19852)+E(f514(x19853,x19854,x19851),f514(x19853,x19854,x19852)) % 165.30/165.06 [1986]~E(x19861,x19862)+E(f572(x19861,x19863,x19864),f572(x19862,x19863,x19864)) % 165.30/165.06 [1987]~E(x19871,x19872)+E(f572(x19873,x19871,x19874),f572(x19873,x19872,x19874)) % 165.30/165.06 [1988]~E(x19881,x19882)+E(f572(x19883,x19884,x19881),f572(x19883,x19884,x19882)) % 165.30/165.06 [1989]~E(x19891,x19892)+E(f660(x19891,x19893,x19894),f660(x19892,x19893,x19894)) % 165.30/165.06 [1990]~E(x19901,x19902)+E(f660(x19903,x19901,x19904),f660(x19903,x19902,x19904)) % 165.30/165.06 [1991]~E(x19911,x19912)+E(f660(x19913,x19914,x19911),f660(x19913,x19914,x19912)) % 165.30/165.06 [1992]~E(x19921,x19922)+E(f777(x19921,x19923,x19924,x19925),f777(x19922,x19923,x19924,x19925)) % 165.30/165.06 [1993]~E(x19931,x19932)+E(f777(x19933,x19931,x19934,x19935),f777(x19933,x19932,x19934,x19935)) % 165.30/165.06 [1994]~E(x19941,x19942)+E(f777(x19943,x19944,x19941,x19945),f777(x19943,x19944,x19942,x19945)) % 165.30/165.06 [1995]~E(x19951,x19952)+E(f777(x19953,x19954,x19955,x19951),f777(x19953,x19954,x19955,x19952)) % 165.30/165.06 [1996]~E(x19961,x19962)+E(f552(x19961,x19963,x19964),f552(x19962,x19963,x19964)) % 165.30/165.06 [1997]~E(x19971,x19972)+E(f552(x19973,x19971,x19974),f552(x19973,x19972,x19974)) % 165.30/165.06 [1998]~E(x19981,x19982)+E(f552(x19983,x19984,x19981),f552(x19983,x19984,x19982)) % 165.30/165.06 [1999]~E(x19991,x19992)+E(f803(x19991,x19993,x19994),f803(x19992,x19993,x19994)) % 165.30/165.06 [2000]~E(x20001,x20002)+E(f803(x20003,x20001,x20004),f803(x20003,x20002,x20004)) % 165.30/165.06 [2001]~E(x20011,x20012)+E(f803(x20013,x20014,x20011),f803(x20013,x20014,x20012)) % 165.30/165.06 [2002]~E(x20021,x20022)+E(f390(x20021,x20023,x20024,x20025),f390(x20022,x20023,x20024,x20025)) % 165.30/165.06 [2003]~E(x20031,x20032)+E(f390(x20033,x20031,x20034,x20035),f390(x20033,x20032,x20034,x20035)) % 165.30/165.06 [2004]~E(x20041,x20042)+E(f390(x20043,x20044,x20041,x20045),f390(x20043,x20044,x20042,x20045)) % 165.30/165.06 [2005]~E(x20051,x20052)+E(f390(x20053,x20054,x20055,x20051),f390(x20053,x20054,x20055,x20052)) % 165.30/165.06 [2006]~E(x20061,x20062)+E(f780(x20061,x20063),f780(x20062,x20063)) % 165.30/165.06 [2007]~E(x20071,x20072)+E(f780(x20073,x20071),f780(x20073,x20072)) % 165.30/165.06 [2008]~E(x20081,x20082)+E(f830(x20081,x20083,x20084,x20085,x20086),f830(x20082,x20083,x20084,x20085,x20086)) % 165.30/165.06 [2009]~E(x20091,x20092)+E(f830(x20093,x20091,x20094,x20095,x20096),f830(x20093,x20092,x20094,x20095,x20096)) % 165.30/165.06 [2010]~E(x20101,x20102)+E(f830(x20103,x20104,x20101,x20105,x20106),f830(x20103,x20104,x20102,x20105,x20106)) % 165.30/165.06 [2011]~E(x20111,x20112)+E(f830(x20113,x20114,x20115,x20111,x20116),f830(x20113,x20114,x20115,x20112,x20116)) % 165.30/165.06 [2012]~E(x20121,x20122)+E(f830(x20123,x20124,x20125,x20126,x20121),f830(x20123,x20124,x20125,x20126,x20122)) % 165.30/165.06 [2013]~E(x20131,x20132)+E(f766(x20131,x20133,x20134,x20135),f766(x20132,x20133,x20134,x20135)) % 165.30/165.06 [2014]~E(x20141,x20142)+E(f766(x20143,x20141,x20144,x20145),f766(x20143,x20142,x20144,x20145)) % 165.30/165.06 [2015]~E(x20151,x20152)+E(f766(x20153,x20154,x20151,x20155),f766(x20153,x20154,x20152,x20155)) % 165.30/165.06 [2016]~E(x20161,x20162)+E(f766(x20163,x20164,x20165,x20161),f766(x20163,x20164,x20165,x20162)) % 165.30/165.06 [2017]~E(x20171,x20172)+E(f704(x20171,x20173,x20174),f704(x20172,x20173,x20174)) % 165.30/165.06 [2018]~E(x20181,x20182)+E(f704(x20183,x20181,x20184),f704(x20183,x20182,x20184)) % 165.30/165.06 [2019]~E(x20191,x20192)+E(f704(x20193,x20194,x20191),f704(x20193,x20194,x20192)) % 165.30/165.06 [2020]~E(x20201,x20202)+E(f356(x20201,x20203,x20204,x20205,x20206),f356(x20202,x20203,x20204,x20205,x20206)) % 165.30/165.06 [2021]~E(x20211,x20212)+E(f356(x20213,x20211,x20214,x20215,x20216),f356(x20213,x20212,x20214,x20215,x20216)) % 165.30/165.06 [2022]~E(x20221,x20222)+E(f356(x20223,x20224,x20221,x20225,x20226),f356(x20223,x20224,x20222,x20225,x20226)) % 165.30/165.06 [2023]~E(x20231,x20232)+E(f356(x20233,x20234,x20235,x20231,x20236),f356(x20233,x20234,x20235,x20232,x20236)) % 165.30/165.06 [2024]~E(x20241,x20242)+E(f356(x20243,x20244,x20245,x20246,x20241),f356(x20243,x20244,x20245,x20246,x20242)) % 165.30/165.06 [2025]~E(x20251,x20252)+E(f671(x20251,x20253,x20254),f671(x20252,x20253,x20254)) % 165.30/165.06 [2026]~E(x20261,x20262)+E(f671(x20263,x20261,x20264),f671(x20263,x20262,x20264)) % 165.30/165.06 [2027]~E(x20271,x20272)+E(f671(x20273,x20274,x20271),f671(x20273,x20274,x20272)) % 165.30/165.06 [2028]~E(x20281,x20282)+E(f723(x20281,x20283,x20284),f723(x20282,x20283,x20284)) % 165.30/165.06 [2029]~E(x20291,x20292)+E(f723(x20293,x20291,x20294),f723(x20293,x20292,x20294)) % 165.30/165.06 [2030]~E(x20301,x20302)+E(f723(x20303,x20304,x20301),f723(x20303,x20304,x20302)) % 165.30/165.06 [2031]~E(x20311,x20312)+E(f598(x20311,x20313,x20314,x20315),f598(x20312,x20313,x20314,x20315)) % 165.30/165.06 [2032]~E(x20321,x20322)+E(f598(x20323,x20321,x20324,x20325),f598(x20323,x20322,x20324,x20325)) % 165.30/165.06 [2033]~E(x20331,x20332)+E(f598(x20333,x20334,x20331,x20335),f598(x20333,x20334,x20332,x20335)) % 165.30/165.06 [2034]~E(x20341,x20342)+E(f598(x20343,x20344,x20345,x20341),f598(x20343,x20344,x20345,x20342)) % 165.30/165.06 [2035]~E(x20351,x20352)+E(f821(x20351,x20353,x20354,x20355),f821(x20352,x20353,x20354,x20355)) % 165.30/165.06 [2036]~E(x20361,x20362)+E(f821(x20363,x20361,x20364,x20365),f821(x20363,x20362,x20364,x20365)) % 165.30/165.06 [2037]~E(x20371,x20372)+E(f821(x20373,x20374,x20371,x20375),f821(x20373,x20374,x20372,x20375)) % 165.30/165.06 [2038]~E(x20381,x20382)+E(f821(x20383,x20384,x20385,x20381),f821(x20383,x20384,x20385,x20382)) % 165.30/165.06 [2039]~E(x20391,x20392)+E(f506(x20391,x20393,x20394,x20395),f506(x20392,x20393,x20394,x20395)) % 165.30/165.06 [2040]~E(x20401,x20402)+E(f506(x20403,x20401,x20404,x20405),f506(x20403,x20402,x20404,x20405)) % 165.30/165.06 [2041]~E(x20411,x20412)+E(f506(x20413,x20414,x20411,x20415),f506(x20413,x20414,x20412,x20415)) % 165.30/165.06 [2042]~E(x20421,x20422)+E(f506(x20423,x20424,x20425,x20421),f506(x20423,x20424,x20425,x20422)) % 165.30/165.06 [2043]~E(x20431,x20432)+E(f315(x20431,x20433,x20434),f315(x20432,x20433,x20434)) % 165.30/165.06 [2044]~E(x20441,x20442)+E(f315(x20443,x20441,x20444),f315(x20443,x20442,x20444)) % 165.30/165.06 [2045]~E(x20451,x20452)+E(f315(x20453,x20454,x20451),f315(x20453,x20454,x20452)) % 165.30/165.06 [2046]~E(x20461,x20462)+E(f719(x20461,x20463,x20464),f719(x20462,x20463,x20464)) % 165.30/165.06 [2047]~E(x20471,x20472)+E(f719(x20473,x20471,x20474),f719(x20473,x20472,x20474)) % 165.30/165.06 [2048]~E(x20481,x20482)+E(f719(x20483,x20484,x20481),f719(x20483,x20484,x20482)) % 165.30/165.06 [2049]~E(x20491,x20492)+E(f569(x20491,x20493,x20494),f569(x20492,x20493,x20494)) % 165.30/165.06 [2050]~E(x20501,x20502)+E(f569(x20503,x20501,x20504),f569(x20503,x20502,x20504)) % 165.30/165.06 [2051]~E(x20511,x20512)+E(f569(x20513,x20514,x20511),f569(x20513,x20514,x20512)) % 165.30/165.06 [2052]~E(x20521,x20522)+E(f523(x20521,x20523,x20524,x20525,x20526),f523(x20522,x20523,x20524,x20525,x20526)) % 165.30/165.06 [2053]~E(x20531,x20532)+E(f523(x20533,x20531,x20534,x20535,x20536),f523(x20533,x20532,x20534,x20535,x20536)) % 165.30/165.06 [2054]~E(x20541,x20542)+E(f523(x20543,x20544,x20541,x20545,x20546),f523(x20543,x20544,x20542,x20545,x20546)) % 165.30/165.06 [2055]~E(x20551,x20552)+E(f523(x20553,x20554,x20555,x20551,x20556),f523(x20553,x20554,x20555,x20552,x20556)) % 165.30/165.06 [2056]~E(x20561,x20562)+E(f523(x20563,x20564,x20565,x20566,x20561),f523(x20563,x20564,x20565,x20566,x20562)) % 165.30/165.06 [2057]~E(x20571,x20572)+E(f348(x20571),f348(x20572)) % 165.30/165.06 [2058]~E(x20581,x20582)+E(f381(x20581,x20583,x20584),f381(x20582,x20583,x20584)) % 165.30/165.06 [2059]~E(x20591,x20592)+E(f381(x20593,x20591,x20594),f381(x20593,x20592,x20594)) % 165.30/165.06 [2060]~E(x20601,x20602)+E(f381(x20603,x20604,x20601),f381(x20603,x20604,x20602)) % 165.30/165.06 [2061]~E(x20611,x20612)+E(f459(x20611,x20613,x20614),f459(x20612,x20613,x20614)) % 165.30/165.06 [2062]~E(x20621,x20622)+E(f459(x20623,x20621,x20624),f459(x20623,x20622,x20624)) % 165.30/165.06 [2063]~E(x20631,x20632)+E(f459(x20633,x20634,x20631),f459(x20633,x20634,x20632)) % 165.30/165.06 [2064]~E(x20641,x20642)+E(f853(x20641,x20643,x20644),f853(x20642,x20643,x20644)) % 165.30/165.06 [2065]~E(x20651,x20652)+E(f853(x20653,x20651,x20654),f853(x20653,x20652,x20654)) % 165.30/165.06 [2066]~E(x20661,x20662)+E(f853(x20663,x20664,x20661),f853(x20663,x20664,x20662)) % 165.30/165.06 [2067]~E(x20671,x20672)+E(f688(x20671,x20673,x20674,x20675,x20676,x20677),f688(x20672,x20673,x20674,x20675,x20676,x20677)) % 165.30/165.06 [2068]~E(x20681,x20682)+E(f688(x20683,x20681,x20684,x20685,x20686,x20687),f688(x20683,x20682,x20684,x20685,x20686,x20687)) % 165.30/165.06 [2069]~E(x20691,x20692)+E(f688(x20693,x20694,x20691,x20695,x20696,x20697),f688(x20693,x20694,x20692,x20695,x20696,x20697)) % 165.30/165.06 [2070]~E(x20701,x20702)+E(f688(x20703,x20704,x20705,x20701,x20706,x20707),f688(x20703,x20704,x20705,x20702,x20706,x20707)) % 165.30/165.06 [2071]~E(x20711,x20712)+E(f688(x20713,x20714,x20715,x20716,x20711,x20717),f688(x20713,x20714,x20715,x20716,x20712,x20717)) % 165.30/165.06 [2072]~E(x20721,x20722)+E(f688(x20723,x20724,x20725,x20726,x20727,x20721),f688(x20723,x20724,x20725,x20726,x20727,x20722)) % 165.30/165.06 [2073]~E(x20731,x20732)+E(f823(x20731,x20733,x20734),f823(x20732,x20733,x20734)) % 165.30/165.06 [2074]~E(x20741,x20742)+E(f823(x20743,x20741,x20744),f823(x20743,x20742,x20744)) % 165.30/165.06 [2075]~E(x20751,x20752)+E(f823(x20753,x20754,x20751),f823(x20753,x20754,x20752)) % 165.30/165.06 [2076]~E(x20761,x20762)+E(f695(x20761,x20763,x20764,x20765),f695(x20762,x20763,x20764,x20765)) % 165.30/165.06 [2077]~E(x20771,x20772)+E(f695(x20773,x20771,x20774,x20775),f695(x20773,x20772,x20774,x20775)) % 165.30/165.06 [2078]~E(x20781,x20782)+E(f695(x20783,x20784,x20781,x20785),f695(x20783,x20784,x20782,x20785)) % 165.30/165.06 [2079]~E(x20791,x20792)+E(f695(x20793,x20794,x20795,x20791),f695(x20793,x20794,x20795,x20792)) % 165.30/165.06 [2080]~E(x20801,x20802)+E(f445(x20801,x20803),f445(x20802,x20803)) % 165.30/165.06 [2081]~E(x20811,x20812)+E(f445(x20813,x20811),f445(x20813,x20812)) % 165.30/165.06 [2082]~E(x20821,x20822)+E(f708(x20821,x20823,x20824),f708(x20822,x20823,x20824)) % 165.30/165.06 [2083]~E(x20831,x20832)+E(f708(x20833,x20831,x20834),f708(x20833,x20832,x20834)) % 165.30/165.06 [2084]~E(x20841,x20842)+E(f708(x20843,x20844,x20841),f708(x20843,x20844,x20842)) % 165.30/165.06 [2085]~E(x20851,x20852)+E(f646(x20851,x20853,x20854,x20855,x20856),f646(x20852,x20853,x20854,x20855,x20856)) % 165.30/165.06 [2086]~E(x20861,x20862)+E(f646(x20863,x20861,x20864,x20865,x20866),f646(x20863,x20862,x20864,x20865,x20866)) % 165.30/165.06 [2087]~E(x20871,x20872)+E(f646(x20873,x20874,x20871,x20875,x20876),f646(x20873,x20874,x20872,x20875,x20876)) % 165.30/165.06 [2088]~E(x20881,x20882)+E(f646(x20883,x20884,x20885,x20881,x20886),f646(x20883,x20884,x20885,x20882,x20886)) % 165.30/165.06 [2089]~E(x20891,x20892)+E(f646(x20893,x20894,x20895,x20896,x20891),f646(x20893,x20894,x20895,x20896,x20892)) % 165.30/165.06 [2090]~E(x20901,x20902)+E(f373(x20901,x20903,x20904,x20905),f373(x20902,x20903,x20904,x20905)) % 165.30/165.06 [2091]~E(x20911,x20912)+E(f373(x20913,x20911,x20914,x20915),f373(x20913,x20912,x20914,x20915)) % 165.30/165.06 [2092]~E(x20921,x20922)+E(f373(x20923,x20924,x20921,x20925),f373(x20923,x20924,x20922,x20925)) % 165.30/165.06 [2093]~E(x20931,x20932)+E(f373(x20933,x20934,x20935,x20931),f373(x20933,x20934,x20935,x20932)) % 165.30/165.06 [2094]~E(x20941,x20942)+E(f570(x20941,x20943,x20944),f570(x20942,x20943,x20944)) % 165.30/165.06 [2095]~E(x20951,x20952)+E(f570(x20953,x20951,x20954),f570(x20953,x20952,x20954)) % 165.30/165.06 [2096]~E(x20961,x20962)+E(f570(x20963,x20964,x20961),f570(x20963,x20964,x20962)) % 165.30/165.06 [2097]~E(x20971,x20972)+E(f406(x20971,x20973,x20974,x20975),f406(x20972,x20973,x20974,x20975)) % 165.30/165.06 [2098]~E(x20981,x20982)+E(f406(x20983,x20981,x20984,x20985),f406(x20983,x20982,x20984,x20985)) % 165.30/165.06 [2099]~E(x20991,x20992)+E(f406(x20993,x20994,x20991,x20995),f406(x20993,x20994,x20992,x20995)) % 165.30/165.06 [2100]~E(x21001,x21002)+E(f406(x21003,x21004,x21005,x21001),f406(x21003,x21004,x21005,x21002)) % 165.30/165.06 [2101]~E(x21011,x21012)+E(f615(x21011,x21013,x21014,x21015,x21016),f615(x21012,x21013,x21014,x21015,x21016)) % 165.30/165.06 [2102]~E(x21021,x21022)+E(f615(x21023,x21021,x21024,x21025,x21026),f615(x21023,x21022,x21024,x21025,x21026)) % 165.30/165.06 [2103]~E(x21031,x21032)+E(f615(x21033,x21034,x21031,x21035,x21036),f615(x21033,x21034,x21032,x21035,x21036)) % 165.30/165.06 [2104]~E(x21041,x21042)+E(f615(x21043,x21044,x21045,x21041,x21046),f615(x21043,x21044,x21045,x21042,x21046)) % 165.30/165.06 [2105]~E(x21051,x21052)+E(f615(x21053,x21054,x21055,x21056,x21051),f615(x21053,x21054,x21055,x21056,x21052)) % 165.30/165.06 [2106]~E(x21061,x21062)+E(f282(x21061,x21063,x21064),f282(x21062,x21063,x21064)) % 165.30/165.06 [2107]~E(x21071,x21072)+E(f282(x21073,x21071,x21074),f282(x21073,x21072,x21074)) % 165.30/165.06 [2108]~E(x21081,x21082)+E(f282(x21083,x21084,x21081),f282(x21083,x21084,x21082)) % 165.30/165.06 [2109]~E(x21091,x21092)+E(f693(x21091,x21093,x21094),f693(x21092,x21093,x21094)) % 165.30/165.06 [2110]~E(x21101,x21102)+E(f693(x21103,x21101,x21104),f693(x21103,x21102,x21104)) % 165.30/165.06 [2111]~E(x21111,x21112)+E(f693(x21113,x21114,x21111),f693(x21113,x21114,x21112)) % 165.30/165.06 [2112]~E(x21121,x21122)+E(f672(x21121,x21123,x21124,x21125),f672(x21122,x21123,x21124,x21125)) % 165.30/165.06 [2113]~E(x21131,x21132)+E(f672(x21133,x21131,x21134,x21135),f672(x21133,x21132,x21134,x21135)) % 165.30/165.06 [2114]~E(x21141,x21142)+E(f672(x21143,x21144,x21141,x21145),f672(x21143,x21144,x21142,x21145)) % 165.30/165.06 [2115]~E(x21151,x21152)+E(f672(x21153,x21154,x21155,x21151),f672(x21153,x21154,x21155,x21152)) % 165.30/165.06 [2116]~E(x21161,x21162)+E(f21(x21161,x21163),f21(x21162,x21163)) % 165.30/165.06 [2117]~E(x21171,x21172)+E(f21(x21173,x21171),f21(x21173,x21172)) % 165.30/165.06 [2118]~E(x21181,x21182)+E(f599(x21181,x21183,x21184,x21185,x21186),f599(x21182,x21183,x21184,x21185,x21186)) % 165.30/165.06 [2119]~E(x21191,x21192)+E(f599(x21193,x21191,x21194,x21195,x21196),f599(x21193,x21192,x21194,x21195,x21196)) % 165.30/165.06 [2120]~E(x21201,x21202)+E(f599(x21203,x21204,x21201,x21205,x21206),f599(x21203,x21204,x21202,x21205,x21206)) % 165.30/165.06 [2121]~E(x21211,x21212)+E(f599(x21213,x21214,x21215,x21211,x21216),f599(x21213,x21214,x21215,x21212,x21216)) % 165.30/165.06 [2122]~E(x21221,x21222)+E(f599(x21223,x21224,x21225,x21226,x21221),f599(x21223,x21224,x21225,x21226,x21222)) % 165.30/165.06 [2123]~E(x21231,x21232)+E(f628(x21231,x21233,x21234),f628(x21232,x21233,x21234)) % 165.30/165.06 [2124]~E(x21241,x21242)+E(f628(x21243,x21241,x21244),f628(x21243,x21242,x21244)) % 165.30/165.06 [2125]~E(x21251,x21252)+E(f628(x21253,x21254,x21251),f628(x21253,x21254,x21252)) % 165.30/165.06 [2126]~E(x21261,x21262)+E(f652(x21261,x21263,x21264,x21265),f652(x21262,x21263,x21264,x21265)) % 165.30/165.06 [2127]~E(x21271,x21272)+E(f652(x21273,x21271,x21274,x21275),f652(x21273,x21272,x21274,x21275)) % 165.30/165.06 [2128]~E(x21281,x21282)+E(f652(x21283,x21284,x21281,x21285),f652(x21283,x21284,x21282,x21285)) % 165.30/165.06 [2129]~E(x21291,x21292)+E(f652(x21293,x21294,x21295,x21291),f652(x21293,x21294,x21295,x21292)) % 165.30/165.06 [2130]~E(x21301,x21302)+E(f621(x21301,x21303,x21304),f621(x21302,x21303,x21304)) % 165.30/165.06 [2131]~E(x21311,x21312)+E(f621(x21313,x21311,x21314),f621(x21313,x21312,x21314)) % 165.30/165.06 [2132]~E(x21321,x21322)+E(f621(x21323,x21324,x21321),f621(x21323,x21324,x21322)) % 165.30/165.06 [2133]~E(x21331,x21332)+E(f198(x21331,x21333,x21334,x21335),f198(x21332,x21333,x21334,x21335)) % 165.30/165.06 [2134]~E(x21341,x21342)+E(f198(x21343,x21341,x21344,x21345),f198(x21343,x21342,x21344,x21345)) % 165.30/165.06 [2135]~E(x21351,x21352)+E(f198(x21353,x21354,x21351,x21355),f198(x21353,x21354,x21352,x21355)) % 165.30/165.06 [2136]~E(x21361,x21362)+E(f198(x21363,x21364,x21365,x21361),f198(x21363,x21364,x21365,x21362)) % 165.30/165.06 [2137]~E(x21371,x21372)+E(f230(x21371,x21373),f230(x21372,x21373)) % 165.30/165.06 [2138]~E(x21381,x21382)+E(f230(x21383,x21381),f230(x21383,x21382)) % 165.30/165.06 [2139]~E(x21391,x21392)+E(f541(x21391,x21393,x21394,x21395),f541(x21392,x21393,x21394,x21395)) % 165.30/165.06 [2140]~E(x21401,x21402)+E(f541(x21403,x21401,x21404,x21405),f541(x21403,x21402,x21404,x21405)) % 165.30/165.06 [2141]~E(x21411,x21412)+E(f541(x21413,x21414,x21411,x21415),f541(x21413,x21414,x21412,x21415)) % 165.30/165.06 [2142]~E(x21421,x21422)+E(f541(x21423,x21424,x21425,x21421),f541(x21423,x21424,x21425,x21422)) % 165.30/165.06 [2143]~E(x21431,x21432)+E(f635(x21431,x21433),f635(x21432,x21433)) % 165.30/165.06 [2144]~E(x21441,x21442)+E(f635(x21443,x21441),f635(x21443,x21442)) % 165.30/165.06 [2145]~E(x21451,x21452)+E(f532(x21451,x21453),f532(x21452,x21453)) % 165.30/165.06 [2146]~E(x21461,x21462)+E(f532(x21463,x21461),f532(x21463,x21462)) % 165.30/165.06 [2147]~E(x21471,x21472)+E(f655(x21471,x21473,x21474,x21475),f655(x21472,x21473,x21474,x21475)) % 165.30/165.06 [2148]~E(x21481,x21482)+E(f655(x21483,x21481,x21484,x21485),f655(x21483,x21482,x21484,x21485)) % 165.30/165.06 [2149]~E(x21491,x21492)+E(f655(x21493,x21494,x21491,x21495),f655(x21493,x21494,x21492,x21495)) % 165.30/165.06 [2150]~E(x21501,x21502)+E(f655(x21503,x21504,x21505,x21501),f655(x21503,x21504,x21505,x21502)) % 165.30/165.06 [2151]~E(x21511,x21512)+E(f554(x21511,x21513,x21514,x21515),f554(x21512,x21513,x21514,x21515)) % 165.30/165.06 [2152]~E(x21521,x21522)+E(f554(x21523,x21521,x21524,x21525),f554(x21523,x21522,x21524,x21525)) % 165.30/165.06 [2153]~E(x21531,x21532)+E(f554(x21533,x21534,x21531,x21535),f554(x21533,x21534,x21532,x21535)) % 165.30/165.06 [2154]~E(x21541,x21542)+E(f554(x21543,x21544,x21545,x21541),f554(x21543,x21544,x21545,x21542)) % 165.30/165.06 [2155]~E(x21551,x21552)+E(f314(x21551,x21553,x21554),f314(x21552,x21553,x21554)) % 165.30/165.06 [2156]~E(x21561,x21562)+E(f314(x21563,x21561,x21564),f314(x21563,x21562,x21564)) % 165.30/165.06 [2157]~E(x21571,x21572)+E(f314(x21573,x21574,x21571),f314(x21573,x21574,x21572)) % 165.30/165.06 [2158]~E(x21581,x21582)+E(f730(x21581,x21583,x21584),f730(x21582,x21583,x21584)) % 165.30/165.06 [2159]~E(x21591,x21592)+E(f730(x21593,x21591,x21594),f730(x21593,x21592,x21594)) % 165.30/165.06 [2160]~E(x21601,x21602)+E(f730(x21603,x21604,x21601),f730(x21603,x21604,x21602)) % 165.30/165.06 [2161]~E(x21611,x21612)+E(f509(x21611,x21613,x21614,x21615),f509(x21612,x21613,x21614,x21615)) % 165.30/165.06 [2162]~E(x21621,x21622)+E(f509(x21623,x21621,x21624,x21625),f509(x21623,x21622,x21624,x21625)) % 165.30/165.06 [2163]~E(x21631,x21632)+E(f509(x21633,x21634,x21631,x21635),f509(x21633,x21634,x21632,x21635)) % 165.30/165.06 [2164]~E(x21641,x21642)+E(f509(x21643,x21644,x21645,x21641),f509(x21643,x21644,x21645,x21642)) % 165.30/165.06 [2165]~E(x21651,x21652)+E(f431(x21651,x21653),f431(x21652,x21653)) % 165.30/165.06 [2166]~E(x21661,x21662)+E(f431(x21663,x21661),f431(x21663,x21662)) % 165.30/165.06 [2167]~E(x21671,x21672)+E(f632(x21671,x21673,x21674),f632(x21672,x21673,x21674)) % 165.30/165.06 [2168]~E(x21681,x21682)+E(f632(x21683,x21681,x21684),f632(x21683,x21682,x21684)) % 165.30/165.06 [2169]~E(x21691,x21692)+E(f632(x21693,x21694,x21691),f632(x21693,x21694,x21692)) % 165.30/165.06 [2170]~E(x21701,x21702)+E(f751(x21701,x21703,x21704,x21705,x21706),f751(x21702,x21703,x21704,x21705,x21706)) % 165.30/165.06 [2171]~E(x21711,x21712)+E(f751(x21713,x21711,x21714,x21715,x21716),f751(x21713,x21712,x21714,x21715,x21716)) % 165.30/165.06 [2172]~E(x21721,x21722)+E(f751(x21723,x21724,x21721,x21725,x21726),f751(x21723,x21724,x21722,x21725,x21726)) % 165.30/165.06 [2173]~E(x21731,x21732)+E(f751(x21733,x21734,x21735,x21731,x21736),f751(x21733,x21734,x21735,x21732,x21736)) % 165.30/165.06 [2174]~E(x21741,x21742)+E(f751(x21743,x21744,x21745,x21746,x21741),f751(x21743,x21744,x21745,x21746,x21742)) % 165.30/165.06 [2175]~E(x21751,x21752)+E(f296(x21751,x21753,x21754,x21755),f296(x21752,x21753,x21754,x21755)) % 165.30/165.06 [2176]~E(x21761,x21762)+E(f296(x21763,x21761,x21764,x21765),f296(x21763,x21762,x21764,x21765)) % 165.30/165.06 [2177]~E(x21771,x21772)+E(f296(x21773,x21774,x21771,x21775),f296(x21773,x21774,x21772,x21775)) % 165.30/165.06 [2178]~E(x21781,x21782)+E(f296(x21783,x21784,x21785,x21781),f296(x21783,x21784,x21785,x21782)) % 165.30/165.06 [2179]~E(x21791,x21792)+E(f753(x21791,x21793,x21794,x21795),f753(x21792,x21793,x21794,x21795)) % 165.30/165.06 [2180]~E(x21801,x21802)+E(f753(x21803,x21801,x21804,x21805),f753(x21803,x21802,x21804,x21805)) % 165.30/165.06 [2181]~E(x21811,x21812)+E(f753(x21813,x21814,x21811,x21815),f753(x21813,x21814,x21812,x21815)) % 165.30/165.06 [2182]~E(x21821,x21822)+E(f753(x21823,x21824,x21825,x21821),f753(x21823,x21824,x21825,x21822)) % 165.30/165.06 [2183]~E(x21831,x21832)+E(f383(x21831,x21833,x21834),f383(x21832,x21833,x21834)) % 165.30/165.06 [2184]~E(x21841,x21842)+E(f383(x21843,x21841,x21844),f383(x21843,x21842,x21844)) % 165.30/165.06 [2185]~E(x21851,x21852)+E(f383(x21853,x21854,x21851),f383(x21853,x21854,x21852)) % 165.30/165.06 [2186]~E(x21861,x21862)+E(f394(x21861,x21863),f394(x21862,x21863)) % 165.30/165.06 [2187]~E(x21871,x21872)+E(f394(x21873,x21871),f394(x21873,x21872)) % 165.30/165.06 [2188]~E(x21881,x21882)+E(f843(x21881,x21883,x21884),f843(x21882,x21883,x21884)) % 165.30/165.06 [2189]~E(x21891,x21892)+E(f843(x21893,x21891,x21894),f843(x21893,x21892,x21894)) % 165.30/165.06 [2190]~E(x21901,x21902)+E(f843(x21903,x21904,x21901),f843(x21903,x21904,x21902)) % 165.30/165.06 [2191]~E(x21911,x21912)+E(f793(x21911),f793(x21912)) % 165.30/165.06 [2192]~E(x21921,x21922)+E(f795(x21921,x21923,x21924),f795(x21922,x21923,x21924)) % 165.30/165.06 [2193]~E(x21931,x21932)+E(f795(x21933,x21931,x21934),f795(x21933,x21932,x21934)) % 165.30/165.06 [2194]~E(x21941,x21942)+E(f795(x21943,x21944,x21941),f795(x21943,x21944,x21942)) % 165.30/165.06 [2195]~E(x21951,x21952)+E(f763(x21951,x21953,x21954),f763(x21952,x21953,x21954)) % 165.30/165.06 [2196]~E(x21961,x21962)+E(f763(x21963,x21961,x21964),f763(x21963,x21962,x21964)) % 165.30/165.06 [2197]~E(x21971,x21972)+E(f763(x21973,x21974,x21971),f763(x21973,x21974,x21972)) % 165.30/165.06 [2198]~E(x21981,x21982)+E(f441(x21981,x21983),f441(x21982,x21983)) % 165.30/165.06 [2199]~E(x21991,x21992)+E(f441(x21993,x21991),f441(x21993,x21992)) % 165.30/165.06 [2200]~E(x22001,x22002)+E(f573(x22001,x22003,x22004,x22005),f573(x22002,x22003,x22004,x22005)) % 165.30/165.06 [2201]~E(x22011,x22012)+E(f573(x22013,x22011,x22014,x22015),f573(x22013,x22012,x22014,x22015)) % 165.30/165.06 [2202]~E(x22021,x22022)+E(f573(x22023,x22024,x22021,x22025),f573(x22023,x22024,x22022,x22025)) % 165.30/165.06 [2203]~E(x22031,x22032)+E(f573(x22033,x22034,x22035,x22031),f573(x22033,x22034,x22035,x22032)) % 165.30/165.06 [2204]~E(x22041,x22042)+E(f637(x22041,x22043,x22044),f637(x22042,x22043,x22044)) % 165.30/165.06 [2205]~E(x22051,x22052)+E(f637(x22053,x22051,x22054),f637(x22053,x22052,x22054)) % 165.30/165.06 [2206]~E(x22061,x22062)+E(f637(x22063,x22064,x22061),f637(x22063,x22064,x22062)) % 165.30/165.06 [2207]~E(x22071,x22072)+E(f694(x22071,x22073,x22074),f694(x22072,x22073,x22074)) % 165.30/165.06 [2208]~E(x22081,x22082)+E(f694(x22083,x22081,x22084),f694(x22083,x22082,x22084)) % 165.30/165.06 [2209]~E(x22091,x22092)+E(f694(x22093,x22094,x22091),f694(x22093,x22094,x22092)) % 165.30/165.06 [2210]~E(x22101,x22102)+E(f682(x22101,x22103,x22104,x22105),f682(x22102,x22103,x22104,x22105)) % 165.30/165.06 [2211]~E(x22111,x22112)+E(f682(x22113,x22111,x22114,x22115),f682(x22113,x22112,x22114,x22115)) % 165.30/165.06 [2212]~E(x22121,x22122)+E(f682(x22123,x22124,x22121,x22125),f682(x22123,x22124,x22122,x22125)) % 165.30/165.06 [2213]~E(x22131,x22132)+E(f682(x22133,x22134,x22135,x22131),f682(x22133,x22134,x22135,x22132)) % 165.30/165.06 [2214]~E(x22141,x22142)+E(f436(x22141,x22143,x22144),f436(x22142,x22143,x22144)) % 165.30/165.06 [2215]~E(x22151,x22152)+E(f436(x22153,x22151,x22154),f436(x22153,x22152,x22154)) % 165.30/165.06 [2216]~E(x22161,x22162)+E(f436(x22163,x22164,x22161),f436(x22163,x22164,x22162)) % 165.30/165.06 [2217]~E(x22171,x22172)+E(f619(x22171,x22173),f619(x22172,x22173)) % 165.30/165.06 [2218]~E(x22181,x22182)+E(f619(x22183,x22181),f619(x22183,x22182)) % 165.30/165.06 [2219]~E(x22191,x22192)+E(f326(x22191,x22193,x22194),f326(x22192,x22193,x22194)) % 165.30/165.06 [2220]~E(x22201,x22202)+E(f326(x22203,x22201,x22204),f326(x22203,x22202,x22204)) % 165.30/165.06 [2221]~E(x22211,x22212)+E(f326(x22213,x22214,x22211),f326(x22213,x22214,x22212)) % 165.30/165.06 [2222]~E(x22221,x22222)+E(f728(x22221,x22223),f728(x22222,x22223)) % 165.30/165.06 [2223]~E(x22231,x22232)+E(f728(x22233,x22231),f728(x22233,x22232)) % 165.30/165.06 [2224]~E(x22241,x22242)+E(f438(x22241,x22243,x22244),f438(x22242,x22243,x22244)) % 165.30/165.06 [2225]~E(x22251,x22252)+E(f438(x22253,x22251,x22254),f438(x22253,x22252,x22254)) % 165.30/165.06 [2226]~E(x22261,x22262)+E(f438(x22263,x22264,x22261),f438(x22263,x22264,x22262)) % 165.30/165.06 [2227]~E(x22271,x22272)+E(f129(x22271),f129(x22272)) % 165.30/165.06 [2228]~E(x22281,x22282)+E(f484(x22281,x22283,x22284,x22285,x22286),f484(x22282,x22283,x22284,x22285,x22286)) % 165.30/165.06 [2229]~E(x22291,x22292)+E(f484(x22293,x22291,x22294,x22295,x22296),f484(x22293,x22292,x22294,x22295,x22296)) % 165.30/165.06 [2230]~E(x22301,x22302)+E(f484(x22303,x22304,x22301,x22305,x22306),f484(x22303,x22304,x22302,x22305,x22306)) % 165.30/165.06 [2231]~E(x22311,x22312)+E(f484(x22313,x22314,x22315,x22311,x22316),f484(x22313,x22314,x22315,x22312,x22316)) % 165.30/165.06 [2232]~E(x22321,x22322)+E(f484(x22323,x22324,x22325,x22326,x22321),f484(x22323,x22324,x22325,x22326,x22322)) % 165.30/165.06 [2233]~E(x22331,x22332)+E(f520(x22331),f520(x22332)) % 165.30/165.06 [2234]~E(x22341,x22342)+E(f861(x22341,x22343,x22344,x22345,x22346),f861(x22342,x22343,x22344,x22345,x22346)) % 165.30/165.06 [2235]~E(x22351,x22352)+E(f861(x22353,x22351,x22354,x22355,x22356),f861(x22353,x22352,x22354,x22355,x22356)) % 165.30/165.06 [2236]~E(x22361,x22362)+E(f861(x22363,x22364,x22361,x22365,x22366),f861(x22363,x22364,x22362,x22365,x22366)) % 165.30/165.06 [2237]~E(x22371,x22372)+E(f861(x22373,x22374,x22375,x22371,x22376),f861(x22373,x22374,x22375,x22372,x22376)) % 165.30/165.06 [2238]~E(x22381,x22382)+E(f861(x22383,x22384,x22385,x22386,x22381),f861(x22383,x22384,x22385,x22386,x22382)) % 165.30/165.06 [2239]~E(x22391,x22392)+E(f515(x22391,x22393,x22394,x22395,x22396,x22397),f515(x22392,x22393,x22394,x22395,x22396,x22397)) % 165.30/165.06 [2240]~E(x22401,x22402)+E(f515(x22403,x22401,x22404,x22405,x22406,x22407),f515(x22403,x22402,x22404,x22405,x22406,x22407)) % 165.30/165.06 [2241]~E(x22411,x22412)+E(f515(x22413,x22414,x22411,x22415,x22416,x22417),f515(x22413,x22414,x22412,x22415,x22416,x22417)) % 165.30/165.06 [2242]~E(x22421,x22422)+E(f515(x22423,x22424,x22425,x22421,x22426,x22427),f515(x22423,x22424,x22425,x22422,x22426,x22427)) % 165.30/165.06 [2243]~E(x22431,x22432)+E(f515(x22433,x22434,x22435,x22436,x22431,x22437),f515(x22433,x22434,x22435,x22436,x22432,x22437)) % 165.30/165.06 [2244]~E(x22441,x22442)+E(f515(x22443,x22444,x22445,x22446,x22447,x22441),f515(x22443,x22444,x22445,x22446,x22447,x22442)) % 165.30/165.06 [2245]~E(x22451,x22452)+E(f736(x22451,x22453,x22454,x22455),f736(x22452,x22453,x22454,x22455)) % 165.30/165.06 [2246]~E(x22461,x22462)+E(f736(x22463,x22461,x22464,x22465),f736(x22463,x22462,x22464,x22465)) % 165.30/165.06 [2247]~E(x22471,x22472)+E(f736(x22473,x22474,x22471,x22475),f736(x22473,x22474,x22472,x22475)) % 165.30/165.06 [2248]~E(x22481,x22482)+E(f736(x22483,x22484,x22485,x22481),f736(x22483,x22484,x22485,x22482)) % 165.30/165.06 [2249]~E(x22491,x22492)+E(f633(x22491,x22493,x22494,x22495),f633(x22492,x22493,x22494,x22495)) % 165.30/165.06 [2250]~E(x22501,x22502)+E(f633(x22503,x22501,x22504,x22505),f633(x22503,x22502,x22504,x22505)) % 165.30/165.06 [2251]~E(x22511,x22512)+E(f633(x22513,x22514,x22511,x22515),f633(x22513,x22514,x22512,x22515)) % 165.30/165.06 [2252]~E(x22521,x22522)+E(f633(x22523,x22524,x22525,x22521),f633(x22523,x22524,x22525,x22522)) % 165.30/165.06 [2253]~E(x22531,x22532)+E(f683(x22531,x22533,x22534,x22535,x22536,x22537,x22538,x22539),f683(x22532,x22533,x22534,x22535,x22536,x22537,x22538,x22539)) % 165.30/165.06 [2254]~E(x22541,x22542)+E(f683(x22543,x22541,x22544,x22545,x22546,x22547,x22548,x22549),f683(x22543,x22542,x22544,x22545,x22546,x22547,x22548,x22549)) % 165.30/165.06 [2255]~E(x22551,x22552)+E(f683(x22553,x22554,x22551,x22555,x22556,x22557,x22558,x22559),f683(x22553,x22554,x22552,x22555,x22556,x22557,x22558,x22559)) % 165.30/165.06 [2256]~E(x22561,x22562)+E(f683(x22563,x22564,x22565,x22561,x22566,x22567,x22568,x22569),f683(x22563,x22564,x22565,x22562,x22566,x22567,x22568,x22569)) % 165.30/165.06 [2257]~E(x22571,x22572)+E(f683(x22573,x22574,x22575,x22576,x22571,x22577,x22578,x22579),f683(x22573,x22574,x22575,x22576,x22572,x22577,x22578,x22579)) % 165.30/165.06 [2258]~E(x22581,x22582)+E(f683(x22583,x22584,x22585,x22586,x22587,x22581,x22588,x22589),f683(x22583,x22584,x22585,x22586,x22587,x22582,x22588,x22589)) % 165.30/165.06 [2259]~E(x22591,x22592)+E(f683(x22593,x22594,x22595,x22596,x22597,x22598,x22591,x22599),f683(x22593,x22594,x22595,x22596,x22597,x22598,x22592,x22599)) % 165.30/165.06 [2260]~E(x22601,x22602)+E(f683(x22603,x22604,x22605,x22606,x22607,x22608,x22609,x22601),f683(x22603,x22604,x22605,x22606,x22607,x22608,x22609,x22602)) % 165.30/165.06 [2261]~E(x22611,x22612)+E(f665(x22611,x22613,x22614,x22615),f665(x22612,x22613,x22614,x22615)) % 165.30/165.06 [2262]~E(x22621,x22622)+E(f665(x22623,x22621,x22624,x22625),f665(x22623,x22622,x22624,x22625)) % 165.30/165.06 [2263]~E(x22631,x22632)+E(f665(x22633,x22634,x22631,x22635),f665(x22633,x22634,x22632,x22635)) % 165.30/165.06 [2264]~E(x22641,x22642)+E(f665(x22643,x22644,x22645,x22641),f665(x22643,x22644,x22645,x22642)) % 165.30/165.06 [2265]~E(x22651,x22652)+E(f68(x22651,x22653,x22654),f68(x22652,x22653,x22654)) % 165.30/165.06 [2266]~E(x22661,x22662)+E(f68(x22663,x22661,x22664),f68(x22663,x22662,x22664)) % 165.30/165.06 [2267]~E(x22671,x22672)+E(f68(x22673,x22674,x22671),f68(x22673,x22674,x22672)) % 165.30/165.06 [2268]~E(x22681,x22682)+E(f518(x22681,x22683,x22684,x22685,x22686),f518(x22682,x22683,x22684,x22685,x22686)) % 165.30/165.06 [2269]~E(x22691,x22692)+E(f518(x22693,x22691,x22694,x22695,x22696),f518(x22693,x22692,x22694,x22695,x22696)) % 165.30/165.06 [2270]~E(x22701,x22702)+E(f518(x22703,x22704,x22701,x22705,x22706),f518(x22703,x22704,x22702,x22705,x22706)) % 165.30/165.06 [2271]~E(x22711,x22712)+E(f518(x22713,x22714,x22715,x22711,x22716),f518(x22713,x22714,x22715,x22712,x22716)) % 165.30/165.06 [2272]~E(x22721,x22722)+E(f518(x22723,x22724,x22725,x22726,x22721),f518(x22723,x22724,x22725,x22726,x22722)) % 165.30/165.06 [2273]~E(x22731,x22732)+E(f816(x22731,x22733),f816(x22732,x22733)) % 165.30/165.06 [2274]~E(x22741,x22742)+E(f816(x22743,x22741),f816(x22743,x22742)) % 165.30/165.06 [2275]~E(x22751,x22752)+E(f808(x22751,x22753,x22754,x22755,x22756),f808(x22752,x22753,x22754,x22755,x22756)) % 165.30/165.06 [2276]~E(x22761,x22762)+E(f808(x22763,x22761,x22764,x22765,x22766),f808(x22763,x22762,x22764,x22765,x22766)) % 165.30/165.06 [2277]~E(x22771,x22772)+E(f808(x22773,x22774,x22771,x22775,x22776),f808(x22773,x22774,x22772,x22775,x22776)) % 165.30/165.06 [2278]~E(x22781,x22782)+E(f808(x22783,x22784,x22785,x22781,x22786),f808(x22783,x22784,x22785,x22782,x22786)) % 165.30/165.06 [2279]~E(x22791,x22792)+E(f808(x22793,x22794,x22795,x22796,x22791),f808(x22793,x22794,x22795,x22796,x22792)) % 165.30/165.06 [2280]~E(x22801,x22802)+E(f442(x22801,x22803),f442(x22802,x22803)) % 165.30/165.06 [2281]~E(x22811,x22812)+E(f442(x22813,x22811),f442(x22813,x22812)) % 165.30/165.06 [2282]~E(x22821,x22822)+E(f561(x22821,x22823,x22824),f561(x22822,x22823,x22824)) % 165.30/165.06 [2283]~E(x22831,x22832)+E(f561(x22833,x22831,x22834),f561(x22833,x22832,x22834)) % 165.30/165.06 [2284]~E(x22841,x22842)+E(f561(x22843,x22844,x22841),f561(x22843,x22844,x22842)) % 165.30/165.06 [2285]~E(x22851,x22852)+E(f840(x22851,x22853,x22854),f840(x22852,x22853,x22854)) % 165.30/165.06 [2286]~E(x22861,x22862)+E(f840(x22863,x22861,x22864),f840(x22863,x22862,x22864)) % 165.30/165.06 [2287]~E(x22871,x22872)+E(f840(x22873,x22874,x22871),f840(x22873,x22874,x22872)) % 165.30/165.06 [2288]~E(x22881,x22882)+E(f300(x22881,x22883,x22884,x22885,x22886),f300(x22882,x22883,x22884,x22885,x22886)) % 165.30/165.06 [2289]~E(x22891,x22892)+E(f300(x22893,x22891,x22894,x22895,x22896),f300(x22893,x22892,x22894,x22895,x22896)) % 165.30/165.06 [2290]~E(x22901,x22902)+E(f300(x22903,x22904,x22901,x22905,x22906),f300(x22903,x22904,x22902,x22905,x22906)) % 165.30/165.06 [2291]~E(x22911,x22912)+E(f300(x22913,x22914,x22915,x22911,x22916),f300(x22913,x22914,x22915,x22912,x22916)) % 165.30/165.06 [2292]~E(x22921,x22922)+E(f300(x22923,x22924,x22925,x22926,x22921),f300(x22923,x22924,x22925,x22926,x22922)) % 165.30/165.06 [2293]~E(x22931,x22932)+E(f411(x22931,x22933,x22934,x22935,x22936),f411(x22932,x22933,x22934,x22935,x22936)) % 165.30/165.06 [2294]~E(x22941,x22942)+E(f411(x22943,x22941,x22944,x22945,x22946),f411(x22943,x22942,x22944,x22945,x22946)) % 165.30/165.06 [2295]~E(x22951,x22952)+E(f411(x22953,x22954,x22951,x22955,x22956),f411(x22953,x22954,x22952,x22955,x22956)) % 165.30/165.06 [2296]~E(x22961,x22962)+E(f411(x22963,x22964,x22965,x22961,x22966),f411(x22963,x22964,x22965,x22962,x22966)) % 165.30/165.06 [2297]~E(x22971,x22972)+E(f411(x22973,x22974,x22975,x22976,x22971),f411(x22973,x22974,x22975,x22976,x22972)) % 165.30/165.06 [2298]~E(x22981,x22982)+E(f765(x22981,x22983,x22984,x22985),f765(x22982,x22983,x22984,x22985)) % 165.30/165.06 [2299]~E(x22991,x22992)+E(f765(x22993,x22991,x22994,x22995),f765(x22993,x22992,x22994,x22995)) % 165.30/165.06 [2300]~E(x23001,x23002)+E(f765(x23003,x23004,x23001,x23005),f765(x23003,x23004,x23002,x23005)) % 165.30/165.06 [2301]~E(x23011,x23012)+E(f765(x23013,x23014,x23015,x23011),f765(x23013,x23014,x23015,x23012)) % 165.30/165.06 [2302]~E(x23021,x23022)+E(f125(x23021),f125(x23022)) % 165.30/165.06 [2303]~E(x23031,x23032)+E(f827(x23031,x23033,x23034,x23035,x23036),f827(x23032,x23033,x23034,x23035,x23036)) % 165.30/165.06 [2304]~E(x23041,x23042)+E(f827(x23043,x23041,x23044,x23045,x23046),f827(x23043,x23042,x23044,x23045,x23046)) % 165.30/165.06 [2305]~E(x23051,x23052)+E(f827(x23053,x23054,x23051,x23055,x23056),f827(x23053,x23054,x23052,x23055,x23056)) % 165.30/165.06 [2306]~E(x23061,x23062)+E(f827(x23063,x23064,x23065,x23061,x23066),f827(x23063,x23064,x23065,x23062,x23066)) % 165.30/165.06 [2307]~E(x23071,x23072)+E(f827(x23073,x23074,x23075,x23076,x23071),f827(x23073,x23074,x23075,x23076,x23072)) % 165.30/165.06 [2308]~E(x23081,x23082)+E(f606(x23081,x23083,x23084),f606(x23082,x23083,x23084)) % 165.30/165.06 [2309]~E(x23091,x23092)+E(f606(x23093,x23091,x23094),f606(x23093,x23092,x23094)) % 165.30/165.06 [2310]~E(x23101,x23102)+E(f606(x23103,x23104,x23101),f606(x23103,x23104,x23102)) % 165.30/165.06 [2311]~E(x23111,x23112)+E(f432(x23111,x23113),f432(x23112,x23113)) % 165.30/165.06 [2312]~E(x23121,x23122)+E(f432(x23123,x23121),f432(x23123,x23122)) % 165.30/165.06 [2313]~E(x23131,x23132)+E(f577(x23131,x23133,x23134,x23135),f577(x23132,x23133,x23134,x23135)) % 165.30/165.06 [2314]~E(x23141,x23142)+E(f577(x23143,x23141,x23144,x23145),f577(x23143,x23142,x23144,x23145)) % 165.30/165.06 [2315]~E(x23151,x23152)+E(f577(x23153,x23154,x23151,x23155),f577(x23153,x23154,x23152,x23155)) % 165.30/165.06 [2316]~E(x23161,x23162)+E(f577(x23163,x23164,x23165,x23161),f577(x23163,x23164,x23165,x23162)) % 165.30/165.06 [2317]~E(x23171,x23172)+E(f639(x23171,x23173,x23174),f639(x23172,x23173,x23174)) % 165.30/165.06 [2318]~E(x23181,x23182)+E(f639(x23183,x23181,x23184),f639(x23183,x23182,x23184)) % 165.30/165.06 [2319]~E(x23191,x23192)+E(f639(x23193,x23194,x23191),f639(x23193,x23194,x23192)) % 165.30/165.06 [2320]~E(x23201,x23202)+E(f761(x23201,x23203,x23204),f761(x23202,x23203,x23204)) % 165.30/165.06 [2321]~E(x23211,x23212)+E(f761(x23213,x23211,x23214),f761(x23213,x23212,x23214)) % 165.30/165.06 [2322]~E(x23221,x23222)+E(f761(x23223,x23224,x23221),f761(x23223,x23224,x23222)) % 165.30/165.06 [2323]~E(x23231,x23232)+E(f226(x23231,x23233),f226(x23232,x23233)) % 165.30/165.06 [2324]~E(x23241,x23242)+E(f226(x23243,x23241),f226(x23243,x23242)) % 165.30/165.06 [2325]~E(x23251,x23252)+E(f608(x23251,x23253),f608(x23252,x23253)) % 165.30/165.06 [2326]~E(x23261,x23262)+E(f608(x23263,x23261),f608(x23263,x23262)) % 165.30/165.06 [2327]~E(x23271,x23272)+E(f533(x23271,x23273),f533(x23272,x23273)) % 165.30/165.06 [2328]~E(x23281,x23282)+E(f533(x23283,x23281),f533(x23283,x23282)) % 165.30/165.06 [2329]~E(x23291,x23292)+E(f481(x23291,x23293,x23294,x23295),f481(x23292,x23293,x23294,x23295)) % 165.30/165.06 [2330]~E(x23301,x23302)+E(f481(x23303,x23301,x23304,x23305),f481(x23303,x23302,x23304,x23305)) % 165.30/165.06 [2331]~E(x23311,x23312)+E(f481(x23313,x23314,x23311,x23315),f481(x23313,x23314,x23312,x23315)) % 165.30/165.06 [2332]~E(x23321,x23322)+E(f481(x23323,x23324,x23325,x23321),f481(x23323,x23324,x23325,x23322)) % 165.30/165.06 [2333]~E(x23331,x23332)+E(f130(x23331,x23333),f130(x23332,x23333)) % 165.30/165.06 [2334]~E(x23341,x23342)+E(f130(x23343,x23341),f130(x23343,x23342)) % 165.30/165.06 [2335]~E(x23351,x23352)+E(f613(x23351,x23353,x23354),f613(x23352,x23353,x23354)) % 165.30/165.06 [2336]~E(x23361,x23362)+E(f613(x23363,x23361,x23364),f613(x23363,x23362,x23364)) % 165.30/165.06 [2337]~E(x23371,x23372)+E(f613(x23373,x23374,x23371),f613(x23373,x23374,x23372)) % 165.30/165.06 [2338]~E(x23381,x23382)+E(f594(x23381,x23383,x23384),f594(x23382,x23383,x23384)) % 165.30/165.06 [2339]~E(x23391,x23392)+E(f594(x23393,x23391,x23394),f594(x23393,x23392,x23394)) % 165.30/165.06 [2340]~E(x23401,x23402)+E(f594(x23403,x23404,x23401),f594(x23403,x23404,x23402)) % 165.30/165.06 [2341]~E(x23411,x23412)+E(f385(x23411,x23413,x23414,x23415),f385(x23412,x23413,x23414,x23415)) % 165.30/165.06 [2342]~E(x23421,x23422)+E(f385(x23423,x23421,x23424,x23425),f385(x23423,x23422,x23424,x23425)) % 165.30/165.06 [2343]~E(x23431,x23432)+E(f385(x23433,x23434,x23431,x23435),f385(x23433,x23434,x23432,x23435)) % 165.30/165.06 [2344]~E(x23441,x23442)+E(f385(x23443,x23444,x23445,x23441),f385(x23443,x23444,x23445,x23442)) % 165.30/165.06 [2345]~E(x23451,x23452)+E(f755(x23451,x23453,x23454,x23455,x23456),f755(x23452,x23453,x23454,x23455,x23456)) % 165.30/165.06 [2346]~E(x23461,x23462)+E(f755(x23463,x23461,x23464,x23465,x23466),f755(x23463,x23462,x23464,x23465,x23466)) % 165.30/165.06 [2347]~E(x23471,x23472)+E(f755(x23473,x23474,x23471,x23475,x23476),f755(x23473,x23474,x23472,x23475,x23476)) % 165.30/165.06 [2348]~E(x23481,x23482)+E(f755(x23483,x23484,x23485,x23481,x23486),f755(x23483,x23484,x23485,x23482,x23486)) % 165.30/165.06 [2349]~E(x23491,x23492)+E(f755(x23493,x23494,x23495,x23496,x23491),f755(x23493,x23494,x23495,x23496,x23492)) % 165.30/165.06 [2350]~E(x23501,x23502)+E(f857(x23501,x23503,x23504,x23505,x23506),f857(x23502,x23503,x23504,x23505,x23506)) % 165.30/165.06 [2351]~E(x23511,x23512)+E(f857(x23513,x23511,x23514,x23515,x23516),f857(x23513,x23512,x23514,x23515,x23516)) % 165.30/165.06 [2352]~E(x23521,x23522)+E(f857(x23523,x23524,x23521,x23525,x23526),f857(x23523,x23524,x23522,x23525,x23526)) % 165.30/165.06 [2353]~E(x23531,x23532)+E(f857(x23533,x23534,x23535,x23531,x23536),f857(x23533,x23534,x23535,x23532,x23536)) % 165.30/165.06 [2354]~E(x23541,x23542)+E(f857(x23543,x23544,x23545,x23546,x23541),f857(x23543,x23544,x23545,x23546,x23542)) % 165.30/165.06 [2355]~E(x23551,x23552)+E(f404(x23551,x23553),f404(x23552,x23553)) % 165.30/165.06 [2356]~E(x23561,x23562)+E(f404(x23563,x23561),f404(x23563,x23562)) % 165.30/165.06 [2357]~E(x23571,x23572)+E(f748(x23571,x23573),f748(x23572,x23573)) % 165.30/165.06 [2358]~E(x23581,x23582)+E(f748(x23583,x23581),f748(x23583,x23582)) % 165.30/165.06 [2359]~E(x23591,x23592)+E(f387(x23591,x23593,x23594,x23595),f387(x23592,x23593,x23594,x23595)) % 165.30/165.06 [2360]~E(x23601,x23602)+E(f387(x23603,x23601,x23604,x23605),f387(x23603,x23602,x23604,x23605)) % 165.30/165.06 [2361]~E(x23611,x23612)+E(f387(x23613,x23614,x23611,x23615),f387(x23613,x23614,x23612,x23615)) % 165.30/165.06 [2362]~E(x23621,x23622)+E(f387(x23623,x23624,x23625,x23621),f387(x23623,x23624,x23625,x23622)) % 165.30/165.06 [2363]~E(x23631,x23632)+E(f696(x23631,x23633,x23634,x23635,x23636),f696(x23632,x23633,x23634,x23635,x23636)) % 165.30/165.06 [2364]~E(x23641,x23642)+E(f696(x23643,x23641,x23644,x23645,x23646),f696(x23643,x23642,x23644,x23645,x23646)) % 165.30/165.06 [2365]~E(x23651,x23652)+E(f696(x23653,x23654,x23651,x23655,x23656),f696(x23653,x23654,x23652,x23655,x23656)) % 165.30/165.06 [2366]~E(x23661,x23662)+E(f696(x23663,x23664,x23665,x23661,x23666),f696(x23663,x23664,x23665,x23662,x23666)) % 165.30/165.06 [2367]~E(x23671,x23672)+E(f696(x23673,x23674,x23675,x23676,x23671),f696(x23673,x23674,x23675,x23676,x23672)) % 165.30/165.06 [2368]~E(x23681,x23682)+E(f566(x23681,x23683,x23684,x23685,x23686,x23687,x23688,x23689),f566(x23682,x23683,x23684,x23685,x23686,x23687,x23688,x23689)) % 165.30/165.06 [2369]~E(x23691,x23692)+E(f566(x23693,x23691,x23694,x23695,x23696,x23697,x23698,x23699),f566(x23693,x23692,x23694,x23695,x23696,x23697,x23698,x23699)) % 165.30/165.06 [2370]~E(x23701,x23702)+E(f566(x23703,x23704,x23701,x23705,x23706,x23707,x23708,x23709),f566(x23703,x23704,x23702,x23705,x23706,x23707,x23708,x23709)) % 165.30/165.06 [2371]~E(x23711,x23712)+E(f566(x23713,x23714,x23715,x23711,x23716,x23717,x23718,x23719),f566(x23713,x23714,x23715,x23712,x23716,x23717,x23718,x23719)) % 165.30/165.06 [2372]~E(x23721,x23722)+E(f566(x23723,x23724,x23725,x23726,x23721,x23727,x23728,x23729),f566(x23723,x23724,x23725,x23726,x23722,x23727,x23728,x23729)) % 165.30/165.06 [2373]~E(x23731,x23732)+E(f566(x23733,x23734,x23735,x23736,x23737,x23731,x23738,x23739),f566(x23733,x23734,x23735,x23736,x23737,x23732,x23738,x23739)) % 165.30/165.06 [2374]~E(x23741,x23742)+E(f566(x23743,x23744,x23745,x23746,x23747,x23748,x23741,x23749),f566(x23743,x23744,x23745,x23746,x23747,x23748,x23742,x23749)) % 165.30/165.06 [2375]~E(x23751,x23752)+E(f566(x23753,x23754,x23755,x23756,x23757,x23758,x23759,x23751),f566(x23753,x23754,x23755,x23756,x23757,x23758,x23759,x23752)) % 165.30/165.06 [2376]~E(x23761,x23762)+E(f630(x23761,x23763),f630(x23762,x23763)) % 165.30/165.06 [2377]~E(x23771,x23772)+E(f630(x23773,x23771),f630(x23773,x23772)) % 165.30/165.06 [2378]~E(x23781,x23782)+E(f457(x23781,x23783,x23784),f457(x23782,x23783,x23784)) % 165.30/165.06 [2379]~E(x23791,x23792)+E(f457(x23793,x23791,x23794),f457(x23793,x23792,x23794)) % 165.30/165.06 [2380]~E(x23801,x23802)+E(f457(x23803,x23804,x23801),f457(x23803,x23804,x23802)) % 165.30/165.06 [2381]~E(x23811,x23812)+E(f528(x23811,x23813,x23814,x23815,x23816,x23817),f528(x23812,x23813,x23814,x23815,x23816,x23817)) % 165.30/165.06 [2382]~E(x23821,x23822)+E(f528(x23823,x23821,x23824,x23825,x23826,x23827),f528(x23823,x23822,x23824,x23825,x23826,x23827)) % 165.30/165.06 [2383]~E(x23831,x23832)+E(f528(x23833,x23834,x23831,x23835,x23836,x23837),f528(x23833,x23834,x23832,x23835,x23836,x23837)) % 165.30/165.06 [2384]~E(x23841,x23842)+E(f528(x23843,x23844,x23845,x23841,x23846,x23847),f528(x23843,x23844,x23845,x23842,x23846,x23847)) % 165.30/165.06 [2385]~E(x23851,x23852)+E(f528(x23853,x23854,x23855,x23856,x23851,x23857),f528(x23853,x23854,x23855,x23856,x23852,x23857)) % 165.30/165.06 [2386]~E(x23861,x23862)+E(f528(x23863,x23864,x23865,x23866,x23867,x23861),f528(x23863,x23864,x23865,x23866,x23867,x23862)) % 165.30/165.06 [2387]~E(x23871,x23872)+E(f796(x23871,x23873,x23874),f796(x23872,x23873,x23874)) % 165.30/165.06 [2388]~E(x23881,x23882)+E(f796(x23883,x23881,x23884),f796(x23883,x23882,x23884)) % 165.30/165.06 [2389]~E(x23891,x23892)+E(f796(x23893,x23894,x23891),f796(x23893,x23894,x23892)) % 165.30/165.06 [2390]~E(x23901,x23902)+E(f365(x23901),f365(x23902)) % 165.30/165.06 [2391]~E(x23911,x23912)+E(f354(x23911,x23913,x23914),f354(x23912,x23913,x23914)) % 165.30/165.06 [2392]~E(x23921,x23922)+E(f354(x23923,x23921,x23924),f354(x23923,x23922,x23924)) % 165.30/165.06 [2393]~E(x23931,x23932)+E(f354(x23933,x23934,x23931),f354(x23933,x23934,x23932)) % 165.30/165.06 [2394]~E(x23941,x23942)+E(f489(x23941,x23943,x23944),f489(x23942,x23943,x23944)) % 165.30/165.06 [2395]~E(x23951,x23952)+E(f489(x23953,x23951,x23954),f489(x23953,x23952,x23954)) % 165.30/165.06 [2396]~E(x23961,x23962)+E(f489(x23963,x23964,x23961),f489(x23963,x23964,x23962)) % 165.30/165.06 [2397]~E(x23971,x23972)+E(f396(x23971),f396(x23972)) % 165.30/165.06 [2398]~E(x23981,x23982)+E(f680(x23981,x23983,x23984,x23985),f680(x23982,x23983,x23984,x23985)) % 165.30/165.06 [2399]~E(x23991,x23992)+E(f680(x23993,x23991,x23994,x23995),f680(x23993,x23992,x23994,x23995)) % 165.30/165.06 [2400]~E(x24001,x24002)+E(f680(x24003,x24004,x24001,x24005),f680(x24003,x24004,x24002,x24005)) % 165.30/165.06 [2401]~E(x24011,x24012)+E(f680(x24013,x24014,x24015,x24011),f680(x24013,x24014,x24015,x24012)) % 165.30/165.06 [2402]~E(x24021,x24022)+E(f496(x24021,x24023),f496(x24022,x24023)) % 165.30/165.06 [2403]~E(x24031,x24032)+E(f496(x24033,x24031),f496(x24033,x24032)) % 165.30/165.06 [2404]~E(x24041,x24042)+E(f722(x24041,x24043,x24044,x24045,x24046),f722(x24042,x24043,x24044,x24045,x24046)) % 165.30/165.06 [2405]~E(x24051,x24052)+E(f722(x24053,x24051,x24054,x24055,x24056),f722(x24053,x24052,x24054,x24055,x24056)) % 165.30/165.06 [2406]~E(x24061,x24062)+E(f722(x24063,x24064,x24061,x24065,x24066),f722(x24063,x24064,x24062,x24065,x24066)) % 165.30/165.06 [2407]~E(x24071,x24072)+E(f722(x24073,x24074,x24075,x24071,x24076),f722(x24073,x24074,x24075,x24072,x24076)) % 165.30/165.06 [2408]~E(x24081,x24082)+E(f722(x24083,x24084,x24085,x24086,x24081),f722(x24083,x24084,x24085,x24086,x24082)) % 165.30/165.06 [2409]~E(x24091,x24092)+E(f666(x24091,x24093,x24094,x24095,x24096),f666(x24092,x24093,x24094,x24095,x24096)) % 165.30/165.06 [2410]~E(x24101,x24102)+E(f666(x24103,x24101,x24104,x24105,x24106),f666(x24103,x24102,x24104,x24105,x24106)) % 165.30/165.06 [2411]~E(x24111,x24112)+E(f666(x24113,x24114,x24111,x24115,x24116),f666(x24113,x24114,x24112,x24115,x24116)) % 165.30/165.06 [2412]~E(x24121,x24122)+E(f666(x24123,x24124,x24125,x24121,x24126),f666(x24123,x24124,x24125,x24122,x24126)) % 165.30/165.06 [2413]~E(x24131,x24132)+E(f666(x24133,x24134,x24135,x24136,x24131),f666(x24133,x24134,x24135,x24136,x24132)) % 165.30/165.06 [2414]~E(x24141,x24142)+E(f612(x24141,x24143,x24144),f612(x24142,x24143,x24144)) % 165.30/165.06 [2415]~E(x24151,x24152)+E(f612(x24153,x24151,x24154),f612(x24153,x24152,x24154)) % 165.30/165.06 [2416]~E(x24161,x24162)+E(f612(x24163,x24164,x24161),f612(x24163,x24164,x24162)) % 165.30/165.06 [2417]~E(x24171,x24172)+E(f376(x24171,x24173,x24174),f376(x24172,x24173,x24174)) % 165.30/165.06 [2418]~E(x24181,x24182)+E(f376(x24183,x24181,x24184),f376(x24183,x24182,x24184)) % 165.30/165.06 [2419]~E(x24191,x24192)+E(f376(x24193,x24194,x24191),f376(x24193,x24194,x24192)) % 165.30/165.06 [2420]~E(x24201,x24202)+E(f568(x24201,x24203),f568(x24202,x24203)) % 165.30/165.06 [2421]~E(x24211,x24212)+E(f568(x24213,x24211),f568(x24213,x24212)) % 165.30/165.06 [2422]~E(x24221,x24222)+E(f624(x24221,x24223,x24224,x24225,x24226),f624(x24222,x24223,x24224,x24225,x24226)) % 165.30/165.06 [2423]~E(x24231,x24232)+E(f624(x24233,x24231,x24234,x24235,x24236),f624(x24233,x24232,x24234,x24235,x24236)) % 165.30/165.06 [2424]~E(x24241,x24242)+E(f624(x24243,x24244,x24241,x24245,x24246),f624(x24243,x24244,x24242,x24245,x24246)) % 165.30/165.06 [2425]~E(x24251,x24252)+E(f624(x24253,x24254,x24255,x24251,x24256),f624(x24253,x24254,x24255,x24252,x24256)) % 165.30/165.06 [2426]~E(x24261,x24262)+E(f624(x24263,x24264,x24265,x24266,x24261),f624(x24263,x24264,x24265,x24266,x24262)) % 165.30/165.06 [2427]~E(x24271,x24272)+E(f768(x24271,x24273,x24274,x24275,x24276,x24277,x24278),f768(x24272,x24273,x24274,x24275,x24276,x24277,x24278)) % 165.30/165.06 [2428]~E(x24281,x24282)+E(f768(x24283,x24281,x24284,x24285,x24286,x24287,x24288),f768(x24283,x24282,x24284,x24285,x24286,x24287,x24288)) % 165.30/165.06 [2429]~E(x24291,x24292)+E(f768(x24293,x24294,x24291,x24295,x24296,x24297,x24298),f768(x24293,x24294,x24292,x24295,x24296,x24297,x24298)) % 165.30/165.06 [2430]~E(x24301,x24302)+E(f768(x24303,x24304,x24305,x24301,x24306,x24307,x24308),f768(x24303,x24304,x24305,x24302,x24306,x24307,x24308)) % 165.30/165.06 [2431]~E(x24311,x24312)+E(f768(x24313,x24314,x24315,x24316,x24311,x24317,x24318),f768(x24313,x24314,x24315,x24316,x24312,x24317,x24318)) % 165.30/165.06 [2432]~E(x24321,x24322)+E(f768(x24323,x24324,x24325,x24326,x24327,x24321,x24328),f768(x24323,x24324,x24325,x24326,x24327,x24322,x24328)) % 165.30/165.06 [2433]~E(x24331,x24332)+E(f768(x24333,x24334,x24335,x24336,x24337,x24338,x24331),f768(x24333,x24334,x24335,x24336,x24337,x24338,x24332)) % 165.30/165.06 [2434]~E(x24341,x24342)+E(f221(x24341,x24343,x24344,x24345),f221(x24342,x24343,x24344,x24345)) % 165.30/165.06 [2435]~E(x24351,x24352)+E(f221(x24353,x24351,x24354,x24355),f221(x24353,x24352,x24354,x24355)) % 165.30/165.06 [2436]~E(x24361,x24362)+E(f221(x24363,x24364,x24361,x24365),f221(x24363,x24364,x24362,x24365)) % 165.30/165.06 [2437]~E(x24371,x24372)+E(f221(x24373,x24374,x24375,x24371),f221(x24373,x24374,x24375,x24372)) % 165.30/165.06 [2438]~E(x24381,x24382)+E(f467(x24381,x24383,x24384,x24385,x24386),f467(x24382,x24383,x24384,x24385,x24386)) % 165.30/165.06 [2439]~E(x24391,x24392)+E(f467(x24393,x24391,x24394,x24395,x24396),f467(x24393,x24392,x24394,x24395,x24396)) % 165.30/165.06 [2440]~E(x24401,x24402)+E(f467(x24403,x24404,x24401,x24405,x24406),f467(x24403,x24404,x24402,x24405,x24406)) % 165.30/165.06 [2441]~E(x24411,x24412)+E(f467(x24413,x24414,x24415,x24411,x24416),f467(x24413,x24414,x24415,x24412,x24416)) % 165.30/165.06 [2442]~E(x24421,x24422)+E(f467(x24423,x24424,x24425,x24426,x24421),f467(x24423,x24424,x24425,x24426,x24422)) % 165.30/165.06 [2443]~E(x24431,x24432)+E(f501(x24431,x24433,x24434),f501(x24432,x24433,x24434)) % 165.30/165.06 [2444]~E(x24441,x24442)+E(f501(x24443,x24441,x24444),f501(x24443,x24442,x24444)) % 165.30/165.06 [2445]~E(x24451,x24452)+E(f501(x24453,x24454,x24451),f501(x24453,x24454,x24452)) % 165.30/165.06 [2446]~E(x24461,x24462)+E(f828(x24461,x24463,x24464,x24465,x24466),f828(x24462,x24463,x24464,x24465,x24466)) % 165.30/165.06 [2447]~E(x24471,x24472)+E(f828(x24473,x24471,x24474,x24475,x24476),f828(x24473,x24472,x24474,x24475,x24476)) % 165.30/165.06 [2448]~E(x24481,x24482)+E(f828(x24483,x24484,x24481,x24485,x24486),f828(x24483,x24484,x24482,x24485,x24486)) % 165.30/165.06 [2449]~E(x24491,x24492)+E(f828(x24493,x24494,x24495,x24491,x24496),f828(x24493,x24494,x24495,x24492,x24496)) % 165.30/165.06 [2450]~E(x24501,x24502)+E(f828(x24503,x24504,x24505,x24506,x24501),f828(x24503,x24504,x24505,x24506,x24502)) % 165.30/165.06 [2451]~E(x24511,x24512)+E(f340(x24511),f340(x24512)) % 165.30/165.06 [2452]~E(x24521,x24522)+E(f345(x24521,x24523),f345(x24522,x24523)) % 165.30/165.06 [2453]~E(x24531,x24532)+E(f345(x24533,x24531),f345(x24533,x24532)) % 165.30/165.06 [2454]~E(x24541,x24542)+E(f205(x24541,x24543,x24544),f205(x24542,x24543,x24544)) % 165.30/165.06 [2455]~E(x24551,x24552)+E(f205(x24553,x24551,x24554),f205(x24553,x24552,x24554)) % 165.30/165.06 [2456]~E(x24561,x24562)+E(f205(x24563,x24564,x24561),f205(x24563,x24564,x24562)) % 165.30/165.06 [2457]~E(x24571,x24572)+E(f343(x24571,x24573),f343(x24572,x24573)) % 165.30/165.06 [2458]~E(x24581,x24582)+E(f343(x24583,x24581),f343(x24583,x24582)) % 165.30/165.06 [2459]~E(x24591,x24592)+E(f618(x24591,x24593),f618(x24592,x24593)) % 165.30/165.06 [2460]~E(x24601,x24602)+E(f618(x24603,x24601),f618(x24603,x24602)) % 165.30/165.06 [2461]~E(x24611,x24612)+E(f379(x24611,x24613,x24614,x24615),f379(x24612,x24613,x24614,x24615)) % 165.30/165.06 [2462]~E(x24621,x24622)+E(f379(x24623,x24621,x24624,x24625),f379(x24623,x24622,x24624,x24625)) % 165.30/165.06 [2463]~E(x24631,x24632)+E(f379(x24633,x24634,x24631,x24635),f379(x24633,x24634,x24632,x24635)) % 165.30/165.06 [2464]~E(x24641,x24642)+E(f379(x24643,x24644,x24645,x24641),f379(x24643,x24644,x24645,x24642)) % 165.30/165.06 [2465]~E(x24651,x24652)+E(f447(x24651,x24653),f447(x24652,x24653)) % 165.30/165.06 [2466]~E(x24661,x24662)+E(f447(x24663,x24661),f447(x24663,x24662)) % 165.30/165.06 [2467]~E(x24671,x24672)+E(f855(x24671,x24673,x24674,x24675,x24676),f855(x24672,x24673,x24674,x24675,x24676)) % 165.30/165.06 [2468]~E(x24681,x24682)+E(f855(x24683,x24681,x24684,x24685,x24686),f855(x24683,x24682,x24684,x24685,x24686)) % 165.30/165.06 [2469]~E(x24691,x24692)+E(f855(x24693,x24694,x24691,x24695,x24696),f855(x24693,x24694,x24692,x24695,x24696)) % 165.30/165.06 [2470]~E(x24701,x24702)+E(f855(x24703,x24704,x24705,x24701,x24706),f855(x24703,x24704,x24705,x24702,x24706)) % 165.30/165.06 [2471]~E(x24711,x24712)+E(f855(x24713,x24714,x24715,x24716,x24711),f855(x24713,x24714,x24715,x24716,x24712)) % 165.30/165.06 [2472]~E(x24721,x24722)+E(f350(x24721,x24723,x24724,x24725,x24726),f350(x24722,x24723,x24724,x24725,x24726)) % 165.30/165.06 [2473]~E(x24731,x24732)+E(f350(x24733,x24731,x24734,x24735,x24736),f350(x24733,x24732,x24734,x24735,x24736)) % 165.30/165.06 [2474]~E(x24741,x24742)+E(f350(x24743,x24744,x24741,x24745,x24746),f350(x24743,x24744,x24742,x24745,x24746)) % 165.30/165.06 [2475]~E(x24751,x24752)+E(f350(x24753,x24754,x24755,x24751,x24756),f350(x24753,x24754,x24755,x24752,x24756)) % 165.30/165.06 [2476]~E(x24761,x24762)+E(f350(x24763,x24764,x24765,x24766,x24761),f350(x24763,x24764,x24765,x24766,x24762)) % 165.30/165.06 [2477]~E(x24771,x24772)+E(f634(x24771,x24773,x24774,x24775,x24776,x24777,x24778,x24779),f634(x24772,x24773,x24774,x24775,x24776,x24777,x24778,x24779)) % 165.30/165.06 [2478]~E(x24781,x24782)+E(f634(x24783,x24781,x24784,x24785,x24786,x24787,x24788,x24789),f634(x24783,x24782,x24784,x24785,x24786,x24787,x24788,x24789)) % 165.30/165.06 [2479]~E(x24791,x24792)+E(f634(x24793,x24794,x24791,x24795,x24796,x24797,x24798,x24799),f634(x24793,x24794,x24792,x24795,x24796,x24797,x24798,x24799)) % 165.30/165.06 [2480]~E(x24801,x24802)+E(f634(x24803,x24804,x24805,x24801,x24806,x24807,x24808,x24809),f634(x24803,x24804,x24805,x24802,x24806,x24807,x24808,x24809)) % 165.30/165.06 [2481]~E(x24811,x24812)+E(f634(x24813,x24814,x24815,x24816,x24811,x24817,x24818,x24819),f634(x24813,x24814,x24815,x24816,x24812,x24817,x24818,x24819)) % 165.30/165.06 [2482]~E(x24821,x24822)+E(f634(x24823,x24824,x24825,x24826,x24827,x24821,x24828,x24829),f634(x24823,x24824,x24825,x24826,x24827,x24822,x24828,x24829)) % 165.30/165.06 [2483]~E(x24831,x24832)+E(f634(x24833,x24834,x24835,x24836,x24837,x24838,x24831,x24839),f634(x24833,x24834,x24835,x24836,x24837,x24838,x24832,x24839)) % 165.30/165.06 [2484]~E(x24841,x24842)+E(f634(x24843,x24844,x24845,x24846,x24847,x24848,x24849,x24841),f634(x24843,x24844,x24845,x24846,x24847,x24848,x24849,x24842)) % 165.30/165.06 [2485]~E(x24851,x24852)+E(f563(x24851,x24853,x24854,x24855,x24856),f563(x24852,x24853,x24854,x24855,x24856)) % 165.30/165.06 [2486]~E(x24861,x24862)+E(f563(x24863,x24861,x24864,x24865,x24866),f563(x24863,x24862,x24864,x24865,x24866)) % 165.30/165.06 [2487]~E(x24871,x24872)+E(f563(x24873,x24874,x24871,x24875,x24876),f563(x24873,x24874,x24872,x24875,x24876)) % 165.30/165.06 [2488]~E(x24881,x24882)+E(f563(x24883,x24884,x24885,x24881,x24886),f563(x24883,x24884,x24885,x24882,x24886)) % 165.30/165.06 [2489]~E(x24891,x24892)+E(f563(x24893,x24894,x24895,x24896,x24891),f563(x24893,x24894,x24895,x24896,x24892)) % 165.30/165.06 [2490]~E(x24901,x24902)+E(f705(x24901),f705(x24902)) % 165.30/165.06 [2491]~E(x24911,x24912)+E(f338(x24911,x24913),f338(x24912,x24913)) % 165.30/165.06 [2492]~E(x24921,x24922)+E(f338(x24923,x24921),f338(x24923,x24922)) % 165.30/165.06 [2493]~E(x24931,x24932)+E(f344(x24931),f344(x24932)) % 165.30/165.06 [2494]~E(x24941,x24942)+E(f478(x24941,x24943,x24944),f478(x24942,x24943,x24944)) % 165.30/165.06 [2495]~E(x24951,x24952)+E(f478(x24953,x24951,x24954),f478(x24953,x24952,x24954)) % 165.30/165.06 [2496]~E(x24961,x24962)+E(f478(x24963,x24964,x24961),f478(x24963,x24964,x24962)) % 165.30/165.06 [2497]~E(x24971,x24972)+E(f737(x24971,x24973),f737(x24972,x24973)) % 165.30/165.06 [2498]~E(x24981,x24982)+E(f737(x24983,x24981),f737(x24983,x24982)) % 165.30/165.06 [2499]~E(x24991,x24992)+E(f622(x24991,x24993,x24994),f622(x24992,x24993,x24994)) % 165.30/165.06 [2500]~E(x25001,x25002)+E(f622(x25003,x25001,x25004),f622(x25003,x25002,x25004)) % 165.30/165.06 [2501]~E(x25011,x25012)+E(f622(x25013,x25014,x25011),f622(x25013,x25014,x25012)) % 165.30/165.06 [2502]~E(x25021,x25022)+E(f382(x25021,x25023),f382(x25022,x25023)) % 165.30/165.06 [2503]~E(x25031,x25032)+E(f382(x25033,x25031),f382(x25033,x25032)) % 165.30/165.06 [2504]~E(x25041,x25042)+E(f707(x25041,x25043,x25044),f707(x25042,x25043,x25044)) % 165.30/165.06 [2505]~E(x25051,x25052)+E(f707(x25053,x25051,x25054),f707(x25053,x25052,x25054)) % 165.30/165.06 [2506]~E(x25061,x25062)+E(f707(x25063,x25064,x25061),f707(x25063,x25064,x25062)) % 165.30/165.06 [2507]~E(x25071,x25072)+E(f349(x25071,x25073),f349(x25072,x25073)) % 165.30/165.06 [2508]~E(x25081,x25082)+E(f349(x25083,x25081),f349(x25083,x25082)) % 165.30/165.06 [2509]~E(x25091,x25092)+E(f623(x25091,x25093,x25094),f623(x25092,x25093,x25094)) % 165.30/165.06 [2510]~E(x25101,x25102)+E(f623(x25103,x25101,x25104),f623(x25103,x25102,x25104)) % 165.30/165.06 [2511]~E(x25111,x25112)+E(f623(x25113,x25114,x25111),f623(x25113,x25114,x25112)) % 165.30/165.06 [2512]~E(x25121,x25122)+E(f535(x25121),f535(x25122)) % 165.30/165.06 [2513]~E(x25131,x25132)+E(f223(x25131,x25133,x25134,x25135,x25136,x25137,x25138),f223(x25132,x25133,x25134,x25135,x25136,x25137,x25138)) % 165.30/165.06 [2514]~E(x25141,x25142)+E(f223(x25143,x25141,x25144,x25145,x25146,x25147,x25148),f223(x25143,x25142,x25144,x25145,x25146,x25147,x25148)) % 165.30/165.06 [2515]~E(x25151,x25152)+E(f223(x25153,x25154,x25151,x25155,x25156,x25157,x25158),f223(x25153,x25154,x25152,x25155,x25156,x25157,x25158)) % 165.30/165.06 [2516]~E(x25161,x25162)+E(f223(x25163,x25164,x25165,x25161,x25166,x25167,x25168),f223(x25163,x25164,x25165,x25162,x25166,x25167,x25168)) % 165.30/165.06 [2517]~E(x25171,x25172)+E(f223(x25173,x25174,x25175,x25176,x25171,x25177,x25178),f223(x25173,x25174,x25175,x25176,x25172,x25177,x25178)) % 165.30/165.06 [2518]~E(x25181,x25182)+E(f223(x25183,x25184,x25185,x25186,x25187,x25181,x25188),f223(x25183,x25184,x25185,x25186,x25187,x25182,x25188)) % 165.30/165.06 [2519]~E(x25191,x25192)+E(f223(x25193,x25194,x25195,x25196,x25197,x25198,x25191),f223(x25193,x25194,x25195,x25196,x25197,x25198,x25192)) % 165.30/165.06 [2520]~E(x25201,x25202)+E(f740(x25201,x25203,x25204),f740(x25202,x25203,x25204)) % 165.30/165.06 [2521]~E(x25211,x25212)+E(f740(x25213,x25211,x25214),f740(x25213,x25212,x25214)) % 165.30/165.06 [2522]~E(x25221,x25222)+E(f740(x25223,x25224,x25221),f740(x25223,x25224,x25222)) % 165.30/165.06 [2523]~E(x25231,x25232)+E(f649(x25231,x25233),f649(x25232,x25233)) % 165.30/165.06 [2524]~E(x25241,x25242)+E(f649(x25243,x25241),f649(x25243,x25242)) % 165.30/165.06 [2525]~E(x25251,x25252)+E(f834(x25251,x25253,x25254,x25255,x25256),f834(x25252,x25253,x25254,x25255,x25256)) % 165.30/165.06 [2526]~E(x25261,x25262)+E(f834(x25263,x25261,x25264,x25265,x25266),f834(x25263,x25262,x25264,x25265,x25266)) % 165.30/165.06 [2527]~E(x25271,x25272)+E(f834(x25273,x25274,x25271,x25275,x25276),f834(x25273,x25274,x25272,x25275,x25276)) % 165.30/165.06 [2528]~E(x25281,x25282)+E(f834(x25283,x25284,x25285,x25281,x25286),f834(x25283,x25284,x25285,x25282,x25286)) % 165.30/165.06 [2529]~E(x25291,x25292)+E(f834(x25293,x25294,x25295,x25296,x25291),f834(x25293,x25294,x25295,x25296,x25292)) % 165.30/165.06 [2530]~E(x25301,x25302)+E(f678(x25301,x25303,x25304,x25305),f678(x25302,x25303,x25304,x25305)) % 165.30/165.06 [2531]~E(x25311,x25312)+E(f678(x25313,x25311,x25314,x25315),f678(x25313,x25312,x25314,x25315)) % 165.30/165.06 [2532]~E(x25321,x25322)+E(f678(x25323,x25324,x25321,x25325),f678(x25323,x25324,x25322,x25325)) % 165.30/165.06 [2533]~E(x25331,x25332)+E(f678(x25333,x25334,x25335,x25331),f678(x25333,x25334,x25335,x25332)) % 165.30/165.06 [2534]~E(x25341,x25342)+E(f393(x25341),f393(x25342)) % 165.30/165.06 [2535]~E(x25351,x25352)+E(f98(x25351,x25353,x25354,x25355),f98(x25352,x25353,x25354,x25355)) % 165.30/165.06 [2536]~E(x25361,x25362)+E(f98(x25363,x25361,x25364,x25365),f98(x25363,x25362,x25364,x25365)) % 165.30/165.06 [2537]~E(x25371,x25372)+E(f98(x25373,x25374,x25371,x25375),f98(x25373,x25374,x25372,x25375)) % 165.30/165.06 [2538]~E(x25381,x25382)+E(f98(x25383,x25384,x25385,x25381),f98(x25383,x25384,x25385,x25382)) % 165.30/165.06 [2539]~E(x25391,x25392)+E(f657(x25391,x25393,x25394,x25395,x25396),f657(x25392,x25393,x25394,x25395,x25396)) % 165.30/165.06 [2540]~E(x25401,x25402)+E(f657(x25403,x25401,x25404,x25405,x25406),f657(x25403,x25402,x25404,x25405,x25406)) % 165.30/165.06 [2541]~E(x25411,x25412)+E(f657(x25413,x25414,x25411,x25415,x25416),f657(x25413,x25414,x25412,x25415,x25416)) % 165.30/165.06 [2542]~E(x25421,x25422)+E(f657(x25423,x25424,x25425,x25421,x25426),f657(x25423,x25424,x25425,x25422,x25426)) % 165.30/165.06 [2543]~E(x25431,x25432)+E(f657(x25433,x25434,x25435,x25436,x25431),f657(x25433,x25434,x25435,x25436,x25432)) % 165.30/165.06 [2544]~E(x25441,x25442)+E(f395(x25441,x25443),f395(x25442,x25443)) % 165.30/165.06 [2545]~E(x25451,x25452)+E(f395(x25453,x25451),f395(x25453,x25452)) % 165.30/165.06 [2546]~E(x25461,x25462)+E(f685(x25461),f685(x25462)) % 165.30/165.06 [2547]~E(x25471,x25472)+E(f546(x25471,x25473,x25474,x25475),f546(x25472,x25473,x25474,x25475)) % 165.30/165.06 [2548]~E(x25481,x25482)+E(f546(x25483,x25481,x25484,x25485),f546(x25483,x25482,x25484,x25485)) % 165.30/165.06 [2549]~E(x25491,x25492)+E(f546(x25493,x25494,x25491,x25495),f546(x25493,x25494,x25492,x25495)) % 165.30/165.06 [2550]~E(x25501,x25502)+E(f546(x25503,x25504,x25505,x25501),f546(x25503,x25504,x25505,x25502)) % 165.30/165.06 [2551]~E(x25511,x25512)+E(f495(x25511,x25513,x25514,x25515),f495(x25512,x25513,x25514,x25515)) % 165.30/165.06 [2552]~E(x25521,x25522)+E(f495(x25523,x25521,x25524,x25525),f495(x25523,x25522,x25524,x25525)) % 165.30/165.06 [2553]~E(x25531,x25532)+E(f495(x25533,x25534,x25531,x25535),f495(x25533,x25534,x25532,x25535)) % 165.30/165.06 [2554]~E(x25541,x25542)+E(f495(x25543,x25544,x25545,x25541),f495(x25543,x25544,x25545,x25542)) % 165.30/165.06 [2555]~E(x25551,x25552)+E(f592(x25551,x25553,x25554),f592(x25552,x25553,x25554)) % 165.30/165.06 [2556]~E(x25561,x25562)+E(f592(x25563,x25561,x25564),f592(x25563,x25562,x25564)) % 165.30/165.06 [2557]~E(x25571,x25572)+E(f592(x25573,x25574,x25571),f592(x25573,x25574,x25572)) % 165.30/165.06 [2558]~E(x25581,x25582)+E(f760(x25581,x25583,x25584),f760(x25582,x25583,x25584)) % 165.30/165.06 [2559]~E(x25591,x25592)+E(f760(x25593,x25591,x25594),f760(x25593,x25592,x25594)) % 165.30/165.06 [2560]~E(x25601,x25602)+E(f760(x25603,x25604,x25601),f760(x25603,x25604,x25602)) % 165.30/165.06 [2561]~E(x25611,x25612)+E(f337(x25611),f337(x25612)) % 165.30/165.06 [2562]~E(x25621,x25622)+E(f412(x25621,x25623),f412(x25622,x25623)) % 165.30/165.06 [2563]~E(x25631,x25632)+E(f412(x25633,x25631),f412(x25633,x25632)) % 165.30/165.06 [2564]~E(x25641,x25642)+E(f605(x25641,x25643,x25644),f605(x25642,x25643,x25644)) % 165.30/165.06 [2565]~E(x25651,x25652)+E(f605(x25653,x25651,x25654),f605(x25653,x25652,x25654)) % 165.30/165.06 [2566]~E(x25661,x25662)+E(f605(x25663,x25664,x25661),f605(x25663,x25664,x25662)) % 165.30/165.06 [2567]~E(x25671,x25672)+E(f274(x25671,x25673,x25674,x25675,x25676),f274(x25672,x25673,x25674,x25675,x25676)) % 165.30/165.06 [2568]~E(x25681,x25682)+E(f274(x25683,x25681,x25684,x25685,x25686),f274(x25683,x25682,x25684,x25685,x25686)) % 165.30/165.06 [2569]~E(x25691,x25692)+E(f274(x25693,x25694,x25691,x25695,x25696),f274(x25693,x25694,x25692,x25695,x25696)) % 165.30/165.06 [2570]~E(x25701,x25702)+E(f274(x25703,x25704,x25705,x25701,x25706),f274(x25703,x25704,x25705,x25702,x25706)) % 165.30/165.06 [2571]~E(x25711,x25712)+E(f274(x25713,x25714,x25715,x25716,x25711),f274(x25713,x25714,x25715,x25716,x25712)) % 165.30/165.06 [2572]~E(x25721,x25722)+E(f721(x25721,x25723,x25724,x25725),f721(x25722,x25723,x25724,x25725)) % 165.30/165.06 [2573]~E(x25731,x25732)+E(f721(x25733,x25731,x25734,x25735),f721(x25733,x25732,x25734,x25735)) % 165.30/165.06 [2574]~E(x25741,x25742)+E(f721(x25743,x25744,x25741,x25745),f721(x25743,x25744,x25742,x25745)) % 165.30/165.06 [2575]~E(x25751,x25752)+E(f721(x25753,x25754,x25755,x25751),f721(x25753,x25754,x25755,x25752)) % 165.30/165.06 [2576]~E(x25761,x25762)+E(f397(x25761,x25763),f397(x25762,x25763)) % 165.30/165.06 [2577]~E(x25771,x25772)+E(f397(x25773,x25771),f397(x25773,x25772)) % 165.30/165.06 [2578]~E(x25781,x25782)+E(f415(x25781,x25783,x25784,x25785,x25786),f415(x25782,x25783,x25784,x25785,x25786)) % 165.30/165.06 [2579]~E(x25791,x25792)+E(f415(x25793,x25791,x25794,x25795,x25796),f415(x25793,x25792,x25794,x25795,x25796)) % 165.30/165.06 [2580]~E(x25801,x25802)+E(f415(x25803,x25804,x25801,x25805,x25806),f415(x25803,x25804,x25802,x25805,x25806)) % 165.30/165.06 [2581]~E(x25811,x25812)+E(f415(x25813,x25814,x25815,x25811,x25816),f415(x25813,x25814,x25815,x25812,x25816)) % 165.30/165.06 [2582]~E(x25821,x25822)+E(f415(x25823,x25824,x25825,x25826,x25821),f415(x25823,x25824,x25825,x25826,x25822)) % 165.30/165.06 [2583]~P1(x25831)+P1(x25832)+~E(x25831,x25832) % 165.30/165.06 [2584]~P4(x25841)+P4(x25842)+~E(x25841,x25842) % 165.30/165.06 [2585]~P24(x25851)+P24(x25852)+~E(x25851,x25852) % 165.30/165.06 [2586]~P25(x25861)+P25(x25862)+~E(x25861,x25862) % 165.30/165.06 [2587]P41(x25872,x25873)+~E(x25871,x25872)+~P41(x25871,x25873) % 165.30/165.06 [2588]P41(x25883,x25882)+~E(x25881,x25882)+~P41(x25883,x25881) % 165.30/165.06 [2589]~P104(x25891)+P104(x25892)+~E(x25891,x25892) % 165.30/165.06 [2590]~P81(x25901)+P81(x25902)+~E(x25901,x25902) % 165.30/165.06 [2591]~P77(x25911)+P77(x25912)+~E(x25911,x25912) % 165.30/165.06 [2592]~P74(x25921)+P74(x25922)+~E(x25921,x25922) % 165.30/165.06 [2593]~P105(x25931)+P105(x25932)+~E(x25931,x25932) % 165.30/165.06 [2594]P144(x25942,x25943,x25944)+~E(x25941,x25942)+~P144(x25941,x25943,x25944) % 165.30/165.06 [2595]P144(x25953,x25952,x25954)+~E(x25951,x25952)+~P144(x25953,x25951,x25954) % 165.30/165.06 [2596]P144(x25963,x25964,x25962)+~E(x25961,x25962)+~P144(x25963,x25964,x25961) % 165.30/165.06 [2597]~P118(x25971)+P118(x25972)+~E(x25971,x25972) % 165.30/165.06 [2598]~P123(x25981)+P123(x25982)+~E(x25981,x25982) % 165.30/165.06 [2599]~P106(x25991)+P106(x25992)+~E(x25991,x25992) % 165.30/165.06 [2600]~P62(x26001)+P62(x26002)+~E(x26001,x26002) % 165.30/165.06 [2601]~P85(x26011)+P85(x26012)+~E(x26011,x26012) % 165.30/165.06 [2602]~P107(x26021)+P107(x26022)+~E(x26021,x26022) % 165.30/165.06 [2603]~P92(x26031)+P92(x26032)+~E(x26031,x26032) % 165.30/165.06 [2604]~P28(x26041)+P28(x26042)+~E(x26041,x26042) % 165.30/165.06 [2605]~P63(x26051)+P63(x26052)+~E(x26051,x26052) % 165.30/165.06 [2606]~P26(x26061)+P26(x26062)+~E(x26061,x26062) % 165.30/165.06 [2607]~P129(x26071)+P129(x26072)+~E(x26071,x26072) % 165.30/165.06 [2608]~P130(x26081)+P130(x26082)+~E(x26081,x26082) % 165.30/165.06 [2609]~P27(x26091)+P27(x26092)+~E(x26091,x26092) % 165.30/165.06 [2610]P32(x26102,x26103)+~E(x26101,x26102)+~P32(x26101,x26103) % 165.30/165.06 [2611]P32(x26113,x26112)+~E(x26111,x26112)+~P32(x26113,x26111) % 165.30/165.06 [2612]~P99(x26121)+P99(x26122)+~E(x26121,x26122) % 165.30/165.06 [2613]~P93(x26131)+P93(x26132)+~E(x26131,x26132) % 165.30/165.06 [2614]P39(x26142,x26143,x26144)+~E(x26141,x26142)+~P39(x26141,x26143,x26144) % 165.30/165.06 [2615]P39(x26153,x26152,x26154)+~E(x26151,x26152)+~P39(x26153,x26151,x26154) % 165.30/165.06 [2616]P39(x26163,x26164,x26162)+~E(x26161,x26162)+~P39(x26163,x26164,x26161) % 165.30/165.06 [2617]~P64(x26171)+P64(x26172)+~E(x26171,x26172) % 165.30/165.06 [2618]~P65(x26181)+P65(x26182)+~E(x26181,x26182) % 165.30/165.06 [2619]P14(x26192,x26193,x26194)+~E(x26191,x26192)+~P14(x26191,x26193,x26194) % 165.30/165.06 [2620]P14(x26203,x26202,x26204)+~E(x26201,x26202)+~P14(x26203,x26201,x26204) % 165.30/165.06 [2621]P14(x26213,x26214,x26212)+~E(x26211,x26212)+~P14(x26213,x26214,x26211) % 165.30/165.06 [2622]~P116(x26221)+P116(x26222)+~E(x26221,x26222) % 165.30/165.06 [2623]~P113(x26231)+P113(x26232)+~E(x26231,x26232) % 165.30/165.06 [2624]~P73(x26241)+P73(x26242)+~E(x26241,x26242) % 165.30/165.06 [2625]~P66(x26251)+P66(x26252)+~E(x26251,x26252) % 165.30/165.06 [2626]~P67(x26261)+P67(x26262)+~E(x26261,x26262) % 165.30/165.06 [2627]~P30(x26271)+P30(x26272)+~E(x26271,x26272) % 165.30/165.06 [2628]~P82(x26281)+P82(x26282)+~E(x26281,x26282) % 165.30/165.06 [2629]~P112(x26291)+P112(x26292)+~E(x26291,x26292) % 165.30/165.06 [2630]~P100(x26301)+P100(x26302)+~E(x26301,x26302) % 165.30/165.06 [2631]P33(x26312,x26313,x26314)+~E(x26311,x26312)+~P33(x26311,x26313,x26314) % 165.30/165.06 [2632]P33(x26323,x26322,x26324)+~E(x26321,x26322)+~P33(x26323,x26321,x26324) % 165.30/165.06 [2633]P33(x26333,x26334,x26332)+~E(x26331,x26332)+~P33(x26333,x26334,x26331) % 165.30/165.06 [2634]P21(x26342,x26343,x26344,x26345)+~E(x26341,x26342)+~P21(x26341,x26343,x26344,x26345) % 165.30/165.06 [2635]P21(x26353,x26352,x26354,x26355)+~E(x26351,x26352)+~P21(x26353,x26351,x26354,x26355) % 165.30/165.06 [2636]P21(x26363,x26364,x26362,x26365)+~E(x26361,x26362)+~P21(x26363,x26364,x26361,x26365) % 165.30/165.06 [2637]P21(x26373,x26374,x26375,x26372)+~E(x26371,x26372)+~P21(x26373,x26374,x26375,x26371) % 165.30/165.06 [2638]~P97(x26381)+P97(x26382)+~E(x26381,x26382) % 165.30/165.06 [2639]P38(x26392,x26393,x26394,x26395,x26396)+~E(x26391,x26392)+~P38(x26391,x26393,x26394,x26395,x26396) % 165.30/165.06 [2640]P38(x26403,x26402,x26404,x26405,x26406)+~E(x26401,x26402)+~P38(x26403,x26401,x26404,x26405,x26406) % 165.30/165.06 [2641]P38(x26413,x26414,x26412,x26415,x26416)+~E(x26411,x26412)+~P38(x26413,x26414,x26411,x26415,x26416) % 165.30/165.06 [2642]P38(x26423,x26424,x26425,x26422,x26426)+~E(x26421,x26422)+~P38(x26423,x26424,x26425,x26421,x26426) % 165.30/165.06 [2643]P38(x26433,x26434,x26435,x26436,x26432)+~E(x26431,x26432)+~P38(x26433,x26434,x26435,x26436,x26431) % 165.30/165.06 [2644]~P138(x26441)+P138(x26442)+~E(x26441,x26442) % 165.30/165.06 [2645]~P78(x26451)+P78(x26452)+~E(x26451,x26452) % 165.30/165.06 [2646]P145(x26462,x26463,x26464)+~E(x26461,x26462)+~P145(x26461,x26463,x26464) % 165.30/165.06 [2647]P145(x26473,x26472,x26474)+~E(x26471,x26472)+~P145(x26473,x26471,x26474) % 165.30/165.06 [2648]P145(x26483,x26484,x26482)+~E(x26481,x26482)+~P145(x26483,x26484,x26481) % 165.30/165.06 [2649]P8(x26492,x26493,x26494)+~E(x26491,x26492)+~P8(x26491,x26493,x26494) % 165.30/165.06 [2650]P8(x26503,x26502,x26504)+~E(x26501,x26502)+~P8(x26503,x26501,x26504) % 165.30/165.06 [2651]P8(x26513,x26514,x26512)+~E(x26511,x26512)+~P8(x26513,x26514,x26511) % 165.30/165.06 [2652]~P68(x26521)+P68(x26522)+~E(x26521,x26522) % 165.30/165.06 [2653]P20(x26532,x26533,x26534)+~E(x26531,x26532)+~P20(x26531,x26533,x26534) % 165.30/165.06 [2654]P20(x26543,x26542,x26544)+~E(x26541,x26542)+~P20(x26543,x26541,x26544) % 165.30/165.06 [2655]P20(x26553,x26554,x26552)+~E(x26551,x26552)+~P20(x26553,x26554,x26551) % 165.30/165.06 [2656]P22(x26562,x26563)+~E(x26561,x26562)+~P22(x26561,x26563) % 165.30/165.06 [2657]P22(x26573,x26572)+~E(x26571,x26572)+~P22(x26573,x26571) % 165.30/165.06 [2658]~P69(x26581)+P69(x26582)+~E(x26581,x26582) % 165.30/165.06 [2659]~P42(x26591)+P42(x26592)+~E(x26591,x26592) % 165.30/165.06 [2660]P54(x26602,x26603,x26604)+~E(x26601,x26602)+~P54(x26601,x26603,x26604) % 165.30/165.06 [2661]P54(x26613,x26612,x26614)+~E(x26611,x26612)+~P54(x26613,x26611,x26614) % 165.30/165.06 [2662]P54(x26623,x26624,x26622)+~E(x26621,x26622)+~P54(x26623,x26624,x26621) % 165.30/165.06 [2663]~P70(x26631)+P70(x26632)+~E(x26631,x26632) % 165.30/165.06 [2664]~P59(x26641)+P59(x26642)+~E(x26641,x26642) % 165.30/165.06 [2665]P43(x26652,x26653,x26654)+~E(x26651,x26652)+~P43(x26651,x26653,x26654) % 165.30/165.06 [2666]P43(x26663,x26662,x26664)+~E(x26661,x26662)+~P43(x26663,x26661,x26664) % 165.30/165.06 [2667]P43(x26673,x26674,x26672)+~E(x26671,x26672)+~P43(x26673,x26674,x26671) % 165.30/165.06 [2668]~P83(x26681)+P83(x26682)+~E(x26681,x26682) % 165.30/165.06 [2669]~P122(x26691)+P122(x26692)+~E(x26691,x26692) % 165.30/165.06 [2670]P55(x26702,x26703,x26704,x26705,x26706)+~E(x26701,x26702)+~P55(x26701,x26703,x26704,x26705,x26706) % 165.30/165.06 [2671]P55(x26713,x26712,x26714,x26715,x26716)+~E(x26711,x26712)+~P55(x26713,x26711,x26714,x26715,x26716) % 165.30/165.06 [2672]P55(x26723,x26724,x26722,x26725,x26726)+~E(x26721,x26722)+~P55(x26723,x26724,x26721,x26725,x26726) % 165.30/165.06 [2673]P55(x26733,x26734,x26735,x26732,x26736)+~E(x26731,x26732)+~P55(x26733,x26734,x26735,x26731,x26736) % 165.30/165.06 [2674]P55(x26743,x26744,x26745,x26746,x26742)+~E(x26741,x26742)+~P55(x26743,x26744,x26745,x26746,x26741) % 165.30/165.06 [2675]~P84(x26751)+P84(x26752)+~E(x26751,x26752) % 165.30/165.06 [2676]~P140(x26761)+P140(x26762)+~E(x26761,x26762) % 165.30/165.06 [2677]P35(x26772,x26773,x26774)+~E(x26771,x26772)+~P35(x26771,x26773,x26774) % 165.30/165.06 [2678]P35(x26783,x26782,x26784)+~E(x26781,x26782)+~P35(x26783,x26781,x26784) % 165.30/165.06 [2679]P35(x26793,x26794,x26792)+~E(x26791,x26792)+~P35(x26793,x26794,x26791) % 165.30/165.06 [2680]~P86(x26801)+P86(x26802)+~E(x26801,x26802) % 165.30/165.06 [2681]~P71(x26811)+P71(x26812)+~E(x26811,x26812) % 165.30/165.06 [2682]~P60(x26821)+P60(x26822)+~E(x26821,x26822) % 165.30/165.06 [2683]~P108(x26831)+P108(x26832)+~E(x26831,x26832) % 165.30/165.06 [2684]P6(x26842,x26843,x26844)+~E(x26841,x26842)+~P6(x26841,x26843,x26844) % 165.30/165.06 [2685]P6(x26853,x26852,x26854)+~E(x26851,x26852)+~P6(x26853,x26851,x26854) % 165.30/165.06 [2686]P6(x26863,x26864,x26862)+~E(x26861,x26862)+~P6(x26863,x26864,x26861) % 165.30/165.06 [2687]P12(x26872,x26873,x26874)+~E(x26871,x26872)+~P12(x26871,x26873,x26874) % 165.30/165.06 [2688]P12(x26883,x26882,x26884)+~E(x26881,x26882)+~P12(x26883,x26881,x26884) % 165.30/165.06 [2689]P12(x26893,x26894,x26892)+~E(x26891,x26892)+~P12(x26893,x26894,x26891) % 165.30/165.06 [2690]P53(x26902,x26903,x26904)+~E(x26901,x26902)+~P53(x26901,x26903,x26904) % 165.30/165.06 [2691]P53(x26913,x26912,x26914)+~E(x26911,x26912)+~P53(x26913,x26911,x26914) % 165.30/165.06 [2692]P53(x26923,x26924,x26922)+~E(x26921,x26922)+~P53(x26923,x26924,x26921) % 165.30/165.06 [2693]~P80(x26931)+P80(x26932)+~E(x26931,x26932) % 165.30/165.06 [2694]~P142(x26941)+P142(x26942)+~E(x26941,x26942) % 165.30/165.06 [2695]P58(x26952,x26953)+~E(x26951,x26952)+~P58(x26951,x26953) % 165.30/165.06 [2696]P58(x26963,x26962)+~E(x26961,x26962)+~P58(x26963,x26961) % 165.30/165.06 [2697]P45(x26972,x26973)+~E(x26971,x26972)+~P45(x26971,x26973) % 165.30/165.06 [2698]P45(x26983,x26982)+~E(x26981,x26982)+~P45(x26983,x26981) % 165.30/165.06 [2699]P46(x26992,x26993,x26994,x26995,x26996,x26997)+~E(x26991,x26992)+~P46(x26991,x26993,x26994,x26995,x26996,x26997) % 165.30/165.06 [2700]P46(x27003,x27002,x27004,x27005,x27006,x27007)+~E(x27001,x27002)+~P46(x27003,x27001,x27004,x27005,x27006,x27007) % 165.30/165.06 [2701]P46(x27013,x27014,x27012,x27015,x27016,x27017)+~E(x27011,x27012)+~P46(x27013,x27014,x27011,x27015,x27016,x27017) % 165.30/165.06 [2702]P46(x27023,x27024,x27025,x27022,x27026,x27027)+~E(x27021,x27022)+~P46(x27023,x27024,x27025,x27021,x27026,x27027) % 165.30/165.06 [2703]P46(x27033,x27034,x27035,x27036,x27032,x27037)+~E(x27031,x27032)+~P46(x27033,x27034,x27035,x27036,x27031,x27037) % 165.30/165.06 [2704]P46(x27043,x27044,x27045,x27046,x27047,x27042)+~E(x27041,x27042)+~P46(x27043,x27044,x27045,x27046,x27047,x27041) % 165.30/165.06 [2705]~P137(x27051)+P137(x27052)+~E(x27051,x27052) % 165.30/165.06 [2706]~P94(x27061)+P94(x27062)+~E(x27061,x27062) % 165.30/165.06 [2707]~P79(x27071)+P79(x27072)+~E(x27071,x27072) % 165.30/165.06 [2708]~P114(x27081)+P114(x27082)+~E(x27081,x27082) % 165.30/165.06 [2709]~P75(x27091)+P75(x27092)+~E(x27091,x27092) % 165.30/165.06 [2710]~P91(x27101)+P91(x27102)+~E(x27101,x27102) % 165.30/165.06 [2711]~P124(x27111)+P124(x27112)+~E(x27111,x27112) % 165.30/165.06 [2712]P15(x27122,x27123,x27124,x27125)+~E(x27121,x27122)+~P15(x27121,x27123,x27124,x27125) % 165.30/165.06 [2713]P15(x27133,x27132,x27134,x27135)+~E(x27131,x27132)+~P15(x27133,x27131,x27134,x27135) % 165.30/165.06 [2714]P15(x27143,x27144,x27142,x27145)+~E(x27141,x27142)+~P15(x27143,x27144,x27141,x27145) % 165.30/165.06 [2715]P15(x27153,x27154,x27155,x27152)+~E(x27151,x27152)+~P15(x27153,x27154,x27155,x27151) % 165.30/165.06 [2716]P34(x27162,x27163)+~E(x27161,x27162)+~P34(x27161,x27163) % 165.30/165.06 [2717]P34(x27173,x27172)+~E(x27171,x27172)+~P34(x27173,x27171) % 165.30/165.06 [2718]~P125(x27181)+P125(x27182)+~E(x27181,x27182) % 165.30/165.06 [2719]~P115(x27191)+P115(x27192)+~E(x27191,x27192) % 165.30/165.06 [2720]P10(x27202,x27203,x27204,x27205,x27206,x27207)+~E(x27201,x27202)+~P10(x27201,x27203,x27204,x27205,x27206,x27207) % 165.30/165.06 [2721]P10(x27213,x27212,x27214,x27215,x27216,x27217)+~E(x27211,x27212)+~P10(x27213,x27211,x27214,x27215,x27216,x27217) % 165.30/165.06 [2722]P10(x27223,x27224,x27222,x27225,x27226,x27227)+~E(x27221,x27222)+~P10(x27223,x27224,x27221,x27225,x27226,x27227) % 165.30/165.06 [2723]P10(x27233,x27234,x27235,x27232,x27236,x27237)+~E(x27231,x27232)+~P10(x27233,x27234,x27235,x27231,x27236,x27237) % 165.30/165.06 [2724]P10(x27243,x27244,x27245,x27246,x27242,x27247)+~E(x27241,x27242)+~P10(x27243,x27244,x27245,x27246,x27241,x27247) % 165.30/165.06 [2725]P10(x27253,x27254,x27255,x27256,x27257,x27252)+~E(x27251,x27252)+~P10(x27253,x27254,x27255,x27256,x27257,x27251) % 165.30/165.06 [2726]P50(x27262,x27263,x27264)+~E(x27261,x27262)+~P50(x27261,x27263,x27264) % 165.30/165.06 [2727]P50(x27273,x27272,x27274)+~E(x27271,x27272)+~P50(x27273,x27271,x27274) % 165.30/165.06 [2728]P50(x27283,x27284,x27282)+~E(x27281,x27282)+~P50(x27283,x27284,x27281) % 165.30/165.06 [2729]P18(x27292,x27293,x27294,x27295,x27296,x27297)+~E(x27291,x27292)+~P18(x27291,x27293,x27294,x27295,x27296,x27297) % 165.30/165.06 [2730]P18(x27303,x27302,x27304,x27305,x27306,x27307)+~E(x27301,x27302)+~P18(x27303,x27301,x27304,x27305,x27306,x27307) % 165.30/165.06 [2731]P18(x27313,x27314,x27312,x27315,x27316,x27317)+~E(x27311,x27312)+~P18(x27313,x27314,x27311,x27315,x27316,x27317) % 165.30/165.06 [2732]P18(x27323,x27324,x27325,x27322,x27326,x27327)+~E(x27321,x27322)+~P18(x27323,x27324,x27325,x27321,x27326,x27327) % 165.30/165.06 [2733]P18(x27333,x27334,x27335,x27336,x27332,x27337)+~E(x27331,x27332)+~P18(x27333,x27334,x27335,x27336,x27331,x27337) % 165.30/165.06 [2734]P18(x27343,x27344,x27345,x27346,x27347,x27342)+~E(x27341,x27342)+~P18(x27343,x27344,x27345,x27346,x27347,x27341) % 165.30/165.06 [2735]P3(x27352,x27353,x27354,x27355,x27356)+~E(x27351,x27352)+~P3(x27351,x27353,x27354,x27355,x27356) % 165.30/165.06 [2736]P3(x27363,x27362,x27364,x27365,x27366)+~E(x27361,x27362)+~P3(x27363,x27361,x27364,x27365,x27366) % 165.30/165.06 [2737]P3(x27373,x27374,x27372,x27375,x27376)+~E(x27371,x27372)+~P3(x27373,x27374,x27371,x27375,x27376) % 165.30/165.06 [2738]P3(x27383,x27384,x27385,x27382,x27386)+~E(x27381,x27382)+~P3(x27383,x27384,x27385,x27381,x27386) % 165.30/165.06 [2739]P3(x27393,x27394,x27395,x27396,x27392)+~E(x27391,x27392)+~P3(x27393,x27394,x27395,x27396,x27391) % 165.30/165.06 [2740]P36(x27402,x27403,x27404,x27405)+~E(x27401,x27402)+~P36(x27401,x27403,x27404,x27405) % 165.30/165.06 [2741]P36(x27413,x27412,x27414,x27415)+~E(x27411,x27412)+~P36(x27413,x27411,x27414,x27415) % 165.30/165.06 [2742]P36(x27423,x27424,x27422,x27425)+~E(x27421,x27422)+~P36(x27423,x27424,x27421,x27425) % 165.30/165.06 [2743]P36(x27433,x27434,x27435,x27432)+~E(x27431,x27432)+~P36(x27433,x27434,x27435,x27431) % 165.30/165.06 [2744]~P126(x27441)+P126(x27442)+~E(x27441,x27442) % 165.30/165.06 [2745]P13(x27452,x27453,x27454)+~E(x27451,x27452)+~P13(x27451,x27453,x27454) % 165.30/165.06 [2746]P13(x27463,x27462,x27464)+~E(x27461,x27462)+~P13(x27463,x27461,x27464) % 165.30/165.06 [2747]P13(x27473,x27474,x27472)+~E(x27471,x27472)+~P13(x27473,x27474,x27471) % 165.30/165.06 [2748]P37(x27482,x27483,x27484)+~E(x27481,x27482)+~P37(x27481,x27483,x27484) % 165.30/165.06 [2749]P37(x27493,x27492,x27494)+~E(x27491,x27492)+~P37(x27493,x27491,x27494) % 165.30/165.06 [2750]P37(x27503,x27504,x27502)+~E(x27501,x27502)+~P37(x27503,x27504,x27501) % 165.30/165.06 [2751]~P95(x27511)+P95(x27512)+~E(x27511,x27512) % 165.30/165.06 [2752]~P109(x27521)+P109(x27522)+~E(x27521,x27522) % 165.30/165.06 [2753]~P98(x27531)+P98(x27532)+~E(x27531,x27532) % 165.30/165.06 [2754]P11(x27542,x27543,x27544)+~E(x27541,x27542)+~P11(x27541,x27543,x27544) % 165.30/165.06 [2755]P11(x27553,x27552,x27554)+~E(x27551,x27552)+~P11(x27553,x27551,x27554) % 165.30/165.06 [2756]P11(x27563,x27564,x27562)+~E(x27561,x27562)+~P11(x27563,x27564,x27561) % 165.30/165.06 [2757]~P31(x27571)+P31(x27572)+~E(x27571,x27572) % 165.30/165.06 [2758]P5(x27582,x27583)+~E(x27581,x27582)+~P5(x27581,x27583) % 165.30/165.06 [2759]P5(x27593,x27592)+~E(x27591,x27592)+~P5(x27593,x27591) % 165.30/165.06 [2760]~P139(x27601)+P139(x27602)+~E(x27601,x27602) % 165.30/165.06 [2761]P16(x27612,x27613,x27614,x27615)+~E(x27611,x27612)+~P16(x27611,x27613,x27614,x27615) % 165.30/165.06 [2762]P16(x27623,x27622,x27624,x27625)+~E(x27621,x27622)+~P16(x27623,x27621,x27624,x27625) % 165.30/165.06 [2763]P16(x27633,x27634,x27632,x27635)+~E(x27631,x27632)+~P16(x27633,x27634,x27631,x27635) % 165.30/165.06 [2764]P16(x27643,x27644,x27645,x27642)+~E(x27641,x27642)+~P16(x27643,x27644,x27645,x27641) % 165.30/165.06 [2765]~P87(x27651)+P87(x27652)+~E(x27651,x27652) % 165.30/165.06 [2766]~P127(x27661)+P127(x27662)+~E(x27661,x27662) % 165.30/165.06 [2767]~P141(x27671)+P141(x27672)+~E(x27671,x27672) % 165.30/165.06 [2768]~P119(x27681)+P119(x27682)+~E(x27681,x27682) % 165.30/165.06 [2769]~P90(x27691)+P90(x27692)+~E(x27691,x27692) % 165.30/165.06 [2770]P56(x27702,x27703)+~E(x27701,x27702)+~P56(x27701,x27703) % 165.30/165.06 [2771]P56(x27713,x27712)+~E(x27711,x27712)+~P56(x27713,x27711) % 165.30/165.06 [2772]~P88(x27721)+P88(x27722)+~E(x27721,x27722) % 165.30/165.06 [2773]~P61(x27731)+P61(x27732)+~E(x27731,x27732) % 165.30/165.06 [2774]~P136(x27741)+P136(x27742)+~E(x27741,x27742) % 165.30/165.06 [2775]P7(x27752,x27753,x27754)+~E(x27751,x27752)+~P7(x27751,x27753,x27754) % 165.30/165.06 [2776]P7(x27763,x27762,x27764)+~E(x27761,x27762)+~P7(x27763,x27761,x27764) % 165.30/165.06 [2777]P7(x27773,x27774,x27772)+~E(x27771,x27772)+~P7(x27773,x27774,x27771) % 165.30/165.06 [2778]~P101(x27781)+P101(x27782)+~E(x27781,x27782) % 165.30/165.06 [2779]P9(x27792,x27793,x27794,x27795)+~E(x27791,x27792)+~P9(x27791,x27793,x27794,x27795) % 165.30/165.06 [2780]P9(x27803,x27802,x27804,x27805)+~E(x27801,x27802)+~P9(x27803,x27801,x27804,x27805) % 165.30/165.06 [2781]P9(x27813,x27814,x27812,x27815)+~E(x27811,x27812)+~P9(x27813,x27814,x27811,x27815) % 165.30/165.06 [2782]P9(x27823,x27824,x27825,x27822)+~E(x27821,x27822)+~P9(x27823,x27824,x27825,x27821) % 165.30/165.06 [2783]~P128(x27831)+P128(x27832)+~E(x27831,x27832) % 165.30/165.06 [2784]P44(x27842,x27843,x27844,x27845)+~E(x27841,x27842)+~P44(x27841,x27843,x27844,x27845) % 165.30/165.06 [2785]P44(x27853,x27852,x27854,x27855)+~E(x27851,x27852)+~P44(x27853,x27851,x27854,x27855) % 165.30/165.06 [2786]P44(x27863,x27864,x27862,x27865)+~E(x27861,x27862)+~P44(x27863,x27864,x27861,x27865) % 165.30/165.06 [2787]P44(x27873,x27874,x27875,x27872)+~E(x27871,x27872)+~P44(x27873,x27874,x27875,x27871) % 165.30/165.06 [2788]P23(x27882,x27883,x27884)+~E(x27881,x27882)+~P23(x27881,x27883,x27884) % 165.30/165.06 [2789]P23(x27893,x27892,x27894)+~E(x27891,x27892)+~P23(x27893,x27891,x27894) % 165.30/165.06 [2790]P23(x27903,x27904,x27902)+~E(x27901,x27902)+~P23(x27903,x27904,x27901) % 165.30/165.06 [2791]~P133(x27911)+P133(x27912)+~E(x27911,x27912) % 165.30/165.06 [2792]P19(x27922,x27923,x27924,x27925,x27926,x27927)+~E(x27921,x27922)+~P19(x27921,x27923,x27924,x27925,x27926,x27927) % 165.30/165.06 [2793]P19(x27933,x27932,x27934,x27935,x27936,x27937)+~E(x27931,x27932)+~P19(x27933,x27931,x27934,x27935,x27936,x27937) % 165.30/165.06 [2794]P19(x27943,x27944,x27942,x27945,x27946,x27947)+~E(x27941,x27942)+~P19(x27943,x27944,x27941,x27945,x27946,x27947) % 165.30/165.06 [2795]P19(x27953,x27954,x27955,x27952,x27956,x27957)+~E(x27951,x27952)+~P19(x27953,x27954,x27955,x27951,x27956,x27957) % 165.30/165.06 [2796]P19(x27963,x27964,x27965,x27966,x27962,x27967)+~E(x27961,x27962)+~P19(x27963,x27964,x27965,x27966,x27961,x27967) % 165.30/165.06 [2797]P19(x27973,x27974,x27975,x27976,x27977,x27972)+~E(x27971,x27972)+~P19(x27973,x27974,x27975,x27976,x27977,x27971) % 165.30/165.06 [2798]~P96(x27981)+P96(x27982)+~E(x27981,x27982) % 165.30/165.06 [2799]~P102(x27991)+P102(x27992)+~E(x27991,x27992) % 165.30/165.06 [2800]~P110(x28001)+P110(x28002)+~E(x28001,x28002) % 165.30/165.06 [2801]P52(x28012,x28013)+~E(x28011,x28012)+~P52(x28011,x28013) % 165.30/165.06 [2802]P52(x28023,x28022)+~E(x28021,x28022)+~P52(x28023,x28021) % 165.30/165.06 [2803]~P121(x28031)+P121(x28032)+~E(x28031,x28032) % 165.30/165.06 [2804]~P72(x28041)+P72(x28042)+~E(x28041,x28042) % 165.30/165.06 [2805]~P40(x28051)+P40(x28052)+~E(x28051,x28052) % 165.30/165.06 [2806]~P29(x28061)+P29(x28062)+~E(x28061,x28062) % 165.30/165.06 [2807]P47(x28072,x28073)+~E(x28071,x28072)+~P47(x28071,x28073) % 165.30/165.06 [2808]P47(x28083,x28082)+~E(x28081,x28082)+~P47(x28083,x28081) % 165.30/165.06 [2809]~P135(x28091)+P135(x28092)+~E(x28091,x28092) % 165.30/165.06 [2810]~P103(x28101)+P103(x28102)+~E(x28101,x28102) % 165.30/165.06 [2811]~P111(x28111)+P111(x28112)+~E(x28111,x28112) % 165.30/165.06 [2812]~P134(x28121)+P134(x28122)+~E(x28121,x28122) % 165.30/165.06 [2813]P49(x28132,x28133)+~E(x28131,x28132)+~P49(x28131,x28133) % 165.30/165.06 [2814]P49(x28143,x28142)+~E(x28141,x28142)+~P49(x28143,x28141) % 165.30/165.06 [2815]~P89(x28151)+P89(x28152)+~E(x28151,x28152) % 165.30/165.06 [2816]P57(x28162,x28163,x28164,x28165)+~E(x28161,x28162)+~P57(x28161,x28163,x28164,x28165) % 165.30/165.06 [2817]P57(x28173,x28172,x28174,x28175)+~E(x28171,x28172)+~P57(x28173,x28171,x28174,x28175) % 165.30/165.06 [2818]P57(x28183,x28184,x28182,x28185)+~E(x28181,x28182)+~P57(x28183,x28184,x28181,x28185) % 165.30/165.06 [2819]P57(x28193,x28194,x28195,x28192)+~E(x28191,x28192)+~P57(x28193,x28194,x28195,x28191) % 165.30/165.06 [2820]~P143(x28201)+P143(x28202)+~E(x28201,x28202) % 165.30/165.06 [2821]~P48(x28211)+P48(x28212)+~E(x28211,x28212) % 165.30/165.06 [2822]P51(x28222,x28223,x28224)+~E(x28221,x28222)+~P51(x28221,x28223,x28224) % 165.30/165.06 [2823]P51(x28233,x28232,x28234)+~E(x28231,x28232)+~P51(x28233,x28231,x28234) % 165.30/165.06 [2824]P51(x28243,x28244,x28242)+~E(x28241,x28242)+~P51(x28243,x28244,x28241) % 165.30/165.06 [2825]~P120(x28251)+P120(x28252)+~E(x28251,x28252) % 165.30/165.06 [2826]~P76(x28261)+P76(x28262)+~E(x28261,x28262) % 165.30/165.06 [2827]P17(x28272,x28273,x28274,x28275,x28276)+~E(x28271,x28272)+~P17(x28271,x28273,x28274,x28275,x28276) % 165.30/165.06 [2828]P17(x28283,x28282,x28284,x28285,x28286)+~E(x28281,x28282)+~P17(x28283,x28281,x28284,x28285,x28286) % 165.30/165.06 [2829]P17(x28293,x28294,x28292,x28295,x28296)+~E(x28291,x28292)+~P17(x28293,x28294,x28291,x28295,x28296) % 165.30/165.06 [2830]P17(x28303,x28304,x28305,x28302,x28306)+~E(x28301,x28302)+~P17(x28303,x28304,x28305,x28301,x28306) % 165.30/165.06 [2831]P17(x28313,x28314,x28315,x28316,x28312)+~E(x28311,x28312)+~P17(x28313,x28314,x28315,x28316,x28311) % 165.30/165.06 [2832]~P117(x28321)+P117(x28322)+~E(x28321,x28322) % 165.30/165.06 [2833]P2(x28332,x28333,x28334)+~E(x28331,x28332)+~P2(x28331,x28333,x28334) % 165.30/165.06 [2834]P2(x28343,x28342,x28344)+~E(x28341,x28342)+~P2(x28343,x28341,x28344) % 165.30/165.06 [2835]P2(x28353,x28354,x28352)+~E(x28351,x28352)+~P2(x28353,x28354,x28351) % 165.30/165.06 [2836]~P131(x28361)+P131(x28362)+~E(x28361,x28362) % 165.30/165.06 [2837]~P132(x28371)+P132(x28372)+~E(x28371,x28372) % 165.30/165.06 % 165.30/165.06 %------------------------------------------- % 165.36/165.12 cnf(10140,plain, % 165.36/165.12 (~E(f332(a115,x101401),x101401)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(10143,plain, % 165.36/165.12 (E(f332(f263(x101431,x101431),f264(x101431,x101432)),x101432)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(10150,plain, % 165.36/165.12 (~E(f332(a115,x101501),x101501)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(10163,plain, % 165.36/165.12 (~E(f332(a115,x101631),x101631)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(10168,plain, % 165.36/165.12 (~P24(f332(f63(x101681,x101682,f196(f875(x101681,a862))),x101683))), % 165.36/165.12 inference(rename_variables,[],[4544])). % 165.36/165.12 cnf(10171,plain, % 165.36/165.12 (~P24(f332(f63(x101711,x101712,f196(f875(x101711,a862))),x101713))), % 165.36/165.12 inference(rename_variables,[],[4544])). % 165.36/165.12 cnf(10174,plain, % 165.36/165.12 (~E(f332(a115,x101741),x101741)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(10177,plain, % 165.36/165.12 (~E(f332(a115,x101771),x101771)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(10180,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x101801),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(10183,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x101831),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(10196,plain, % 165.36/165.12 (~P24(f332(f196(f875(x101961,a862)),x101962))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,3041,3213,3084,3149,3092,3239,4520,10180,4517,4467,4527,3230,4507,4544,10168,4548,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022])). % 165.36/165.12 cnf(10200,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x102001)),x102001))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(10203,plain, % 165.36/165.12 (~E(f332(f332(f152(x102031),x102032),x102033),x102033)), % 165.36/165.12 inference(rename_variables,[],[4472])). % 165.36/165.12 cnf(10209,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x102091),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(10211,plain, % 165.36/165.12 (E(f45(a868,f332(f263(x102111,x102111),f264(x102111,f332(f332(f82(a868),x102112),x102113))),x102112),f2(a868))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,3041,3213,10143,3084,3149,3114,3092,4472,3239,4520,10180,10183,4517,4467,4529,4527,3230,4507,4544,10168,4548,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050])). % 165.36/165.12 cnf(10212,plain, % 165.36/165.12 (E(f332(f263(x102121,x102121),f264(x102121,x102122)),x102122)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(10215,plain, % 165.36/165.12 (E(f332(f263(x102151,x102151),f264(x102151,x102152)),x102152)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(10222,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),f332(f332(f81(a868),x102221),x102222)),x102222))), % 165.36/165.12 inference(rename_variables,[],[4546])). % 165.36/165.12 cnf(10225,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),f332(f332(f81(a868),x102251),x102252)),x102252))), % 165.36/165.12 inference(rename_variables,[],[4546])). % 165.36/165.12 cnf(10232,plain, % 165.36/165.12 (~E(x102321,f332(a115,x102321))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,3041,3213,10143,10212,3084,3149,3114,3092,4472,3326,3239,4520,10180,10183,4517,4467,4529,4098,4527,3230,4507,4544,10168,4548,4546,10222,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164])). % 165.36/165.12 cnf(10246,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x102461),x102461))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(10249,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f45(a868,x102491,x102492)),x102491))), % 165.36/165.12 inference(rename_variables,[],[3722])). % 165.36/165.12 cnf(10272,plain, % 165.36/165.12 (E(f332(f38(a868),f332(f253(a868),x102721)),x102721)), % 165.36/165.12 inference(rename_variables,[],[3145])). % 165.36/165.12 cnf(10280,plain, % 165.36/165.12 (~E(f332(a115,x102801),x102801)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(10283,plain, % 165.36/165.12 (~E(f332(a115,x102831),x102831)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(10286,plain, % 165.36/165.12 (~E(f332(a115,x102861),x102861)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(10288,plain, % 165.36/165.12 (P24(f332(a201,a100))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,3041,3213,10143,10212,3084,3149,3114,3092,3183,4472,3145,4553,3165,3326,3239,4520,10180,10183,3856,3258,4517,4467,4516,10246,3352,3786,3722,4529,10200,4098,4527,4506,3230,4507,4511,4544,10168,4548,4546,10222,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312])). % 165.36/165.12 cnf(10291,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x102911),f332(a115,x102911)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(10300,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x103001),x103001))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(10307,plain, % 165.36/165.12 (E(f332(f263(x103071,x103071),f264(x103071,x103072)),x103072)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(10310,plain, % 165.36/165.12 (E(f332(f263(x103101,x103101),f264(x103101,x103102)),x103102)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(10329,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x103291),x103291))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(10338,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x103381),x103381))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(10343,plain, % 165.36/165.12 (~E(f332(f332(f332(f73(x103431,f872(x103432)),x103433),x103434),f332(f208(x103432),x103435)),f332(f16(f872(x103432),x103431),f209(x103432)))), % 165.36/165.12 inference(rename_variables,[],[4541])). % 165.36/165.12 cnf(10347,plain, % 165.36/165.12 (E(f332(f332(f81(a868),x103471),f791(x103471,x103471)),x103471)), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,3041,3213,10143,10212,10215,10307,3084,3149,3114,3092,3183,4541,4472,3145,4054,4553,3165,3326,10291,3239,4520,10180,10183,3704,3856,3285,3258,4517,4467,4006,3255,10300,3256,3257,4516,10246,3352,3786,3722,10249,4529,10200,4098,4527,4506,3230,4507,4511,4544,10168,4548,3746,4546,10222,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456])). % 165.36/165.12 cnf(10370,plain, % 165.36/165.12 (~E(f332(f332(f152(x103701),x103702),x103703),x103703)), % 165.36/165.12 inference(rename_variables,[],[4472])). % 165.36/165.12 cnf(10373,plain, % 165.36/165.12 (~E(f332(a28,x103731),f34(x103732,x103733))), % 165.36/165.12 inference(rename_variables,[],[4462])). % 165.36/165.12 cnf(10384,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x103841),x103841))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(10389,plain, % 165.36/165.12 (~E(f332(a115,x103891),x103891)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(10396,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x103961),x103961))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(10409,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x104091),f332(a115,x104091)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(10430,plain, % 165.36/165.12 (~P24(f332(f63(x104301,x104302,f196(f875(x104301,a862))),x104303))), % 165.36/165.12 inference(rename_variables,[],[4544])). % 165.36/165.12 cnf(10449,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x104491),x104491))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(10461,plain, % 165.36/165.12 (E(f332(f332(f257(a868),f332(f106(a868),a100)),x104611),f332(f332(f257(a868),f2(a868)),x104611))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,4462,3041,3213,10143,10212,10215,10307,3084,3149,3114,3092,3737,3183,4541,4472,10203,3145,4054,4553,3165,3627,3326,10291,10409,3239,4520,10180,10183,10209,4536,3704,3856,3283,3285,3258,4517,4467,4006,3255,10300,10396,3256,10329,3257,4516,10246,10338,3352,3786,3722,10249,4529,10200,4098,4527,4506,3230,3234,4508,4507,4511,4544,10168,10171,4548,3746,4546,10222,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819])). % 165.36/165.12 cnf(10464,plain, % 165.36/165.12 (~E(f332(a28,x104641),f34(x104642,x104643))), % 165.36/165.12 inference(rename_variables,[],[4462])). % 165.36/165.12 cnf(10470,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),f2(a868)),f332(a107,f79(a1))))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,4462,10373,3041,3213,10143,10212,10215,10307,3084,3149,3114,3092,3737,3183,4541,4472,10203,3145,4054,4553,3165,3627,3326,10291,10409,3239,4520,10180,10183,10209,4536,3704,3856,3283,3285,3258,4517,4467,4006,3255,10300,10396,3256,10329,3257,4516,10246,10338,3352,3786,3722,10249,4529,10200,4098,4527,4506,3230,3234,4508,4507,4511,4544,10168,10171,4548,3746,4546,10222,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879])). % 165.36/165.12 cnf(10473,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x104731),x104731))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(10478,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x104781),f332(a115,x104781)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(10481,plain, % 165.36/165.12 (~P24(f332(f63(x104811,x104812,f196(f875(x104811,a862))),x104813))), % 165.36/165.12 inference(rename_variables,[],[4544])). % 165.36/165.12 cnf(10484,plain, % 165.36/165.12 (~P24(f332(f63(x104841,x104842,f196(f875(x104841,a862))),x104843))), % 165.36/165.12 inference(rename_variables,[],[4544])). % 165.36/165.12 cnf(10489,plain, % 165.36/165.12 (~P24(f332(f63(x104891,x104892,f196(f875(x104891,a862))),x104893))), % 165.36/165.12 inference(rename_variables,[],[4544])). % 165.36/165.12 cnf(10499,plain, % 165.36/165.12 (~E(f332(f170(x104991),f332(a115,f332(f332(f135(x104991),f332(f170(x104991),x104992)),f332(f332(f152(x104991),x104993),f116(x104991))))),f332(f332(f152(x104991),x104993),x104992))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,4462,10373,3041,3213,10143,10212,10215,10307,3084,3149,3114,3092,3737,3183,4541,4472,10203,3145,4054,4553,3165,3627,3326,10291,10409,10478,3239,4520,10180,10183,10209,4536,3704,3856,3283,3285,3258,4517,4467,4006,3255,10300,10396,3256,10329,3257,4516,10246,10338,10449,3352,3786,3722,10249,4529,10200,4098,4527,4506,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4548,3746,4546,10222,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995])). % 165.36/165.12 cnf(10500,plain, % 165.36/165.12 (~E(f332(a115,x105001),x105001)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(10518,plain, % 165.36/165.12 (P24(f332(f332(f247(a102),f332(a3,x105181)),f332(a3,f332(a115,x105181))))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,4462,10373,3041,3213,10143,10212,10215,10307,3084,3149,3114,3092,3737,3183,4541,4472,10203,3145,4054,4553,3165,3627,3326,10291,10409,10478,3717,3239,4520,10180,10183,10209,4536,3704,3856,3283,3285,3258,4517,4467,4006,3255,10300,10396,3256,10329,3257,4516,10246,10338,10449,3352,3786,3722,10249,4529,10200,4098,4527,4506,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4548,3746,4546,10222,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078])). % 165.36/165.12 cnf(10525,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x105251),x105251))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(10528,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x105281),f332(f332(f82(a868),x105281),x105281)))), % 165.36/165.12 inference(rename_variables,[],[3530])). % 165.36/165.12 cnf(10530,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x105301),f332(f332(f82(a868),f332(a115,x105301)),f332(a115,x105301))))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,4462,10373,3041,3213,10143,10212,10215,10307,3084,3149,3114,3092,3737,3183,4541,4472,10203,3145,4054,4553,3165,3627,3326,10291,10409,10478,3717,3239,4520,10180,10183,10209,4536,3704,3856,3283,3285,3258,4517,4467,4006,3255,10300,10396,3256,10329,3257,4516,10246,10338,10449,3352,3786,3722,10249,4529,10200,4098,4527,4506,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,3530,10528,4548,3746,4546,10222,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100])). % 165.36/165.12 cnf(10531,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x105311),f332(f332(f82(a868),x105311),x105311)))), % 165.36/165.12 inference(rename_variables,[],[3530])). % 165.36/165.12 cnf(10534,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x105341),f332(a115,f332(f332(f81(a868),x105342),x105341))))), % 165.36/165.12 inference(rename_variables,[],[3715])). % 165.36/165.12 cnf(10539,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x105391),f332(a115,x105391)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(10542,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x105421),f332(a115,x105421)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(10545,plain, % 165.36/165.12 (P24(f332(f332(f334(x105451),x105452),f255(f875(x105451,a862))))), % 165.36/165.12 inference(rename_variables,[],[3416])). % 165.36/165.12 cnf(10564,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x105641)),x105641))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(10567,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x105671)),x105671))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(10570,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),f332(f332(f81(a868),x105701),x105702)),x105702))), % 165.36/165.12 inference(rename_variables,[],[4546])). % 165.36/165.12 cnf(10573,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),f332(f332(f81(a868),x105731),x105732)),x105732))), % 165.36/165.12 inference(rename_variables,[],[4546])). % 165.36/165.12 cnf(10576,plain, % 165.36/165.12 (P24(f332(f255(f875(x105761,a862)),x105762))), % 165.36/165.12 inference(rename_variables,[],[3319])). % 165.36/165.12 cnf(10579,plain, % 165.36/165.12 (E(f332(f38(a868),f332(f253(a868),x105791)),x105791)), % 165.36/165.12 inference(rename_variables,[],[3145])). % 165.36/165.12 cnf(10582,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x105821),f332(a115,x105821)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(10589,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x105891),x105891))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(10594,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x105941),x105941))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(10603,plain, % 165.36/165.12 (E(f332(f263(x106031,x106031),f264(x106031,x106032)),x106032)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(10606,plain, % 165.36/165.12 (P24(f332(f255(f875(x106061,a862)),x106062))), % 165.36/165.12 inference(rename_variables,[],[3319])). % 165.36/165.12 cnf(10609,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f2(a868)),x106091))), % 165.36/165.12 inference(rename_variables,[],[3277])). % 165.36/165.12 cnf(10612,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x106121,a862)),f196(f875(x106121,a862))),x106122))), % 165.36/165.12 inference(rename_variables,[],[3713])). % 165.36/165.12 cnf(10615,plain, % 165.36/165.12 (P24(f332(f255(f875(x106151,a862)),x106152))), % 165.36/165.12 inference(rename_variables,[],[3319])). % 165.36/165.12 cnf(10617,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(f332(f82(a868),f332(a115,x106171)),f332(a115,x106171))),x106171))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,4462,10373,3041,3213,10143,10212,10215,10307,10310,3084,3149,3114,3092,3737,3183,4541,4472,10203,3145,10272,4054,4553,3165,3627,3566,3326,10291,10409,10478,10539,10542,3717,3239,4520,10180,10183,10209,4536,3704,3472,3856,3283,3285,3258,4517,4467,4006,3255,10300,10396,10525,3256,10329,10384,3257,4516,10246,10338,10449,3416,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,3277,4098,4527,4506,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4551,3713,3530,10528,10531,4548,3746,4546,10222,10225,10570,3715,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314])). % 165.36/165.12 cnf(10618,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x106181),f332(f332(f82(a868),x106181),x106181)))), % 165.36/165.12 inference(rename_variables,[],[3530])). % 165.36/165.12 cnf(10622,plain, % 165.36/165.12 (E(f332(f170(x106221),f175(x106222,f332(f332(f135(x106221),f332(f170(x106221),x106223)),f332(f332(f152(x106221),x106224),f116(x106221))),f116(x106222))),f332(f332(f152(x106221),x106224),x106223))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,4462,10373,3041,3213,10143,10212,10215,10307,10310,3190,3084,3149,3114,3092,3737,3183,4541,4472,10203,3145,10272,4054,4553,3165,3627,3566,3326,10291,10409,10478,10539,10542,3717,3239,4520,10180,10183,10209,4536,3704,3472,3856,3283,3285,3258,4517,4467,4006,3255,10300,10396,10525,3256,10329,10384,3257,4516,10246,10338,10449,3416,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,3277,4098,4527,4506,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4551,3713,3530,10528,10531,4548,3746,4546,10222,10225,10570,3715,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355])). % 165.36/165.12 cnf(10627,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,f332(a115,f332(f332(f81(a868),x106271),x106272)))),f332(a115,x106272)))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,4462,10373,3041,3213,10143,10212,10215,10307,10310,3190,3084,3149,3114,3092,3737,3183,4541,4472,10203,3145,10272,4054,4553,3165,3627,3566,3326,10291,10409,10478,10539,10542,10582,3717,3239,4520,10180,10183,10209,4536,3704,3472,3856,3283,3285,3258,4517,4467,4006,3255,10300,10396,10525,3256,10329,10384,3257,4516,10246,10338,10449,3416,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,3277,4098,4527,4506,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4551,3713,3530,10528,10531,4548,3746,4546,10222,10225,10570,3715,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359])). % 165.36/165.12 cnf(10635,plain, % 165.36/165.12 (~P24(f332(f332(f247(a102),f332(a3,x106351)),f332(a3,f2(a868))))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,4462,10373,3041,3213,10143,10212,10215,10307,10310,3190,3084,3149,3114,3092,3737,3183,4541,4472,10203,3145,10272,4054,4553,3165,3627,3566,3326,10291,10409,10478,10539,10542,10582,3717,3239,4520,10180,10183,10209,4536,3704,3472,3856,3283,3285,3258,4517,4467,4006,3255,10300,10396,10525,3256,10329,10384,3257,4516,10246,10338,10449,3416,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,3277,4098,4527,4506,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4551,3713,3530,10528,10531,4548,3746,4546,10222,10225,10570,3715,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364])). % 165.36/165.12 cnf(10658,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x106581),x106581))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(10669,plain, % 165.36/165.12 (~P24(f332(f332(f196(f875(x106691,f875(x106692,a862))),x106693),x106694))), % 165.36/165.12 inference(rename_variables,[],[4549])). % 165.36/165.12 cnf(10676,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x106761),f332(a115,x106761)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(10678,plain, % 165.36/165.12 (P24(f332(f332(f247(a1),f332(f332(f22(a1),x106781),f79(a1))),x106781))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,4462,10373,3041,3213,10143,10212,10215,10307,10310,3190,3084,3149,3114,3092,3737,3183,4541,4472,10203,3145,10272,4054,3908,4553,3165,3627,3566,3326,10291,10409,10478,10539,10542,10582,3717,3239,4520,10180,10183,10209,4536,3704,3472,3856,3283,3285,3258,4517,4467,4006,3255,10300,10396,10525,10589,10658,3256,10329,10384,10594,3257,4516,10246,10338,10449,3416,4532,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,3277,4098,4527,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4551,3713,3530,10528,10531,4548,4549,3746,4546,10222,10225,10570,3715,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619])). % 165.36/165.12 cnf(10679,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x106791),x106791))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(10684,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x106841),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(10697,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x106971),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(10700,plain, % 165.36/165.12 (~P24(f332(f332(f247(f875(x107001,a862)),x107002),f196(f875(x107001,a862))))), % 165.36/165.12 inference(rename_variables,[],[4542])). % 165.36/165.12 cnf(10703,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x107031),x107031))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(10706,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x107061),x107061))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(10720,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x107201),f332(f332(f22(a868),x107201),x107202)))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,4462,10373,3041,3213,10143,10212,10215,10307,10310,3190,3084,3149,3114,3092,3737,3183,4541,4472,10203,3145,10272,4054,3908,4553,3165,3627,3566,3326,10291,10409,10478,10539,10542,10582,3717,3239,4520,10180,10183,10209,10684,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,4006,4542,3255,10300,10396,10525,10589,10658,10703,10706,3256,10329,10384,10594,3257,4516,10246,10338,10449,10473,3416,4532,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,3277,4098,4527,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4551,3713,3530,10528,10531,4548,4549,3746,4546,10222,10225,10570,3715,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781])). % 165.36/165.12 cnf(10721,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x107211),x107211))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(10730,plain, % 165.36/165.12 (~P24(f332(f332(f334(x107301),x107302),f196(f875(x107301,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(10739,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x107391),x107391))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(10742,plain, % 165.36/165.12 (~P24(f332(f332(f334(x107421),x107422),f196(f875(x107421,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(10745,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x107451,a862)),f332(f311(x107452,x107451,x107453),f332(f312(x107452,x107451,x107453),x107454))),x107454))), % 165.36/165.12 inference(rename_variables,[],[4158])). % 165.36/165.12 cnf(10752,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x107521,a862)),f332(f174(x107521),f332(f137(x107521,x107522),x107523))),f332(f174(x107521),x107523)))), % 165.36/165.12 inference(rename_variables,[],[3919])). % 165.36/165.12 cnf(10755,plain, % 165.36/165.12 (E(f332(f311(x107551,x107551,f5(x107551)),x107552),x107552)), % 165.36/165.12 inference(rename_variables,[],[3315])). % 165.36/165.12 cnf(10760,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f2(a868)),x107601))), % 165.36/165.12 inference(rename_variables,[],[3277])). % 165.36/165.12 cnf(10763,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x107631),x107631))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(10766,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x107661),x107661))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(10769,plain, % 165.36/165.12 (~P24(f332(f332(f196(f875(x107691,f875(x107692,a862))),x107693),x107694))), % 165.36/165.12 inference(rename_variables,[],[4549])). % 165.36/165.12 cnf(10776,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x107761),x107761))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(10787,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x107871),f332(f332(f82(a868),x107871),x107871)))), % 165.36/165.12 inference(rename_variables,[],[3530])). % 165.36/165.12 cnf(10793,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x107931),f332(a115,f332(f332(f81(a868),x107932),x107931))))), % 165.36/165.12 inference(rename_variables,[],[3715])). % 165.36/165.12 cnf(10800,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x108001),x108001))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(10803,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x108031),x108031))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(10806,plain, % 165.36/165.12 (~E(f332(a115,x108061),x108061)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(10811,plain, % 165.36/165.12 (P24(f332(f332(f334(x108111),x108112),f255(f875(x108111,a862))))), % 165.36/165.12 inference(rename_variables,[],[3416])). % 165.36/165.12 cnf(10816,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x108161),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(10818,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x108181,a862)),x108182),f40(f875(x108181,a862),f332(f309(x108181),x108182))))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,4462,10373,3041,3213,10143,10212,10215,10307,10310,3190,3084,3149,3114,3092,3737,3315,3183,4541,4472,10203,3145,10272,4054,3908,4553,3165,3462,3627,3566,3326,10291,10409,10478,10539,10542,10582,10676,3717,3239,4520,10180,10183,10209,10684,10697,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3628,4006,4542,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,4532,10730,10742,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,3277,10609,4098,4527,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4551,3713,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486])). % 165.36/165.12 cnf(10831,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f2(a868)),x108311))), % 165.36/165.12 inference(rename_variables,[],[3277])). % 165.36/165.12 cnf(10838,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x108381),x108381))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(10847,plain, % 165.36/165.12 (~P24(f332(f332(f334(x108471),x108472),f196(f875(x108471,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(10849,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x108491,a862)),f41(f875(x108491,a862),f332(f309(x108491),x108492))),x108492))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,4462,10373,3041,3213,10143,10212,10215,10307,10310,3190,3084,3149,3114,3092,3737,3315,3183,4541,4472,10203,3145,10272,4054,3908,4553,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,3717,3239,4520,10180,10183,10209,10684,10697,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3628,4006,4542,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,4532,10730,10742,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4551,3713,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761])). % 165.36/165.12 cnf(10851,plain, % 165.36/165.12 (E(f332(f332(f104(f875(x108511,a862)),f332(f332(f104(f875(x108511,a862)),x108512),f332(f80(f875(x108511,a862)),x108513))),x108513),f196(f875(x108511,a862)))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,4462,10373,3041,3213,10143,10212,10215,10307,10310,3190,3084,3149,3114,3092,3737,3315,3183,4541,4472,10203,3145,10272,4054,3908,4553,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,3717,3239,4520,10180,10183,10209,10684,10697,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3628,4006,4542,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,4532,10730,10742,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4551,3713,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763])). % 165.36/165.12 cnf(10854,plain, % 165.36/165.12 (P24(f332(f332(f334(f869(x108541)),x108542),f162(x108541,f255(f875(x108541,a862)))))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,4462,10373,3041,3213,10143,10212,10215,10307,10310,3190,3084,3149,3114,3092,3737,3315,3183,4541,4472,10203,3145,10272,4054,3908,4553,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,3717,3239,4520,10180,10183,10209,10684,10697,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3628,4006,4542,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,4532,10730,10742,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4551,3713,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772])). % 165.36/165.12 cnf(10855,plain, % 165.36/165.12 (P24(f332(f332(f334(x108551),x108552),f255(f875(x108551,a862))))), % 165.36/165.12 inference(rename_variables,[],[3416])). % 165.36/165.12 cnf(10858,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x108581),f869(x108581))),f332(f332(f267(f869(x108581),f869(x108581)),x108582),f116(x108581))),f148(x108581,x108583)))), % 165.36/165.12 inference(rename_variables,[],[4553])). % 165.36/165.12 cnf(10864,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(x108641,x108641)),x108642),f264(x108641,f196(f875(x108641,a862)))))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,4462,10373,3041,3213,10143,10212,10215,10307,10310,3190,3084,3149,3114,3092,3737,3315,3183,4541,4472,10203,3145,10272,4054,3908,4553,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,3717,3239,4520,10180,10183,10209,10684,10697,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3628,4006,4542,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,4532,10730,10742,10847,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4551,3713,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901])). % 165.36/165.12 cnf(10865,plain, % 165.36/165.12 (~P24(f332(f332(f334(x108651),x108652),f196(f875(x108651,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(10867,plain, % 165.36/165.12 (~P24(f332(f332(f334(x108671),x108672),f332(f312(x108671,x108673,x108674),f196(f875(x108673,a862)))))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,4462,10373,3041,3213,10143,10212,10215,10307,10310,3190,3084,3149,3114,3092,3737,3315,3183,4541,4472,10203,3145,10272,4054,3908,4553,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,3717,3239,4520,10180,10183,10209,10684,10697,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3628,4006,4542,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,4532,10730,10742,10847,10865,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4551,3713,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935])). % 165.36/165.12 cnf(10868,plain, % 165.36/165.12 (~P24(f332(f332(f334(x108681),x108682),f196(f875(x108681,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(10871,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x108711,a862)),x108712),f332(f332(f310(x108711),x108713),x108712)))), % 165.36/165.12 inference(rename_variables,[],[3711])). % 165.36/165.12 cnf(10874,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x108741),x108741))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(10877,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x108771,a862)),x108772),f332(f332(f310(x108771),x108773),x108772)))), % 165.36/165.12 inference(rename_variables,[],[3711])). % 165.36/165.12 cnf(10879,plain, % 165.36/165.12 (P38(x108791,x108792,x108793,f117(x108791,f116(x108791)),f116(x108792))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,4462,10373,3041,3094,3213,10143,10212,10215,10307,10310,3190,3084,3149,3114,3092,3737,3315,3183,4541,4472,10203,3145,10272,4054,3908,4553,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,3717,3239,4520,10180,10183,10209,10684,10697,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3628,4006,4542,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,4532,10730,10742,10847,10865,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,4551,3711,10871,3713,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039])). % 165.36/165.12 cnf(10892,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x108921,a862)),x108922),f332(f332(f310(x108921),x108923),x108922)))), % 165.36/165.12 inference(rename_variables,[],[3711])). % 165.36/165.12 cnf(10897,plain, % 165.36/165.12 (~P24(f332(f63(x108971,x108972,f196(f875(x108971,a862))),x108973))), % 165.36/165.12 inference(rename_variables,[],[4544])). % 165.36/165.12 cnf(10901,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(a868,a868)),f332(f332(f267(a868,a868),f332(a115,x109011)),x109011)),f308(a868,a322)))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,4462,10373,3041,3094,3213,10143,10212,10215,10307,10310,3190,3084,3149,3114,3092,3737,3315,3183,4541,4472,10203,3145,10272,4054,3908,4553,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,3717,3239,4520,10180,10183,10209,10684,10697,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3628,4006,4542,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3713,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357])). % 165.36/165.12 cnf(10910,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x109101),f332(a115,x109101)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(10920,plain, % 165.36/165.12 (~E(f332(f311(x109201,f875(x109201,a862),x109202),x109203),f332(f309(x109201),x109203))), % 165.36/165.12 inference(rename_variables,[],[4530])). % 165.36/165.12 cnf(10923,plain, % 165.36/165.12 (~P24(f332(f332(f334(x109231),x109232),f196(f875(x109231,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(10926,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(x109261,x109261)),f332(f332(f267(x109261,x109261),x109262),x109262)),f308(x109261,x109263)))), % 165.36/165.12 inference(rename_variables,[],[3908])). % 165.36/165.12 cnf(10929,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x109291,a862)),x109292),f255(f875(x109291,a862))))), % 165.36/165.12 inference(rename_variables,[],[3646])). % 165.36/165.12 cnf(10932,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x109321,a862)),f332(f174(x109321),f172(x109321,x109322,x109323))),f332(f174(x109321),x109323)))), % 165.36/165.12 inference(rename_variables,[],[3970])). % 165.36/165.12 cnf(10948,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x109481,a862)),f196(f875(x109481,a862))),x109482))), % 165.36/165.12 inference(rename_variables,[],[3713])). % 165.36/165.12 cnf(10959,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x109591),f869(x109591))),f332(f332(f267(f869(x109591),f869(x109591)),x109592),f116(x109591))),f148(x109591,x109593)))), % 165.36/165.12 inference(rename_variables,[],[4553])). % 165.36/165.12 cnf(10970,plain, % 165.36/165.12 (~E(f332(a115,x109701),x109701)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(10973,plain, % 165.36/165.12 (~E(f332(a115,x109731),x109731)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(10975,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(f869(x109751),f869(x109751))),f332(f332(f267(f869(x109751),f869(x109751)),f116(x109751)),f116(x109751))),f332(f332(f289(f869(x109751),f869(x109751),f869(x109751)),f159(x109751,x109752)),f308(f869(x109751),f159(x109751,x109752)))))), % 165.36/165.12 inference(scs_inference,[],[4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,4541,3906,4472,10203,4530,3145,10272,4054,3908,10926,4553,10858,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,4542,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3713,10612,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576])). % 165.36/165.12 cnf(10985,plain, % 165.36/165.12 (P21(x109851,x109851,f5(x109851),x109852)), % 165.36/165.12 inference(rename_variables,[],[3502])). % 165.36/165.12 cnf(10990,plain, % 165.36/165.12 (~E(f332(f311(x109901,f875(x109901,a862),x109902),x109903),f332(f309(x109901),x109903))), % 165.36/165.12 inference(rename_variables,[],[4530])). % 165.36/165.12 cnf(10995,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x109951,a862)),x109952),f255(f875(x109951,a862))))), % 165.36/165.12 inference(rename_variables,[],[3646])). % 165.36/165.12 cnf(11009,plain, % 165.36/165.12 (~P24(f332(f332(f334(x110091),x110092),f196(f875(x110091,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11012,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x110121)),x110121))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(11017,plain, % 165.36/165.12 (~P24(f332(f332(f334(x110171),x110172),f196(f875(x110171,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11029,plain, % 165.36/165.12 (~P24(f332(f332(f334(a868),f332(a115,f332(f143(a868,a868,f81(a868),f2(a868)),x110291))),f332(f174(a868),x110291)))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,4541,3906,4472,10203,4530,10920,3363,3145,10272,4054,3908,10926,4553,10858,10959,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,10929,4542,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3713,10612,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793])). % 165.36/165.12 cnf(11030,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x110301)),x110301))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(11033,plain, % 165.36/165.12 (~P24(f332(f332(f334(x110331),x110332),f196(f875(x110331,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11041,plain, % 165.36/165.12 (E(f332(f137(x110411,f255(f875(x110412,a862))),f712(x110413,x110414,f332(f332(f152(x110411),x110414),x110413),f255(f875(x110412,a862)),x110411)),x110413)), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,4541,3906,4472,10203,4530,10920,3363,3145,10272,4054,3908,10926,4553,10858,10959,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,10929,4542,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3713,10612,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866])). % 165.36/165.12 cnf(11043,plain, % 165.36/165.12 (E(f332(x110431,f827(f332(x110431,x110432),f332(f208(x110433),x110432),x110431,x110434,x110433)),f332(x110431,x110432))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,4530,10920,3363,3145,10272,4054,3908,10926,4553,10858,10959,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,10929,4542,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3713,10612,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868])). % 165.36/165.12 cnf(11052,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(x110521,x110521)),f332(f332(f267(x110521,x110521),x110522),x110522)),f308(x110521,x110523)))), % 165.36/165.12 inference(rename_variables,[],[3908])). % 165.36/165.12 cnf(11057,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x110571),f869(x110571))),f332(f332(f267(f869(x110571),f869(x110571)),x110572),f116(x110571))),f148(x110571,x110573)))), % 165.36/165.12 inference(rename_variables,[],[4553])). % 165.36/165.12 cnf(11060,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x110601),f869(x110601))),f332(f332(f267(f869(x110601),f869(x110601)),x110602),f116(x110601))),f146(x110601,x110603)))), % 165.36/165.12 inference(rename_variables,[],[4554])). % 165.36/165.12 cnf(11063,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x110631),f869(x110631))),f332(f332(f267(f869(x110631),f869(x110631)),x110632),f116(x110631))),f158(x110631,x110633)))), % 165.36/165.12 inference(rename_variables,[],[4555])). % 165.36/165.12 cnf(11065,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x110651),f869(x110651))),f332(f332(f267(f869(x110651),f869(x110651)),f116(x110651)),x110652)),f332(f287(f869(x110651),f869(x110651)),f148(x110651,x110653))))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,4530,10920,3363,3145,10272,4054,3908,10926,4553,10858,10959,11057,4554,4555,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,10929,4542,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3713,10612,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005])). % 165.36/165.12 cnf(11068,plain, % 165.36/165.12 (~P24(f332(f332(f247(f875(x110681,a862)),x110682),f196(f875(x110681,a862))))), % 165.36/165.12 inference(rename_variables,[],[4542])). % 165.36/165.12 cnf(11070,plain, % 165.36/165.12 (~P24(f332(f332(f334(x110701),x110702),f332(f311(x110703,x110701,x110704),f196(f875(x110703,a862)))))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,4530,10920,3363,3145,10272,4054,3908,10926,4553,10858,10959,11057,4554,4555,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,10929,4542,10700,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3713,10612,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028])). % 165.36/165.12 cnf(11071,plain, % 165.36/165.12 (~P24(f332(f332(f334(x110711),x110712),f196(f875(x110711,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11075,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x110751,a862)),x110752),f332(f332(f113(f875(x110751,a862)),x110753),f255(f875(x110751,a862)))))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,4530,10920,3363,3145,10272,4054,3908,10926,4553,10858,10959,11057,4554,4555,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,10929,10995,4542,10700,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3713,10612,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057])). % 165.36/165.12 cnf(11076,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x110761,a862)),x110762),f255(f875(x110761,a862))))), % 165.36/165.12 inference(rename_variables,[],[3646])). % 165.36/165.12 cnf(11085,plain, % 165.36/165.12 (~P24(f332(f332(f334(x110851),x110852),f196(f875(x110851,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11088,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(x110881,x110881)),f332(f332(f267(x110881,x110881),x110882),x110883)),f154(x110881,f116(f875(x110881,a868)))))), % 165.36/165.12 inference(rename_variables,[],[4551])). % 165.36/165.12 cnf(11091,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x110911,a862)),x110912),x110912))), % 165.36/165.12 inference(rename_variables,[],[3562])). % 165.36/165.12 cnf(11094,plain, % 165.36/165.12 (~P24(f332(f332(f334(x110941),x110942),f196(f875(x110941,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11096,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x110961,a862)),f332(f286(x110962,x110961,f196(f875(f874(x110962,x110961),a862))),x110963)),x110964))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,4530,10920,3363,3145,10272,4054,3908,10926,4553,10858,10959,11057,4554,4555,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,10929,10995,4542,10700,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3562,3713,10612,10948,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221])). % 165.36/165.12 cnf(11097,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x110971,a862)),f196(f875(x110971,a862))),x110972))), % 165.36/165.12 inference(rename_variables,[],[3713])). % 165.36/165.12 cnf(11100,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(x111001,x111001)),f332(f332(f267(x111001,x111001),x111002),x111002)),f308(x111001,x111003)))), % 165.36/165.12 inference(rename_variables,[],[3908])). % 165.36/165.12 cnf(11102,plain, % 165.36/165.12 (~P38(x111021,x111022,x111023,f332(f332(f155(x111024,x111021),x111025),f332(a115,f116(x111024))),f116(x111022))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,4530,10920,3363,3145,10272,4054,3908,10926,11052,4553,10858,10959,11057,4554,4555,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,10929,10995,4542,10700,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3562,3713,10612,10948,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227])). % 165.36/165.12 cnf(11106,plain, % 165.36/165.12 (P38(x111061,x111062,x111063,f332(f332(f155(x111064,x111061),x111065),f117(x111064,f116(x111064))),f116(x111062))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,4530,10920,3363,3145,10272,4054,3908,10926,11052,4553,10858,10959,11057,4554,4555,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,10929,10995,4542,10700,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3562,3713,10612,10948,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248])). % 165.36/165.12 cnf(11110,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x111101),f869(x111101))),f332(f332(f267(f869(x111101),f869(x111101)),x111102),f116(x111101))),f332(f287(f869(x111101),f869(x111101)),f158(x111101,x111103))))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,4530,10920,3363,3145,10272,4054,3908,10926,11052,4553,10858,10959,11057,4554,4555,11063,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,10929,10995,4542,10700,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3562,3713,10612,10948,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335])). % 165.36/165.12 cnf(11111,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x111111),f869(x111111))),f332(f332(f267(f869(x111111),f869(x111111)),x111112),f116(x111111))),f158(x111111,x111113)))), % 165.36/165.12 inference(rename_variables,[],[4555])). % 165.36/165.12 cnf(11114,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x111141),f869(x111141))),f332(f332(f267(f869(x111141),f869(x111141)),f116(x111141)),x111142)),f146(x111141,x111143)))), % 165.36/165.12 inference(rename_variables,[],[4556])). % 165.36/165.12 cnf(11119,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f875(x111191,a862),f875(x111191,a862))),f332(f332(f267(f875(x111191,a862),f875(x111191,a862)),x111192),f196(f875(x111191,a862)))),f307(x111191)))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,4530,10920,3363,3145,10272,4054,3908,10926,11052,4553,10858,10959,11057,4554,4555,11063,4556,4557,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,10929,10995,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3562,3713,10612,10948,3530,10528,10531,10618,10787,4548,4549,10669,4158,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372])). % 165.36/165.12 cnf(11122,plain, % 165.36/165.12 (P24(f332(f332(f334(x111221),x111222),f255(f875(x111221,a862))))), % 165.36/165.12 inference(rename_variables,[],[3416])). % 165.36/165.12 cnf(11127,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x111271,a862)),f196(f875(x111271,a862))),x111272))), % 165.36/165.12 inference(rename_variables,[],[3713])). % 165.36/165.12 cnf(11130,plain, % 165.36/165.12 (~P24(f332(f332(f334(x111301),x111302),f196(f875(x111301,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11133,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x111331,a862)),x111332),f255(f875(x111331,a862))))), % 165.36/165.12 inference(rename_variables,[],[3646])). % 165.36/165.12 cnf(11137,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x111371,a862)),f332(f286(x111372,x111371,x111373),f196(f875(x111372,a862)))),x111374))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,4530,10920,3363,3145,10272,4054,3908,10926,11052,4553,10858,10959,11057,4554,4555,11063,4556,4557,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,4549,10669,4158,4059,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472])). % 165.36/165.12 cnf(11138,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x111381,a862)),f196(f875(x111381,a862))),x111382))), % 165.36/165.12 inference(rename_variables,[],[3713])). % 165.36/165.12 cnf(11140,plain, % 165.36/165.12 (~P24(f332(f67(a868,x111401,x111402,x111403,f255(f875(a868,a862))),x111404))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,4530,10920,3363,3145,10272,4054,3908,10926,11052,4553,10858,10959,11057,4554,4555,11063,4556,4557,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,3319,10576,10606,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,4549,10669,4158,4059,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494])). % 165.36/165.12 cnf(11151,plain, % 165.36/165.12 (P24(f332(f255(f875(x111511,a862)),x111512))), % 165.36/165.12 inference(rename_variables,[],[3319])). % 165.36/165.12 cnf(11159,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x111591),f869(x111591))),f332(f332(f267(f869(x111591),f869(x111591)),x111592),f116(x111591))),f148(x111591,x111593)))), % 165.36/165.12 inference(rename_variables,[],[4553])). % 165.36/165.12 cnf(11162,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x111621),f869(x111621))),f332(f332(f267(f869(x111621),f869(x111621)),x111622),f116(x111621))),f146(x111621,x111623)))), % 165.36/165.12 inference(rename_variables,[],[4554])). % 165.36/165.12 cnf(11165,plain, % 165.36/165.12 (~E(f332(f332(f152(x111651),x111652),x111653),x111653)), % 165.36/165.12 inference(rename_variables,[],[4472])). % 165.36/165.12 cnf(11168,plain, % 165.36/165.12 (~E(f332(a115,x111681),x111681)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11171,plain, % 165.36/165.12 (~P24(f332(f332(f334(x111711),x111712),f196(f875(x111711,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11176,plain, % 165.36/165.12 (~P24(f332(f332(f334(x111761),x111762),f196(f875(x111761,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11179,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(f869(x111791),f869(x111791))),f332(f332(f267(f869(x111791),f869(x111791)),x111792),x111792)),f159(x111791,f308(x111791,x111793))))), % 165.36/165.12 inference(rename_variables,[],[4048])). % 165.36/165.12 cnf(11184,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x111841),f869(x111841))),f332(f332(f267(f869(x111841),f869(x111841)),x111842),f116(x111841))),f148(x111841,x111843)))), % 165.36/165.12 inference(rename_variables,[],[4553])). % 165.36/165.12 cnf(11188,plain, % 165.36/165.12 (E(f332(f332(f152(x111881),f564(f308(x111881,x111882),f332(f332(f152(x111881),x111883),x111884),x111884,x111883,x111881)),f565(f308(x111881,x111882),f332(f332(f152(x111881),x111883),x111884),x111884,x111883,x111881)),f332(f332(f152(x111881),x111883),x111884))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,10370,4530,10920,3363,3145,10272,4054,3908,10926,11052,4553,10858,10959,11057,11159,4554,11060,4555,11063,4556,11114,4557,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4048,11179,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,3319,10576,10606,10615,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,4549,10669,4158,4059,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665])). % 165.36/165.12 cnf(11193,plain, % 165.36/165.12 (~P24(f332(f332(f334(x111931),x111932),f188(x111933,x111931,f190(x111933,x111931,x111934,f196(f875(x111933,a862))))))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,10370,4530,10920,3363,3145,10272,4054,3908,10926,11052,4553,10858,10959,11057,11159,4554,11060,4555,11063,4556,11114,4557,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4048,11179,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,3319,10576,10606,10615,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,3873,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,4549,10669,4158,4059,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688])). % 165.36/165.12 cnf(11194,plain, % 165.36/165.12 (~P24(f332(f332(f334(x111941),x111942),f196(f875(x111941,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11197,plain, % 165.36/165.12 (~P24(f332(f332(f334(x111971),x111972),f196(f875(x111971,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11200,plain, % 165.36/165.12 (~P24(f332(f332(f334(x112001),x112002),f196(f875(x112001,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11203,plain, % 165.36/165.12 (P24(f332(f332(f334(x112031),x112032),f255(f875(x112031,a862))))), % 165.36/165.12 inference(rename_variables,[],[3416])). % 165.36/165.12 cnf(11206,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x112061),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(11211,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(x112111,x112111)),f332(f332(f267(x112111,x112111),x112112),x112113)),f154(x112111,f116(f875(x112111,a868)))))), % 165.36/165.12 inference(rename_variables,[],[4551])). % 165.36/165.12 cnf(11214,plain, % 165.36/165.12 (~E(f332(f311(x112141,f875(x112141,a862),x112142),x112143),f332(f309(x112141),x112143))), % 165.36/165.12 inference(rename_variables,[],[4530])). % 165.36/165.12 cnf(11217,plain, % 165.36/165.12 (~E(f332(f311(x112171,f875(x112171,a862),x112172),x112173),f332(f309(x112171),x112173))), % 165.36/165.12 inference(rename_variables,[],[4530])). % 165.36/165.12 cnf(11219,plain, % 165.36/165.12 (E(f332(f332(f267(a868,a868),f778(f308(a868,a322),a322,a868,f332(f332(f267(a868,a868),x112191),f332(a115,x112191)),a868,a868)),f785(f308(a868,a322),a322,a868,f332(f332(f267(a868,a868),x112191),f332(a115,x112191)),a868,a868)),f332(f332(f267(a868,a868),x112191),f332(a115,x112191)))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,10370,4530,10920,10990,11214,3363,3145,10272,4054,3908,10926,11052,4553,10858,10959,11057,11159,4554,11060,4555,11063,4556,11114,4557,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4048,11179,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,11122,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,3319,10576,10606,10615,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,11088,3873,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,4549,10669,4158,4059,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859])). % 165.36/165.12 cnf(11222,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x112221),f869(x112221))),f332(f332(f267(f869(x112221),f869(x112221)),x112222),f116(x112221))),f148(x112221,x112223)))), % 165.36/165.12 inference(rename_variables,[],[4553])). % 165.36/165.12 cnf(11228,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x112281),f869(x112281))),f332(f332(f267(f869(x112281),f869(x112281)),x112282),f116(x112281))),f148(x112281,x112283)))), % 165.36/165.12 inference(rename_variables,[],[4553])). % 165.36/165.12 cnf(11231,plain, % 165.36/165.12 (~P24(f332(f332(f334(x112311),x112312),f196(f875(x112311,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11235,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(x112351,x112352)),f332(f332(f267(x112351,x112352),f332(x112353,x112354)),f332(x112355,x112354))),f332(f311(f874(x112356,x112356),f874(x112351,x112352),f272(x112356,x112351,x112356,x112352,x112353,x112355)),f308(x112356,x112357))))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,4462,10373,10464,3041,3094,3213,10143,10212,10215,10307,10310,3190,3725,3084,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,10370,4530,10920,10990,11214,3363,3145,10272,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,4536,3704,3472,3856,3283,3285,3258,4517,4467,4048,11179,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,11122,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,3319,10576,10606,10615,3352,3786,3722,10249,4529,10200,10564,10567,11012,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4544,10168,10171,10430,10481,10484,10489,4551,11088,3873,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,4549,10669,4158,4059,3746,4546,10222,10225,10570,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987])). % 165.36/165.12 cnf(11238,plain, % 165.36/165.12 (~P24(f332(f332(f334(x112381),x112382),f196(f875(x112381,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11241,plain, % 165.36/165.12 (~P24(f332(f332(f334(x112411),x112412),f196(f875(x112411,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11244,plain, % 165.36/165.12 (P24(f332(f332(f334(x112441),f332(x112442,x112443)),f332(f311(x112444,x112441,x112442),f255(f875(x112444,a862)))))), % 165.36/165.12 inference(rename_variables,[],[3873])). % 165.36/165.12 cnf(11247,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(x112471,x112471)),f332(f332(f267(x112471,x112471),x112472),x112473)),f154(x112471,f116(f875(x112471,a868)))))), % 165.36/165.12 inference(rename_variables,[],[4551])). % 165.36/165.12 cnf(11255,plain, % 165.36/165.12 (E(f117(x112551,f116(x112551)),f116(x112551))), % 165.36/165.12 inference(rename_variables,[],[3094])). % 165.36/165.12 cnf(11258,plain, % 165.36/165.12 (~E(f332(a115,x112581),x112581)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11265,plain, % 165.36/165.12 (~E(f332(a115,x112651),x112651)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11270,plain, % 165.36/165.12 (E(f332(f263(x112701,x112701),f264(x112701,x112702)),x112702)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(11273,plain, % 165.36/165.12 (E(f332(f263(x112731,x112731),f264(x112731,x112732)),x112732)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(11279,plain, % 165.36/165.12 (~E(f332(a115,x112791),x112791)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11286,plain, % 165.36/165.12 (~E(f332(f332(f81(a1),x112861),x112861),a100)), % 165.36/165.12 inference(rename_variables,[],[4470])). % 165.36/165.12 cnf(11295,plain, % 165.36/165.12 (E(f332(f332(f22(a868),f2(a868)),x112951),f2(a868))), % 165.36/165.12 inference(rename_variables,[],[3166])). % 165.36/165.12 cnf(11298,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x112981),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(11305,plain, % 165.36/165.12 (E(f332(f332(f81(a1),f332(f332(f82(a1),x113051),f332(f332(f39(a1),x113052),x113051))),f45(a1,x113052,x113051)),x113052)), % 165.36/165.12 inference(rename_variables,[],[3819])). % 165.36/165.12 cnf(11331,plain, % 165.36/165.12 (~E(f332(a115,x113311),x113311)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11334,plain, % 165.36/165.12 (~E(f332(a115,x113341),x113341)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11360,plain, % 165.36/165.12 (~P24(f332(f63(x113601,x113602,f196(f875(x113601,a862))),x113603))), % 165.36/165.12 inference(rename_variables,[],[4544])). % 165.36/165.12 cnf(11363,plain, % 165.36/165.12 (~P24(f332(f332(f196(f875(x113631,f875(x113632,a862))),x113633),x113634))), % 165.36/165.12 inference(rename_variables,[],[4549])). % 165.36/165.12 cnf(11366,plain, % 165.36/165.12 (P24(f332(f332(f334(x113661),x113662),f255(f875(x113661,a862))))), % 165.36/165.12 inference(rename_variables,[],[3416])). % 165.36/165.12 cnf(11378,plain, % 165.36/165.12 (~E(f332(a115,x113781),x113781)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11381,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x113811),x113811))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(11388,plain, % 165.36/165.12 (P24(f332(f67(x113881,x113882,x113883,x113884,f196(f875(x113881,a862))),x113884))), % 165.36/165.12 inference(rename_variables,[],[4198])). % 165.36/165.12 cnf(11389,plain, % 165.36/165.12 (E(f332(f263(x113891,x113891),f264(x113891,x113892)),x113892)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(11394,plain, % 165.36/165.12 (~P24(f332(f332(f196(f875(x113941,f875(x113942,a862))),x113943),x113944))), % 165.36/165.12 inference(rename_variables,[],[4549])). % 165.36/165.12 cnf(11405,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),f332(f332(f81(a868),x114051),x114052)),x114052))), % 165.36/165.12 inference(rename_variables,[],[4546])). % 165.36/165.12 cnf(11408,plain, % 165.36/165.12 (~P24(f332(f332(f247(a1),f332(f103(a1),x114081)),f2(a1)))), % 165.36/165.12 inference(rename_variables,[],[4536])). % 165.36/165.12 cnf(11424,plain, % 165.36/165.12 (~E(f332(f332(f104(a868),f332(a115,x114241)),x114241),f332(a115,x114241))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,4462,10373,10464,3170,2848,2854,2858,2859,2862,2867,2875,2876,2881,2889,2911,2917,2918,2935,2938,2953,2989,2993,2994,3004,3018,3025,3041,4443,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,3190,3725,3084,3819,11305,3149,3114,3092,3737,3315,3183,3362,4541,3906,4472,10203,10370,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4470,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,11206,11298,4536,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,10803,3257,4516,10246,10338,10449,10473,10721,10766,3416,10545,10811,10855,11122,11203,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,3319,10576,10606,10615,3352,3786,3722,10249,4529,10200,10564,10567,11012,11030,3277,10609,10760,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,4198,4544,10168,10171,10430,10481,10484,10489,10897,4551,11088,11211,3873,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,4538,4549,10669,10769,11363,4158,4059,3746,4546,10222,10225,10570,10573,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358])). % 165.36/165.12 cnf(11431,plain, % 165.36/165.12 (E(f332(f263(x114311,x114311),f264(x114311,x114312)),x114312)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(11436,plain, % 165.36/165.12 (E(f332(f263(x114361,x114361),f264(x114361,x114362)),x114362)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(11439,plain, % 165.36/165.12 (~P24(f332(f332(f247(a1),f332(f103(a1),x114391)),f2(a1)))), % 165.36/165.12 inference(rename_variables,[],[4536])). % 165.36/165.12 cnf(11444,plain, % 165.36/165.12 (~E(f332(a115,x114441),x114441)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11453,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x114531),x114531))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11474,plain, % 165.36/165.12 (~P24(f332(f332(f247(a1),f332(f103(a1),x114741)),f2(a1)))), % 165.36/165.12 inference(rename_variables,[],[4536])). % 165.36/165.12 cnf(11489,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x114891)),x114891))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(11490,plain, % 165.36/165.12 (~E(f332(a115,x114901),x114901)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11500,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),f332(f332(f81(a868),x115001),x115002)),x115001))), % 165.36/165.12 inference(rename_variables,[],[4547])). % 165.36/165.12 cnf(11503,plain, % 165.36/165.12 (~P24(f332(f332(f247(a1),f332(f103(a1),x115031)),f2(a1)))), % 165.36/165.12 inference(rename_variables,[],[4536])). % 165.36/165.12 cnf(11506,plain, % 165.36/165.12 (~E(f332(a115,x115061),x115061)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11519,plain, % 165.36/165.12 (P24(f332(f332(f334(x115191),x115192),f332(f332(f310(x115191),x115192),x115193)))), % 165.36/165.12 inference(rename_variables,[],[3577])). % 165.36/165.12 cnf(11520,plain, % 165.36/165.12 (~P24(f332(f332(f246(a1),f2(a1)),f332(f80(a1),f332(f103(a1),f332(a115,x115201)))))), % 165.36/165.12 inference(rename_variables,[],[4548])). % 165.36/165.12 cnf(11523,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),f332(f332(f22(a868),x115231),x115232)),f332(a115,x115231)))), % 165.36/165.12 inference(rename_variables,[],[3717])). % 165.36/165.12 cnf(11526,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f45(a868,x115261,x115262)),x115261))), % 165.36/165.12 inference(rename_variables,[],[3722])). % 165.36/165.12 cnf(11532,plain, % 165.36/165.12 (E(f332(f263(x115321,x115321),f264(x115321,x115322)),x115322)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(11537,plain, % 165.36/165.12 (E(f332(f332(f135(x115371),f171(x115371,x115372,x115373)),f171(x115371,x115374,x115373)),f332(f332(f135(x115371),f171(x115371,x115374,x115373)),f171(x115371,x115372,x115373)))), % 165.36/165.12 inference(rename_variables,[],[3834])). % 165.36/165.12 cnf(11542,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x115421)),x115421))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(11551,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x115511),x115511))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11554,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f45(a868,x115541,x115542)),x115541))), % 165.36/165.12 inference(rename_variables,[],[3722])). % 165.36/165.12 cnf(11555,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f2(a868)),x115551))), % 165.36/165.12 inference(rename_variables,[],[3277])). % 165.36/165.12 cnf(11557,plain, % 165.36/165.12 (~P24(f332(f332(f246(a1),f79(a1)),f2(a1)))), % 165.36/165.12 inference(scs_inference,[],[3502,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,4462,10373,10464,3170,2847,2848,2854,2855,2858,2859,2862,2867,2868,2875,2876,2881,2882,2889,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,3190,3725,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,3239,4520,10180,10183,10209,10684,10697,10816,11206,11298,4536,11408,11439,11474,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,3256,10329,10384,10594,10679,10803,3257,4516,10246,10338,10449,10473,10721,10766,10776,11453,3416,10545,10811,10855,11122,11203,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,3319,10576,10606,10615,3358,3352,3786,3722,10249,11526,4529,10200,10564,10567,11012,11030,11489,3277,10609,10760,10831,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,4551,11088,11211,3873,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,4538,4549,10669,10769,11363,4158,4059,3746,4546,10222,10225,10570,10573,4547,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798])). % 165.36/165.12 cnf(11572,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x115721),x115721))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11575,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x115751),x115751))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11578,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x115781),x115781))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11581,plain, % 165.36/165.12 (P24(f332(f332(f334(x115811),f332(x115812,x115813)),f332(f311(x115814,x115811,x115812),f255(f875(x115814,a862)))))), % 165.36/165.12 inference(rename_variables,[],[3873])). % 165.36/165.12 cnf(11582,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x115821)),x115821))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(11585,plain, % 165.36/165.12 (P24(f332(f332(f334(x115851),f332(x115852,x115853)),f332(f311(x115854,x115851,x115852),f255(f875(x115854,a862)))))), % 165.36/165.12 inference(rename_variables,[],[3873])). % 165.36/165.12 cnf(11586,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),f332(f332(f81(a868),x115861),x115862)),x115862))), % 165.36/165.12 inference(rename_variables,[],[4546])). % 165.36/165.12 cnf(11591,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),f332(f332(f81(a868),x115911),x115912)),x115911))), % 165.36/165.12 inference(rename_variables,[],[4547])). % 165.36/165.12 cnf(11594,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x115941),x115941))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11597,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x115971),x115971))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(11603,plain, % 165.36/165.12 (~P39(x116031,x116032,f116(x116031))), % 165.36/165.12 inference(rename_variables,[],[4483])). % 165.36/165.12 cnf(11606,plain, % 165.36/165.12 (P24(f332(f332(f334(x116061),x116062),f255(f875(x116061,a862))))), % 165.36/165.12 inference(rename_variables,[],[3416])). % 165.36/165.12 cnf(11607,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x116071)),x116071))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(11610,plain, % 165.36/165.12 (~P24(f332(f63(x116101,x116102,f196(f875(x116101,a862))),x116103))), % 165.36/165.12 inference(rename_variables,[],[4544])). % 165.36/165.12 cnf(11623,plain, % 165.36/165.12 (~P24(f332(f332(f334(x116231),x116232),f196(f875(x116231,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11626,plain, % 165.36/165.12 (E(f332(f332(f16(x116261,x116262),x116263),x116264),x116263)), % 165.36/165.12 inference(rename_variables,[],[3246])). % 165.36/165.12 cnf(11629,plain, % 165.36/165.12 (E(f332(f332(f16(x116291,x116292),x116293),x116294),x116293)), % 165.36/165.12 inference(rename_variables,[],[3246])). % 165.36/165.12 cnf(11641,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),f2(a868)),f332(a115,x116411)))), % 165.36/165.12 inference(rename_variables,[],[3338])). % 165.36/165.12 cnf(11644,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x116441),x116441))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(11647,plain, % 165.36/165.12 (P24(f332(f332(f334(x116471),f332(x116472,x116473)),f332(f311(x116474,x116471,x116472),f255(f875(x116474,a862)))))), % 165.36/165.12 inference(rename_variables,[],[3873])). % 165.36/165.12 cnf(11650,plain, % 165.36/165.12 (P24(f332(f62(x116501),f332(f174(x116501),x116502)))), % 165.36/165.12 inference(rename_variables,[],[3297])). % 165.36/165.12 cnf(11653,plain, % 165.36/165.12 (P24(f332(f62(x116531),f332(f174(x116531),x116532)))), % 165.36/165.12 inference(rename_variables,[],[3297])). % 165.36/165.12 cnf(11656,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),f332(f80(a1),f332(f103(a1),x116561))),f332(f103(a1),x116562)))), % 165.36/165.12 inference(rename_variables,[],[3747])). % 165.36/165.12 cnf(11659,plain, % 165.36/165.12 (~P24(f332(f332(f334(x116591),x116592),f196(f875(x116591,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11673,plain, % 165.36/165.12 (~P24(f332(f332(f334(a868),f2(a868)),f332(f304(a868),x116731)))), % 165.36/165.12 inference(scs_inference,[],[3502,4482,4483,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,4462,10373,10464,3170,2847,2848,2851,2854,2855,2858,2859,2862,2867,2868,2875,2876,2881,2882,2889,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,3190,3725,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,11523,3239,3338,4520,10180,10183,10209,10684,10697,10816,11206,11298,4536,11408,11439,11474,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,3256,10329,10384,10594,10679,10803,3257,3334,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,3416,10545,10811,10855,11122,11203,11366,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,3319,10576,10606,10615,3358,3352,3786,3722,10249,11526,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,3277,10609,10760,10831,3747,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,4158,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133])). % 165.36/165.12 cnf(11675,plain, % 165.36/165.12 (~P24(f332(f332(f334(a868),x116751),f332(f253(a868),f2(a868))))), % 165.36/165.12 inference(scs_inference,[],[3502,4482,4483,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,4462,10373,10464,3170,2847,2848,2851,2854,2855,2858,2859,2862,2867,2868,2875,2876,2881,2882,2889,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,3190,3725,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,11523,3239,3338,4520,10180,10183,10209,10684,10697,10816,11206,11298,4536,11408,11439,11474,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,3256,10329,10384,10594,10679,10803,3257,3334,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,3416,10545,10811,10855,11122,11203,11366,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,3319,10576,10606,10615,3358,3352,3786,3722,10249,11526,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,3277,10609,10760,10831,3747,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,4158,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134])). % 165.36/165.12 cnf(11677,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),f45(a868,x116771,f196(a868))),x116771))), % 165.36/165.12 inference(scs_inference,[],[3502,4482,4483,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,4462,10373,10464,3170,2847,2848,2851,2854,2855,2858,2859,2862,2867,2868,2875,2876,2881,2882,2889,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,3190,3725,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,11523,3239,3338,4520,10180,10183,10209,10684,10697,10816,11206,11298,4536,11408,11439,11474,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,3256,10329,10384,10594,10679,10803,11381,3257,3334,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,3416,10545,10811,10855,11122,11203,11366,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,3319,10576,10606,10615,3358,3352,3786,3722,10249,11526,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,3277,10609,10760,10831,3747,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,4158,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173])). % 165.36/165.12 cnf(11678,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x116781),x116781))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(11681,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x116811),x116811))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(11690,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x116901),x116901))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(11693,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x116931),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(11698,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x116981),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(11705,plain, % 165.36/165.12 (P24(f332(f255(f875(x117051,a862)),x117052))), % 165.36/165.12 inference(rename_variables,[],[3319])). % 165.36/165.12 cnf(11710,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f2(a868)),x117101))), % 165.36/165.12 inference(rename_variables,[],[3277])). % 165.36/165.12 cnf(11711,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x117111)),x117111))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(11714,plain, % 165.36/165.12 (~P24(f332(f63(x117141,x117142,f196(f875(x117141,a862))),x117143))), % 165.36/165.12 inference(rename_variables,[],[4544])). % 165.36/165.12 cnf(11729,plain, % 165.36/165.12 (~P24(f332(f332(f247(a1),f332(f103(a1),f332(a115,x117291))),f332(f80(a1),f2(a1))))), % 165.36/165.12 inference(scs_inference,[],[3502,4482,4483,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,4462,10373,10464,3170,2847,2848,2851,2854,2855,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2908,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,3190,3725,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,11523,3239,3338,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,3256,10329,10384,10594,10679,10803,11381,11678,11681,3257,3334,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,3416,10545,10811,10855,11122,11203,11366,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,3319,10576,10606,10615,11151,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,3277,10609,10760,10831,11555,3747,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,4158,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427])). % 165.36/165.12 cnf(11733,plain, % 165.36/165.12 (P24(f332(f332(f247(a1),f332(f80(a1),f79(a1))),f2(a1)))), % 165.36/165.12 inference(scs_inference,[],[3502,4482,4483,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,4462,10373,10464,3170,2847,2848,2851,2854,2855,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2908,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,3190,3725,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,11523,3239,3338,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,3256,10329,10384,10594,10679,10803,11381,11678,11681,3257,3334,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,3416,10545,10811,10855,11122,11203,11366,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,3319,10576,10606,10615,11151,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,3277,10609,10760,10831,11555,3747,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,4158,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443])). % 165.36/165.12 cnf(11736,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x117361)),x117361))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(11739,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x117391)),x117391))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(11742,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x117421)),x117421))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(11745,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x117451)),x117451))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(11748,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x117481),x117481))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11751,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x117511),x117511))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11754,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x117541),x117541))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11757,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x117571),x117571))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11773,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f332(f332(f22(a868),x117731),f332(a115,x117731))),f2(a868)))), % 165.36/165.12 inference(scs_inference,[],[3502,4482,4483,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,4462,10373,10464,3170,2847,2848,2851,2854,2855,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2908,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,3190,3725,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,11523,3239,3338,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,3256,10329,10384,10594,10679,10803,11381,11678,11681,3257,3334,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,3416,10545,10811,10855,11122,11203,11366,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,3319,10576,10606,10615,11151,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,3277,10609,10760,10831,11555,3747,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,4158,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520])). % 165.36/165.12 cnf(11774,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x117741),x117741))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(11779,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x117791),f332(f76(a1),x117791)))), % 165.36/165.12 inference(scs_inference,[],[3502,4482,4483,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,4462,10373,10464,3471,3170,2847,2848,2851,2854,2855,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2908,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,3190,3725,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,3717,11523,3239,3338,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,4017,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,3257,3334,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,3416,10545,10811,10855,11122,11203,11366,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,3319,10576,10606,10615,11151,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,3277,10609,10760,10831,11555,3747,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,4158,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539])). % 165.36/165.12 cnf(11780,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x117801),x117801))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(11791,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x117911),x117911))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(11794,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(f874(f869(x117941),f869(x117941)),a862)),f159(x117941,x117942)),f308(f869(x117941),f158(x117941,x117942))))), % 165.36/165.12 inference(rename_variables,[],[3975])). % 165.36/165.12 cnf(11801,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x118011),f332(a115,x118011)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(11804,plain, % 165.36/165.12 (P24(f332(f332(f334(f875(x118041,a862)),x118042),f332(f309(x118041),x118042)))), % 165.36/165.12 inference(rename_variables,[],[3628])). % 165.36/165.12 cnf(11805,plain, % 165.36/165.12 (~E(f332(a115,x118051),x118051)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11810,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x118101),x118101))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(11815,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x118151),x118151))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(11826,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x118261,a862)),x118262),f332(f332(f310(x118261),x118263),x118262)))), % 165.36/165.12 inference(rename_variables,[],[3711])). % 165.36/165.12 cnf(11829,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x118291),x118291))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(11830,plain, % 165.36/165.12 (~E(f332(a115,x118301),x118301)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11841,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x118411),x118411))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11842,plain, % 165.36/165.12 (~E(f332(a115,x118421),x118421)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11845,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x118451),x118451))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(11848,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x118481),x118481))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(11851,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x118511),x118511))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(11854,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x118541),x118541))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(11856,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),f332(a107,f2(a1))),f332(a115,x118561)))), % 165.36/165.12 inference(scs_inference,[],[3502,4482,4483,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,4462,10373,10464,3471,3170,2847,2848,2851,2854,2855,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2908,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,3190,3725,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,3717,11523,3239,3338,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,4017,3975,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,3257,3334,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,3416,10545,10811,10855,11122,11203,11366,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,3319,10576,10606,10615,11151,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,3277,10609,10760,10831,11555,3747,4098,4527,3794,4506,4509,3230,3234,4508,4507,4511,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,10892,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,4158,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782])). % 165.36/165.12 cnf(11857,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x118571),x118571))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(11860,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x118601),x118601))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11863,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x118631),x118631))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11864,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x118641),f332(a115,x118641)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(11871,plain, % 165.36/165.12 (~E(f332(a115,x118711),x118711)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11876,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x118761),x118761))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11877,plain, % 165.36/165.12 (~E(f332(a115,x118771),x118771)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11880,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x118801),x118801))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(11897,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x118971),x118971))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(11902,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f2(a868)),x119021))), % 165.36/165.12 inference(rename_variables,[],[3277])). % 165.36/165.12 cnf(11919,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x119191),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(11922,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x119221),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(11925,plain, % 165.36/165.12 (~P24(f332(f332(f334(x119251),x119252),f196(f875(x119251,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11928,plain, % 165.36/165.12 (~P24(f332(f332(f334(x119281),x119282),f196(f875(x119281,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11930,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x119301),f332(f332(f104(a868),x119302),x119301)))), % 165.36/165.12 inference(scs_inference,[],[3502,4482,4483,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,4462,10373,10464,3471,3170,2847,2848,2851,2854,2855,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2908,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,3190,3198,3725,3967,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,3717,11523,3239,3338,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,4017,3975,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,3416,10545,10811,10855,11122,11203,11366,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,3319,10576,10606,10615,11151,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,3277,10609,10760,10831,11555,11710,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,10892,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,4158,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018])). % 165.36/165.12 cnf(11931,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x119311),x119311))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11933,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x119331),f332(f332(f104(a868),x119331),x119332)))), % 165.36/165.12 inference(scs_inference,[],[3502,4482,4483,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,4462,10373,10464,3471,3170,2847,2848,2851,2854,2855,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2908,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,3190,3198,3725,3967,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,3717,11523,3239,3338,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,4017,3975,3919,10752,3970,3628,4006,3646,10929,10995,11076,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,3416,10545,10811,10855,11122,11203,11366,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,3319,10576,10606,10615,11151,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,3277,10609,10760,10831,11555,11710,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,10892,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,4158,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019])). % 165.36/165.12 cnf(11934,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x119341),x119341))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11937,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x119371),x119371))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11940,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x119401),x119401))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(11943,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x119431),f332(a115,x119431)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(11950,plain, % 165.36/165.12 (P24(f332(f332(f334(f875(x119501,a862)),x119502),f332(f309(x119501),x119502)))), % 165.36/165.12 inference(rename_variables,[],[3628])). % 165.36/165.12 cnf(11955,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x119551,a862)),x119552),f332(f332(f310(x119551),x119553),x119552)))), % 165.36/165.12 inference(rename_variables,[],[3711])). % 165.36/165.12 cnf(11962,plain, % 165.36/165.12 (~P24(f332(f332(f334(x119621),x119622),f196(f875(x119621,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(11971,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x119711,a862)),x119712),f255(f875(x119711,a862))))), % 165.36/165.12 inference(rename_variables,[],[3646])). % 165.36/165.12 cnf(11972,plain, % 165.36/165.12 (~E(f332(a115,x119721),x119721)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(11975,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x119751,a862)),f332(f311(x119752,x119751,x119753),f332(f312(x119752,x119751,x119753),x119754))),x119754))), % 165.36/165.12 inference(rename_variables,[],[4158])). % 165.36/165.12 cnf(11978,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x119781,a862)),f332(f174(x119781),f332(f137(x119781,x119782),x119783))),f332(f174(x119781),x119783)))), % 165.36/165.12 inference(rename_variables,[],[3919])). % 165.36/165.12 cnf(11984,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x119841),f332(a115,x119841)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(11992,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(x119921,x119921)),x119922),f154(x119921,f116(f875(x119921,a868)))))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,4482,4483,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,4462,10373,10464,3471,3170,2847,2848,2850,2851,2854,2855,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2908,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,3190,3198,3725,3967,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,3717,11523,3239,3338,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,4017,3975,3919,10752,3970,3628,11804,4006,3646,10929,10995,11076,11133,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,3416,10545,10811,10855,11122,11203,11366,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,3319,10576,10606,10615,11151,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,3277,10609,10760,10831,11555,11710,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,10892,11826,3562,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,4158,10745,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235])). % 165.36/165.12 cnf(11993,plain, % 165.36/165.12 (E(f332(f263(x119931,x119931),f264(x119931,x119932)),x119932)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12004,plain, % 165.36/165.12 (~P24(f332(f332(f246(a868),f332(a115,x120041)),x120041))), % 165.36/165.12 inference(rename_variables,[],[4529])). % 165.36/165.12 cnf(12005,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x120051),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(12008,plain, % 165.36/165.12 (P24(f332(f62(x120081),f196(f875(x120081,a862))))), % 165.36/165.12 inference(rename_variables,[],[3334])). % 165.36/165.12 cnf(12009,plain, % 165.36/165.12 (~P24(f332(f332(f334(x120091),x120092),f196(f875(x120091,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12014,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x120141),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(12015,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x120151),x120151))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(12020,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x120201,a862)),f332(f174(x120201),f172(x120201,x120202,x120203))),f332(f174(x120201),x120203)))), % 165.36/165.12 inference(rename_variables,[],[3970])). % 165.36/165.12 cnf(12023,plain, % 165.36/165.12 (P21(x120231,x120231,f5(x120231),x120232)), % 165.36/165.12 inference(rename_variables,[],[3502])). % 165.36/165.12 cnf(12028,plain, % 165.36/165.12 (P24(f332(f332(f334(f875(x120281,a862)),x120282),f332(f309(x120281),x120282)))), % 165.36/165.12 inference(rename_variables,[],[3628])). % 165.36/165.12 cnf(12035,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x120351),x120351))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12038,plain, % 165.36/165.12 (~P24(f332(f332(f334(x120381),x120382),f196(f875(x120381,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12041,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x120411,a862)),x120412),f332(f332(f310(x120411),x120413),x120412)))), % 165.36/165.12 inference(rename_variables,[],[3711])). % 165.36/165.12 cnf(12042,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x120421,a862)),x120422),f255(f875(x120421,a862))))), % 165.36/165.12 inference(rename_variables,[],[3646])). % 165.36/165.12 cnf(12049,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x120491),x120491))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12052,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x120521),x120521))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12055,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x120551),x120551))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12058,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x120581),x120581))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12061,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x120611),f332(a115,x120611)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(12064,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x120641),f332(a115,x120641)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(12067,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x120671,a862)),x120672),x120672))), % 165.36/165.12 inference(rename_variables,[],[3562])). % 165.36/165.12 cnf(12069,plain, % 165.36/165.12 (~P24(f332(f332(f246(a1),f332(f332(f22(a1),a84),a100)),f2(a1)))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,4482,4483,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,4462,10373,10464,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2908,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,3190,3198,3725,3967,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,3717,11523,3239,3338,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,11653,4017,3975,3919,10752,3970,10932,3628,11804,11950,4006,3646,10929,10995,11076,11133,11971,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,3416,10545,10811,10855,11122,11203,11366,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,3319,10576,10606,10615,11151,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,3277,10609,10760,10831,11555,11710,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,10892,11826,11955,3562,11091,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,4158,10745,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624])). % 165.36/165.12 cnf(12074,plain, % 165.36/165.12 (P24(f332(f332(f334(f875(x120741,a862)),x120742),f332(f309(x120741),x120742)))), % 165.36/165.12 inference(rename_variables,[],[3628])). % 165.36/165.12 cnf(12080,plain, % 165.36/165.12 (~P24(f332(f332(f247(a1),f332(f332(f81(a1),a84),a84)),f2(a1)))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,4482,4483,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,4462,10373,10464,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2908,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,3190,3198,3725,3967,3084,3465,3819,11305,3149,3114,3109,3092,3093,3737,3315,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,3717,11523,3239,3338,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,11653,4017,3975,3919,10752,3970,10932,3628,11804,11950,12028,4006,3646,10929,10995,11076,11133,11971,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,3416,10545,10811,10855,11122,11203,11366,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,3319,10576,10606,10615,11151,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,3277,10609,10760,10831,11555,11710,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,10892,11826,11955,3562,11091,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,4158,10745,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661])). % 165.36/165.12 cnf(12083,plain, % 165.36/165.12 (~E(f332(a115,x120831),x120831)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(12084,plain, % 165.36/165.12 (E(f332(f311(x120841,x120841,f5(x120841)),x120842),x120842)), % 165.36/165.12 inference(rename_variables,[],[3315])). % 165.36/165.12 cnf(12087,plain, % 165.36/165.12 (P36(x120871,x120872,f116(x120871),f116(x120871))), % 165.36/165.12 inference(rename_variables,[],[3511])). % 165.36/165.12 cnf(12090,plain, % 165.36/165.12 (~E(f332(a115,x120901),x120901)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(12093,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x120931,a862)),f332(f174(x120931),f172(x120931,x120932,x120933))),f332(f174(x120931),x120933)))), % 165.36/165.12 inference(rename_variables,[],[3970])). % 165.36/165.12 cnf(12094,plain, % 165.36/165.12 (P24(f332(f62(x120941),f332(f174(x120941),x120942)))), % 165.36/165.12 inference(rename_variables,[],[3297])). % 165.36/165.12 cnf(12105,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x121051),x121051))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(12108,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x121081),x121081))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(12113,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f2(a868)),x121131))), % 165.36/165.12 inference(rename_variables,[],[3277])). % 165.36/165.12 cnf(12120,plain, % 165.36/165.12 (P32(a868,f332(f170(a868),f332(f332(f155(f869(x121201),a868),f197(f869(x121201))),f182(x121201,x121202))))), % 165.36/165.12 inference(rename_variables,[],[3829])). % 165.36/165.12 cnf(12123,plain, % 165.36/165.12 (P21(x121231,x121231,f5(x121231),x121232)), % 165.36/165.12 inference(rename_variables,[],[3502])). % 165.36/165.12 cnf(12126,plain, % 165.36/165.12 (P24(f332(f332(f334(f869(x121261)),f116(x121261)),f162(x121261,x121262)))), % 165.36/165.12 inference(rename_variables,[],[3462])). % 165.36/165.12 cnf(12129,plain, % 165.36/165.12 (~P24(f332(f332(f196(f875(x121291,f875(x121292,a862))),x121293),x121294))), % 165.36/165.12 inference(rename_variables,[],[4549])). % 165.36/165.12 cnf(12134,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x121341),x121341))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12135,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f2(a868)),x121351))), % 165.36/165.12 inference(rename_variables,[],[3277])). % 165.36/165.12 cnf(12137,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),f2(a1)),f419(x121371,f196(f875(x121372,f875(x121373,a862))),f79(a1))))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,12023,3511,4482,4483,4465,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,4462,10373,10464,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2908,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,3190,3198,3725,3967,3084,3465,3819,11305,3149,3114,3109,3092,3093,3098,3737,3129,3315,10755,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,3627,4338,4339,4470,3566,3782,3829,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,3717,11523,3239,3338,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,11653,4017,3975,3919,10752,3970,10932,12020,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,3416,10545,10811,10855,11122,11203,11366,11606,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,3319,10576,10606,10615,11151,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,10892,11826,11955,3562,11091,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,11394,12129,4158,10745,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938])). % 165.36/165.12 cnf(12138,plain, % 165.36/165.12 (~P24(f332(f332(f196(f875(x121381,f875(x121382,a862))),x121383),x121384))), % 165.36/165.12 inference(rename_variables,[],[4549])). % 165.36/165.12 cnf(12141,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(f874(f869(x121411),f869(x121411)),a862)),f159(x121411,x121412)),f308(f869(x121411),f158(x121411,x121412))))), % 165.36/165.12 inference(rename_variables,[],[3975])). % 165.36/165.12 cnf(12147,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x121471,a862)),f332(f174(x121471),f172(x121471,x121472,x121473))),f332(f174(x121471),x121473)))), % 165.36/165.12 inference(rename_variables,[],[3970])). % 165.36/165.12 cnf(12148,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x121481,a862)),f332(f174(x121481),f332(f137(x121481,x121482),x121483))),f332(f174(x121481),x121483)))), % 165.36/165.12 inference(rename_variables,[],[3919])). % 165.36/165.12 cnf(12151,plain, % 165.36/165.12 (~P24(f332(f332(f247(f875(x121511,a862)),x121512),f196(f875(x121511,a862))))), % 165.36/165.12 inference(rename_variables,[],[4542])). % 165.36/165.12 cnf(12154,plain, % 165.36/165.12 (P21(x121541,f872(x121541),f208(x121541),x121542)), % 165.36/165.12 inference(rename_variables,[],[3512])). % 165.36/165.12 cnf(12159,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x121591,a862)),f332(f311(x121592,x121591,x121593),f332(f312(x121592,x121591,x121593),x121594))),x121594))), % 165.36/165.12 inference(rename_variables,[],[4158])). % 165.36/165.12 cnf(12162,plain, % 165.36/165.12 (P24(f332(f62(f872(x121621)),f332(f311(x121622,f872(x121621),f332(f180(x121622,x121621),x121623)),f255(f875(x121622,a862)))))), % 165.36/165.12 inference(rename_variables,[],[3983])). % 165.36/165.12 cnf(12167,plain, % 165.36/165.12 (P24(f332(f332(f334(f869(x121671)),f116(x121671)),f162(x121671,x121672)))), % 165.36/165.12 inference(rename_variables,[],[3462])). % 165.36/165.12 cnf(12170,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x121701),f869(x121701))),f332(f332(f267(f869(x121701),f869(x121701)),x121702),f116(x121701))),f148(x121701,x121703)))), % 165.36/165.12 inference(rename_variables,[],[4553])). % 165.36/165.12 cnf(12173,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x121731),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(12175,plain, % 165.36/165.12 (~P24(f332(f62(x121751),f255(f875(x121751,a862))))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,12023,3511,3512,3224,4482,4483,3123,4465,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,4462,10373,10464,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2908,2911,2917,2918,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,3190,3198,3725,3967,3084,3465,3819,11305,3149,3114,3109,3092,3093,3098,3737,3129,3315,10755,3183,3362,4541,3906,4472,10203,10370,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,3908,10926,11052,11100,4553,10858,10959,11057,11159,11184,11222,11228,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,3627,4338,4339,4470,3566,3782,3829,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,3717,11523,3239,3338,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3454,4537,4048,11179,3587,3297,11650,11653,4017,3975,11794,12141,3919,10752,11978,3970,10932,12020,12093,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,3416,10545,10811,10855,11122,11203,11366,11606,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,3319,10576,10606,10615,11151,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,3983,3873,11244,11581,11585,3711,10871,10877,10892,11826,11955,3562,11091,12067,3713,10612,10948,11097,11127,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,11394,12129,4158,10745,11975,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,98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% 165.36/165.12 cnf(12176,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x121761,a862)),x121762),x121762))), % 165.36/165.12 inference(rename_variables,[],[3562])). % 165.36/165.12 cnf(12179,plain, % 165.36/165.12 (~P24(f332(f332(f334(x121791),x121792),f196(f875(x121791,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12182,plain, % 165.36/165.12 (~P24(f332(f332(f196(f875(x121821,f875(x121822,a862))),x121823),x121824))), % 165.36/165.12 inference(rename_variables,[],[4549])). % 165.36/165.12 cnf(12185,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x121851,a862)),f332(f311(x121852,x121851,x121853),f332(f312(x121852,x121851,x121853),x121854))),x121854))), % 165.36/165.12 inference(rename_variables,[],[4158])). % 165.36/165.12 cnf(12186,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x121861,a862)),x121862),x121862))), % 165.36/165.12 inference(rename_variables,[],[3562])). % 165.36/165.12 cnf(12191,plain, % 165.36/165.12 (E(f332(f263(x121911,x121911),f264(x121911,x121912)),x121912)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12194,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x121941,a862)),f332(f174(x121941),f172(x121941,x121942,x121943))),f332(f174(x121941),x121943)))), % 165.36/165.12 inference(rename_variables,[],[3970])). % 165.36/165.12 cnf(12195,plain, % 165.36/165.12 (P24(f332(f62(x121951),f332(f174(x121951),x121952)))), % 165.36/165.12 inference(rename_variables,[],[3297])). % 165.36/165.12 cnf(12198,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x121981),x121981))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12201,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x122011),x122011))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(12204,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x122041),x122041))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(12215,plain, % 165.36/165.12 (P21(x122151,x122151,f5(x122151),x122152)), % 165.36/165.12 inference(rename_variables,[],[3502])). % 165.36/165.12 cnf(12220,plain, % 165.36/165.12 (~P24(f332(f332(f334(x122201),x122202),f196(f875(x122201,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12223,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(x122231,x122231)),f332(f332(f267(x122231,x122231),x122232),x122232)),f308(x122231,x122233)))), % 165.36/165.12 inference(rename_variables,[],[3908])). % 165.36/165.12 cnf(12226,plain, % 165.36/165.12 (~P24(f332(f332(f334(x122261),x122262),f196(f875(x122261,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12229,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(x122291,x122291)),f332(f332(f267(x122291,x122291),x122292),x122292)),f308(x122291,x122293)))), % 165.36/165.12 inference(rename_variables,[],[3908])). % 165.36/165.12 cnf(12239,plain, % 165.36/165.12 (~E(f332(f332(f152(x122391),x122392),x122393),x122393)), % 165.36/165.12 inference(rename_variables,[],[4472])). % 165.36/165.12 cnf(12242,plain, % 165.36/165.12 (P24(f332(f332(f334(x122421),x122422),f255(f875(x122421,a862))))), % 165.36/165.12 inference(rename_variables,[],[3416])). % 165.36/165.12 cnf(12243,plain, % 165.36/165.12 (~E(f332(a115,x122431),x122431)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(12246,plain, % 165.36/165.12 (P24(f332(f332(f334(f869(x122461)),f116(x122461)),f162(x122461,x122462)))), % 165.36/165.12 inference(rename_variables,[],[3462])). % 165.36/165.12 cnf(12247,plain, % 165.36/165.12 (~E(f332(f332(f152(x122471),x122472),x122473),f116(x122471))), % 165.36/165.12 inference(rename_variables,[],[4481])). % 165.36/165.12 cnf(12250,plain, % 165.36/165.12 (P24(f332(f332(f334(x122501),f332(x122502,x122503)),f332(f311(x122504,x122501,x122502),f255(f875(x122504,a862)))))), % 165.36/165.12 inference(rename_variables,[],[3873])). % 165.36/165.12 cnf(12251,plain, % 165.36/165.12 (P21(x122511,x122511,f5(x122511),x122512)), % 165.36/165.12 inference(rename_variables,[],[3502])). % 165.36/165.12 cnf(12254,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x122541,a862)),f196(f875(x122541,a862))),x122542))), % 165.36/165.12 inference(rename_variables,[],[3713])). % 165.36/165.12 cnf(12255,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x122551,a862)),x122552),x122552))), % 165.36/165.12 inference(rename_variables,[],[3562])). % 165.36/165.12 cnf(12258,plain, % 165.36/165.12 (P24(f332(f332(f334(x122581),f332(x122582,x122583)),f332(f311(x122584,x122581,x122582),f255(f875(x122584,a862)))))), % 165.36/165.12 inference(rename_variables,[],[3873])). % 165.36/165.12 cnf(12259,plain, % 165.36/165.12 (P21(x122591,x122591,f5(x122591),x122592)), % 165.36/165.12 inference(rename_variables,[],[3502])). % 165.36/165.12 cnf(12262,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(f869(x122621),f869(x122621))),f332(f332(f267(f869(x122621),f869(x122621)),f116(x122621)),f116(x122621))),f159(x122621,x122622)))), % 165.36/165.12 inference(rename_variables,[],[4054])). % 165.36/165.12 cnf(12265,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x122651),x122651))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(12266,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x122661),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(12272,plain, % 165.36/165.12 (E(f332(f332(f135(x122721),x122722),f116(x122721)),x122722)), % 165.36/165.12 inference(rename_variables,[],[3184])). % 165.36/165.12 cnf(12273,plain, % 165.36/165.12 (~E(f332(f332(f152(x122731),x122732),x122733),x122733)), % 165.36/165.12 inference(rename_variables,[],[4472])). % 165.36/165.12 cnf(12276,plain, % 165.36/165.12 (E(f332(f332(f135(x122761),x122762),f116(x122761)),x122762)), % 165.36/165.12 inference(rename_variables,[],[3184])). % 165.36/165.12 cnf(12277,plain, % 165.36/165.12 (~E(f332(f332(f152(x122771),x122772),x122773),x122773)), % 165.36/165.12 inference(rename_variables,[],[4472])). % 165.36/165.12 cnf(12280,plain, % 165.36/165.12 (E(f332(f332(f135(x122801),x122802),f116(x122801)),x122802)), % 165.36/165.12 inference(rename_variables,[],[3184])). % 165.36/165.12 cnf(12289,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x122891,a862)),x122892),f255(f875(x122891,a862))))), % 165.36/165.12 inference(rename_variables,[],[3646])). % 165.36/165.12 cnf(12293,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x122931),x122931))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(12294,plain, % 165.36/165.12 (~E(f332(a115,x122941),x122941)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(12297,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x122971,a862)),f196(f875(x122971,a862))),x122972))), % 165.36/165.12 inference(rename_variables,[],[3713])). % 165.36/165.12 cnf(12300,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x123001),x123001))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12303,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x123031,a862)),x123032),x123032))), % 165.36/165.12 inference(rename_variables,[],[3562])). % 165.36/165.12 cnf(12308,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x123081,a862)),x123082),f332(f332(f310(x123081),x123083),x123082)))), % 165.36/165.12 inference(rename_variables,[],[3711])). % 165.36/165.12 cnf(12311,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x123111,a862)),x123112),x123112))), % 165.36/165.12 inference(rename_variables,[],[3562])). % 165.36/165.12 cnf(12312,plain, % 165.36/165.12 (~P24(f332(f332(f334(x123121),x123122),f196(f875(x123121,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12315,plain, % 165.36/165.12 (~P24(f332(f332(f334(x123151),x123152),f196(f875(x123151,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12323,plain, % 165.36/165.12 (~P24(f332(f332(f246(f875(f874(x123231,x123231),a862)),f332(f311(f874(x123231,x123231),f874(x123231,x123231),f5(f874(x123231,x123231))),f255(f875(f874(x123231,x123231),a862)))),f332(f311(f874(x123231,x123231),f874(x123231,x123231),f5(f874(x123231,x123231))),f196(f875(f874(x123231,x123231),a862)))))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,3511,3512,3224,4482,4483,3123,4465,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,4462,10373,10464,3314,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2908,2911,2917,2918,2925,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,3184,12272,12276,3190,3198,3725,3967,3084,4459,3465,3819,11305,3149,3114,3109,3092,3093,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,12262,3908,10926,11052,11100,12223,12229,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3782,3829,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,3717,11523,3239,3338,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3655,3454,4537,4048,11179,3587,3297,11650,11653,12094,4017,3975,11794,12141,3919,10752,11978,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,3416,10545,10811,10855,11122,11203,11366,11606,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,3319,10576,10606,10615,11151,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,3873,11244,11581,11585,11647,12250,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,11394,12129,12138,4158,10745,11975,12159,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,887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% 165.36/165.12 cnf(12324,plain, % 165.36/165.12 (P21(x123241,x123241,f5(x123241),x123242)), % 165.36/165.12 inference(rename_variables,[],[3502])). % 165.36/165.12 cnf(12327,plain, % 165.36/165.12 (E(f332(f197(f869(x123271)),f171(x123271,x123272,x123273)),x123272)), % 165.36/165.12 inference(rename_variables,[],[3325])). % 165.36/165.12 cnf(12330,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x123301),x123301))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(12331,plain, % 165.36/165.12 (P24(f332(f255(f875(x123311,a862)),x123312))), % 165.36/165.12 inference(rename_variables,[],[3319])). % 165.36/165.12 cnf(12334,plain, % 165.36/165.12 (~P24(f332(f332(f334(x123341),x123342),f196(f875(x123341,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12337,plain, % 165.36/165.12 (P24(f332(f332(f334(x123371),f332(x123372,x123373)),f332(f311(x123374,x123371,x123372),f255(f875(x123374,a862)))))), % 165.36/165.12 inference(rename_variables,[],[3873])). % 165.36/165.12 cnf(12338,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(x123381,x123381)),f332(f332(f267(x123381,x123381),x123382),x123382)),f308(x123381,x123383)))), % 165.36/165.12 inference(rename_variables,[],[3908])). % 165.36/165.12 cnf(12341,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(x123411,x123411)),f332(f332(f267(x123411,x123411),x123412),x123412)),f308(x123411,x123413)))), % 165.36/165.12 inference(rename_variables,[],[3908])). % 165.36/165.12 cnf(12344,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x123441),x123441))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12345,plain, % 165.36/165.12 (P24(f332(f255(f875(x123451,a862)),x123452))), % 165.36/165.12 inference(rename_variables,[],[3319])). % 165.36/165.12 cnf(12348,plain, % 165.36/165.12 (P24(f332(f62(x123481),f332(f174(x123481),x123482)))), % 165.36/165.12 inference(rename_variables,[],[3297])). % 165.36/165.12 cnf(12353,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(f869(x123531),f869(x123531))),f332(f332(f267(f869(x123531),f869(x123531)),f116(x123531)),f116(x123531))),f332(f332(f289(f869(x123531),f869(x123531),f869(x123531)),f159(x123531,x123532)),f159(x123531,x123532))))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,3511,3512,3224,4482,4483,3123,4465,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,4462,10373,10464,3314,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2908,2911,2917,2918,2925,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,3184,12272,12276,12280,3190,3198,3725,3325,3967,3084,4459,3465,3819,11305,3149,3114,3109,3092,3093,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,12262,3908,10926,11052,11100,12223,12229,12338,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3782,3829,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,3717,11523,3239,3338,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3655,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,4017,3975,11794,12141,3919,10752,11978,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,3416,10545,10811,10855,11122,11203,11366,11606,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,3319,10576,10606,10615,11151,11705,12331,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,3873,11244,11581,11585,11647,12250,12258,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,11394,12129,12138,4158,10745,11975,12159,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367])). % 165.36/165.12 cnf(12355,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(x123551,x123551)),f332(f332(f267(x123551,x123551),x123552),x123552)),f332(f332(f289(x123551,x123551,x123551),f308(x123551,x123553)),f308(x123551,f308(x123551,x123553)))))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,3511,3512,3224,4482,4483,3123,4465,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,4462,10373,10464,3314,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2908,2911,2917,2918,2925,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,3184,12272,12276,12280,3190,3198,3725,3325,3967,3084,4459,3465,3819,11305,3149,3114,3109,3092,3093,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,12262,3908,10926,11052,11100,12223,12229,12338,12341,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3782,3829,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,3717,11523,3239,3338,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3655,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,4017,3975,11794,12141,3919,10752,11978,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,3416,10545,10811,10855,11122,11203,11366,11606,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,3319,10576,10606,10615,11151,11705,12331,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,3873,11244,11581,11585,11647,12250,12258,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,11394,12129,12138,4158,10745,11975,12159,4059,3746,3690,4546,10222,10225,10570,10573,11405,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374])). % 165.36/165.12 cnf(12358,plain, % 165.36/165.12 (~P24(f332(f332(f196(f875(x123581,f875(x123582,a862))),x123583),x123584))), % 165.36/165.12 inference(rename_variables,[],[4549])). % 165.36/165.12 cnf(12361,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x123611,a862)),x123612),f255(f875(x123611,a862))))), % 165.36/165.12 inference(rename_variables,[],[3646])). % 165.36/165.12 cnf(12364,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(x123641,x123641)),f332(f332(f267(x123641,x123641),x123642),x123642)),f308(x123641,x123643)))), % 165.36/165.12 inference(rename_variables,[],[3908])). % 165.36/165.12 cnf(12367,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),f332(f332(f81(a868),x123671),x123672)),x123672))), % 165.36/165.12 inference(rename_variables,[],[4546])). % 165.36/165.12 cnf(12368,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x123681),f332(a115,x123681)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(12371,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x123711,a862)),f332(f174(x123711),f332(f137(x123711,x123712),x123713))),f332(f174(x123711),x123713)))), % 165.36/165.12 inference(rename_variables,[],[3919])). % 165.36/165.12 cnf(12374,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x123741,a862)),x123742),f255(f875(x123741,a862))))), % 165.36/165.12 inference(rename_variables,[],[3646])). % 165.36/165.12 cnf(12377,plain, % 165.36/165.12 (E(f332(f263(x123771,x123771),f264(x123771,x123772)),x123772)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12384,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(f874(f869(x123841),f869(x123841)),f874(f869(x123841),f869(x123841)))),f549(f308(f874(f869(x123841),f869(x123841)),x123842),f148(x123841,x123843),f874(f869(x123841),f869(x123841)))),f308(f874(f869(x123841),f869(x123841)),x123842)))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,3511,3512,3224,4482,4483,3123,4465,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,4462,10373,10464,3314,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2908,2911,2917,2918,2925,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3601,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,3184,12272,12276,12280,3190,3198,3725,3325,3967,3084,4459,3465,3819,11305,3149,3114,3109,3092,3093,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,12262,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3782,3829,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,3717,11523,3239,3338,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3655,4192,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,4017,3975,11794,12141,3919,10752,11978,12148,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,3416,10545,10811,10855,11122,11203,11366,11606,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,3319,10576,10606,10615,11151,11705,12331,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,3873,11244,11581,11585,11647,12250,12258,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,4052,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,11394,12129,12138,12182,4158,10745,11975,12159,4059,3746,3690,4546,10222,10225,10570,10573,11405,11586,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442])). % 165.36/165.12 cnf(12388,plain, % 165.36/165.12 (~P24(f332(f332(f334(x123881),x123882),f196(f875(x123881,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12389,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(f869(x123891),f869(x123891))),f332(f332(f267(f869(x123891),f869(x123891)),f116(x123891)),f116(x123891))),f159(x123891,x123892)))), % 165.36/165.12 inference(rename_variables,[],[4054])). % 165.36/165.12 cnf(12391,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(a868,a868)),f332(f332(f267(a868,a868),f332(a115,x123911)),f332(a115,f332(a115,x123911)))),f332(f332(f289(a868,a868,a868),f308(a868,a322)),f308(a868,f308(a868,a322)))))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,3511,3512,3224,4482,4483,3123,4465,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,4462,10373,10464,3314,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2908,2911,2917,2918,2925,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3601,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,3184,12272,12276,12280,3190,3198,3725,3325,3967,3084,4459,3465,3819,11305,3149,3114,3109,3092,3093,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,12262,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3782,3829,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,3717,11523,3239,3338,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3655,4192,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,4017,3975,11794,12141,3919,10752,11978,12148,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,3416,10545,10811,10855,11122,11203,11366,11606,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,3319,10576,10606,10615,11151,11705,12331,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,3873,11244,11581,11585,11647,12250,12258,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,4052,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,11394,12129,12138,12182,4158,10745,11975,12159,4059,3746,3690,4546,10222,10225,10570,10573,11405,11586,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470])). % 165.36/165.12 cnf(12394,plain, % 165.36/165.12 (~P24(f332(f332(f334(x123941),x123942),f196(f875(x123941,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12397,plain, % 165.36/165.12 (P35(x123971,x123972,f116(x123971))), % 165.36/165.12 inference(rename_variables,[],[3189])). % 165.36/165.12 cnf(12400,plain, % 165.36/165.12 (E(f332(f197(f869(x124001)),f171(x124001,x124002,x124003)),x124002)), % 165.36/165.12 inference(rename_variables,[],[3325])). % 165.36/165.12 cnf(12403,plain, % 165.36/165.12 (~P24(f332(f332(f334(x124031),x124032),f196(f875(x124031,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12407,plain, % 165.36/165.12 (~P24(f332(f332(f334(f874(f869(x124071),f869(x124071))),f332(f332(f267(f869(x124071),f869(x124071)),x124072),x124072)),f148(x124071,f154(x124071,f116(f875(x124071,a868))))))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,3511,3512,3224,3189,4482,4483,3123,4465,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,4462,10373,10464,3314,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2908,2911,2917,2918,2925,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3601,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,3184,12272,12276,12280,3190,3198,3725,3325,12327,3967,3084,4459,3465,3819,11305,3149,3114,3109,3092,3093,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3782,3829,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,3717,11523,3239,3338,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3655,4192,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,4017,3975,11794,12141,3919,10752,11978,12148,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,3416,10545,10811,10855,11122,11203,11366,11606,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,3319,10576,10606,10615,11151,11705,12331,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,3873,11244,11581,11585,11647,12250,12258,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,4052,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,11394,12129,12138,12182,4158,10745,11975,12159,4059,3746,3690,4546,10222,10225,10570,10573,11405,11586,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842])). % 165.36/165.12 cnf(12409,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x124091),x124091))), % 165.36/165.12 inference(rename_variables,[],[4516])). % 165.36/165.12 cnf(12411,plain, % 165.36/165.12 (P24(f332(f332(f334(f874(f869(x124111),f869(x124111))),f332(f332(f267(f869(x124111),f869(x124111)),f171(x124111,f332(f197(f869(x124111)),x124112),x124113)),x124112)),f159(x124111,f255(f875(f874(x124111,x124111),a862)))))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,3511,3512,3224,3189,4482,4483,3123,4465,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,4462,10373,10464,3314,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2908,2911,2917,2918,2925,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,3041,4443,3601,3834,11537,3094,11255,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3084,4459,3465,3819,11305,3149,3114,3109,3092,3093,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,4530,10920,10990,11214,11217,3363,3144,3145,10272,10579,3421,3063,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3782,3829,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,3717,11523,3239,3338,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3655,4192,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,4017,3975,11794,12141,3919,10752,11978,12148,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,3416,10545,10811,10855,11122,11203,11366,11606,12242,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,3319,10576,10606,10615,11151,11705,12331,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,3873,11244,11581,11585,11647,12250,12258,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,4052,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,11394,12129,12138,12182,4158,10745,11975,12159,4059,3746,3690,4546,10222,10225,10570,10573,11405,11586,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,85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% 165.36/165.12 cnf(12412,plain, % 165.36/165.12 (P24(f332(f332(f334(x124121),x124122),f255(f875(x124121,a862))))), % 165.36/165.12 inference(rename_variables,[],[3416])). % 165.36/165.12 cnf(12420,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x124201,a862)),x124202),x124202))), % 165.36/165.12 inference(rename_variables,[],[3562])). % 165.36/165.12 cnf(12423,plain, % 165.36/165.12 (~P24(f332(f332(f334(x124231),x124232),f196(f875(x124231,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12426,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),f2(a1)),f332(f332(f257(a1),f332(f76(a1),x124261)),x124262)))), % 165.36/165.12 inference(rename_variables,[],[3746])). % 165.36/165.12 cnf(12429,plain, % 165.36/165.12 (~E(f332(a115,x124291),x124291)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(12431,plain, % 165.36/165.12 (E(f332(f263(x124311,x124311),f264(x124311,x124312)),x124312)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12433,plain, % 165.36/165.12 (P41(x124331,f154(x124331,x124332))), % 165.36/165.12 inference(rename_variables,[],[3123])). % 165.36/165.12 cnf(12437,plain, % 165.36/165.12 (E(f332(f263(x124371,x124371),f264(x124371,x124372)),x124372)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12442,plain, % 165.36/165.12 (E(f332(f263(x124421,x124421),f264(x124421,x124422)),x124422)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12444,plain, % 165.36/165.12 (E(f332(f263(x124441,x124441),f264(x124441,x124442)),x124442)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12452,plain, % 165.36/165.12 (E(f332(f263(x124521,x124521),f264(x124521,x124522)),x124522)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12454,plain, % 165.36/165.12 (E(f332(f263(x124541,x124541),f264(x124541,x124542)),x124542)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12456,plain, % 165.36/165.12 (E(f332(f263(x124561,x124561),f264(x124561,x124562)),x124562)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12458,plain, % 165.36/165.12 (P33(x124581,f2(a868),f332(f332(f332(f93(x124581),x124582),f332(a28,x124583)),x124584))), % 165.36/165.12 inference(rename_variables,[],[3639])). % 165.36/165.12 cnf(12464,plain, % 165.36/165.12 (P21(x124641,x124641,f5(x124641),x124642)), % 165.36/165.12 inference(rename_variables,[],[3502])). % 165.36/165.12 cnf(12466,plain, % 165.36/165.12 (P21(x124661,x124661,f5(x124661),x124662)), % 165.36/165.12 inference(rename_variables,[],[3502])). % 165.36/165.12 cnf(12479,plain, % 165.36/165.12 (P20(x124791,x124792,f196(f875(f867(x124791),a862)))), % 165.36/165.12 inference(rename_variables,[],[3313])). % 165.36/165.12 cnf(12485,plain, % 165.36/165.12 (E(f332(f263(x124851,x124851),f264(x124851,x124852)),x124852)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12487,plain, % 165.36/165.12 (P54(x124871,f196(f875(x124871,a862)),x124872)), % 165.36/165.12 inference(rename_variables,[],[3275])). % 165.36/165.12 cnf(12491,plain, % 165.36/165.12 (P43(x124911,x124912,f264(x124911,x124912))), % 165.36/165.12 inference(rename_variables,[],[3223])). % 165.36/165.12 cnf(12493,plain, % 165.36/165.12 (P43(x124931,x124932,f264(x124931,x124932))), % 165.36/165.12 inference(rename_variables,[],[3223])). % 165.36/165.12 cnf(12505,plain, % 165.36/165.12 (E(f196(f875(f874(x125051,x125051),a862)),f264(x125051,f196(f875(x125051,a862))))), % 165.36/165.12 inference(rename_variables,[],[3329])). % 165.36/165.12 cnf(12507,plain, % 165.36/165.12 (P53(x125071,x125071,f264(x125071,x125072))), % 165.36/165.12 inference(rename_variables,[],[3224])). % 165.36/165.12 cnf(12518,plain, % 165.36/165.12 (P46(x125181,x125182,x125183,x125184,f196(f875(x125181,a862)),x125184)), % 165.36/165.12 inference(rename_variables,[],[4222])). % 165.36/165.12 cnf(12521,plain, % 165.36/165.12 (P46(x125211,x125212,x125213,x125214,f196(f875(x125211,a862)),x125214)), % 165.36/165.12 inference(rename_variables,[],[4222])). % 165.36/165.12 cnf(12526,plain, % 165.36/165.12 (P36(x125261,x125262,f116(x125261),f116(x125261))), % 165.36/165.12 inference(rename_variables,[],[3511])). % 165.36/165.12 cnf(12528,plain, % 165.36/165.12 (P36(x125281,x125282,f116(x125281),f116(x125281))), % 165.36/165.12 inference(rename_variables,[],[3511])). % 165.36/165.12 cnf(12532,plain, % 165.36/165.12 (E(f332(f263(x125321,x125321),f264(x125321,x125322)),x125322)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12534,plain, % 165.36/165.12 (P11(x125341,f875(x125341,a862),f310(x125341))), % 165.36/165.12 inference(rename_variables,[],[3227])). % 165.36/165.12 cnf(12538,plain, % 165.36/165.12 (E(f332(f263(x125381,x125381),f264(x125381,x125382)),x125382)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12546,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),f2(a868)),f332(a115,x125461)))), % 165.36/165.12 inference(rename_variables,[],[3338])). % 165.36/165.12 cnf(12547,plain, % 165.36/165.12 (~E(f332(a115,x125471),x125471)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(12553,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x125531),f332(a115,x125531)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(12558,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x125581),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(12560,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),a84),f2(a1)))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,4462,10373,10464,3314,3275,12487,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2908,2911,2917,2918,2925,2935,2938,2953,2989,2993,2994,3002,3004,3008,3009,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3644,4426,3092,3093,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,4530,10920,10990,11214,11217,3664,3363,3588,3329,12505,3144,3145,10272,10579,3421,3137,3063,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3782,3829,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,3717,11523,3239,3338,11641,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,4536,11408,11439,11474,11503,3704,3472,3856,3283,3285,3258,4517,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,4017,3975,11794,12141,3919,10752,11978,12148,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,3416,10545,10811,10855,11122,11203,11366,11606,12242,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,3319,10576,10606,10615,11151,11705,12331,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,3747,4098,4527,3758,3794,4506,4509,3230,3234,4508,4507,4511,3765,3577,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,3873,11244,11581,11585,11647,12250,12258,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,12311,4052,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,4548,11520,4538,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,4059,3746,3690,4546,10222,10225,10570,10573,11405,11586,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,740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% 165.36/165.12 cnf(12567,plain, % 165.36/165.12 (~P24(f332(f332(f247(a1),f332(f103(a1),x125671)),f332(f80(a1),f332(f103(a1),x125672))))), % 165.36/165.12 inference(rename_variables,[],[4543])). % 165.36/165.12 cnf(12577,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x125771),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(12580,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x125801),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(12583,plain, % 165.36/165.12 (P24(f332(f62(a868),f305(a868,x125831,x125832)))), % 165.36/165.12 inference(rename_variables,[],[3473])). % 165.36/165.12 cnf(12586,plain, % 165.36/165.12 (P24(f332(f62(a868),f305(a868,x125861,x125862)))), % 165.36/165.12 inference(rename_variables,[],[3473])). % 165.36/165.12 cnf(12589,plain, % 165.36/165.12 (P24(f332(f62(a868),f305(a868,x125891,x125892)))), % 165.36/165.12 inference(rename_variables,[],[3473])). % 165.36/165.12 cnf(12592,plain, % 165.36/165.12 (P24(f332(f62(a868),f305(a868,x125921,x125922)))), % 165.36/165.12 inference(rename_variables,[],[3473])). % 165.36/165.12 cnf(12599,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),f332(f80(a1),f332(f103(a1),x125991))),f332(f103(a1),x125992)))), % 165.36/165.12 inference(rename_variables,[],[3747])). % 165.36/165.12 cnf(12601,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),f2(a1)),f332(f106(a1),f2(a1))))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,4462,10373,10464,3314,3275,12487,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2908,2911,2917,2918,2925,2935,2938,2953,2989,2993,2994,3001,3002,3004,3008,3009,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,4530,10920,10990,11214,11217,3664,3363,3588,3329,12505,3144,3145,10272,10579,3421,3137,3063,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3782,3829,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,3717,11523,3239,3338,11641,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,4536,11408,11439,11474,11503,3704,3472,3473,12583,12586,12589,3856,3283,3285,3258,4517,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,4017,3975,11794,12141,3919,10752,11978,12148,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,3416,10545,10811,10855,11122,11203,11366,11606,12242,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,3319,10576,10606,10615,11151,11705,12331,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,3747,11656,4098,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,3765,3577,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,3873,11244,11581,11585,11647,12250,12258,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,12311,4052,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,4059,3746,3690,3691,4546,10222,10225,10570,10573,11405,11586,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001])). % 165.36/165.12 cnf(12604,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x126041),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(12605,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x126051),x126051))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12612,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x126121),f332(a115,x126121)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(12614,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),f2(a1)),a84))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,4462,10373,10464,3314,3275,12487,3471,3170,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2908,2911,2917,2918,2925,2935,2938,2953,2989,2993,2994,3001,3002,3004,3008,3009,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,4530,10920,10990,11214,11217,3664,3363,3588,3329,12505,3144,3145,10272,10579,3421,3137,3063,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3604,3782,3829,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,3717,11523,3239,3338,11641,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,4536,11408,11439,11474,11503,3704,3472,3473,12583,12586,12589,3856,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,4017,3975,11794,12141,3919,10752,11978,12148,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,3416,10545,10811,10855,11122,11203,11366,11606,12242,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,3319,10576,10606,10615,11151,11705,12331,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,3747,11656,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,3765,3577,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,3873,11244,11581,11585,11647,12250,12258,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,12311,4052,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,4059,3746,3690,3691,4546,10222,10225,10570,10573,11405,11586,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105])). % 165.36/165.12 cnf(12617,plain, % 165.36/165.12 (P24(f332(f332(f334(x126171),f332(x126172,x126173)),f332(f311(x126174,x126171,x126172),f255(f875(x126174,a862)))))), % 165.36/165.12 inference(rename_variables,[],[3873])). % 165.36/165.12 cnf(12618,plain, % 165.36/165.12 (~E(f332(a115,x126181),f2(a868))), % 165.36/165.12 inference(rename_variables,[],[4457])). % 165.36/165.12 cnf(12620,plain, % 165.36/165.12 (~P24(f332(f332(f247(a1),f2(a1)),f332(f106(a1),f2(a1))))), % 165.36/165.12 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,4462,10373,10464,3314,3275,12487,3471,3170,4457,2847,2848,2850,2851,2854,2855,2857,2858,2859,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2908,2911,2917,2918,2925,2935,2938,2953,2989,2993,2994,3001,3002,3004,3008,3009,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,4530,10920,10990,11214,11217,3664,3363,3588,3329,12505,3144,3145,10272,10579,3421,3137,3063,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3604,3782,3829,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,3717,11523,3239,3338,11641,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,4536,11408,11439,11474,11503,3704,3472,3473,12583,12586,12589,3856,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,4017,3975,11794,12141,3919,10752,11978,12148,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,3257,3334,12008,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,3416,10545,10811,10855,11122,11203,11366,11606,12242,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,3319,10576,10606,10615,11151,11705,12331,3358,3352,3786,3722,10249,11526,11554,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,3747,11656,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,3765,3577,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,12311,4052,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,4059,3746,3690,3691,4546,10222,10225,10570,10573,11405,11586,4547,11500,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259])). % 165.36/165.12 cnf(12623,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x126231),x126231))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(12626,plain, % 165.36/165.12 (P24(f332(f62(a868),f305(a868,x126261,x126262)))), % 165.36/165.12 inference(rename_variables,[],[3473])). % 165.36/165.12 cnf(12629,plain, % 165.36/165.12 (P24(f332(f62(a868),f305(a868,x126291,x126292)))), % 165.36/165.12 inference(rename_variables,[],[3473])). % 165.36/165.12 cnf(12632,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x126321),x126321))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12633,plain, % 165.36/165.12 (~E(f332(a115,x126331),f2(a868))), % 165.36/165.12 inference(rename_variables,[],[4457])). % 165.36/165.12 cnf(12650,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f45(a868,x126501,x126502)),x126501))), % 165.36/165.12 inference(rename_variables,[],[3722])). % 165.36/165.12 cnf(12655,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x126551),f332(a115,x126551)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(12658,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x126581),f332(a115,x126581)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(12659,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x126591),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(12668,plain, % 165.36/165.12 (~P24(f332(f332(f247(a1),f332(f103(a1),x126681)),f2(a1)))), % 165.36/165.12 inference(rename_variables,[],[4536])). % 165.36/165.12 cnf(12669,plain, % 165.36/165.12 (P24(f332(f255(f875(x126691,a862)),x126692))), % 165.36/165.12 inference(rename_variables,[],[3319])). % 165.36/165.12 cnf(12672,plain, % 165.36/165.12 (~P24(f332(f332(f247(a1),f332(f103(a1),x126721)),f2(a1)))), % 165.36/165.12 inference(rename_variables,[],[4536])). % 165.36/165.12 cnf(12673,plain, % 165.36/165.12 (P24(f332(f255(f875(x126731,a862)),x126732))), % 165.36/165.12 inference(rename_variables,[],[3319])). % 165.36/165.12 cnf(12676,plain, % 165.36/165.12 (P24(f332(f255(f875(x126761,a862)),x126762))), % 165.36/165.12 inference(rename_variables,[],[3319])). % 165.36/165.12 cnf(12687,plain, % 165.36/165.12 (~P24(f332(f332(f334(x126871),x126872),f196(f875(x126871,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12688,plain, % 165.36/165.12 (P24(f332(f62(x126881),f196(f875(x126881,a862))))), % 165.36/165.12 inference(rename_variables,[],[3334])). % 165.36/165.12 cnf(12697,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),f2(a868)),x126971))), % 165.36/165.12 inference(rename_variables,[],[3277])). % 165.36/165.12 cnf(12700,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x127001),f332(a115,x127001)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(12701,plain, % 165.36/165.12 (~E(f332(a115,x127011),x127011)), % 165.36/165.12 inference(rename_variables,[],[4447])). % 165.36/165.12 cnf(12704,plain, % 165.36/165.12 (~P24(f332(f332(f334(x127041),x127042),f196(f875(x127041,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12707,plain, % 165.36/165.12 (~P24(f332(f332(f334(x127071),x127072),f196(f875(x127071,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12710,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x127101),x127101))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12718,plain, % 165.36/165.12 (P24(f332(f332(f247(a868),x127181),f332(a115,x127181)))), % 165.36/165.12 inference(rename_variables,[],[3326])). % 165.36/165.12 cnf(12721,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x127211),x127211))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12726,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x127261),x127261))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12729,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x127291),x127291))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12732,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x127321),x127321))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12735,plain, % 165.36/165.12 (E(f332(f332(f22(f875(x127351,a862)),f196(f875(x127351,a862))),x127352),f196(f875(x127351,a862)))), % 165.36/165.12 inference(rename_variables,[],[3533])). % 165.36/165.12 cnf(12736,plain, % 165.36/165.12 (P24(f332(f62(x127361),f196(f875(x127361,a862))))), % 165.36/165.12 inference(rename_variables,[],[3334])). % 165.36/165.12 cnf(12739,plain, % 165.36/165.12 (E(f332(f332(f22(f875(x127391,a862)),f196(f875(x127391,a862))),x127392),f196(f875(x127391,a862)))), % 165.36/165.12 inference(rename_variables,[],[3533])). % 165.36/165.12 cnf(12740,plain, % 165.36/165.12 (P24(f332(f62(x127401),f196(f875(x127401,a862))))), % 165.36/165.12 inference(rename_variables,[],[3334])). % 165.36/165.12 cnf(12743,plain, % 165.36/165.12 (E(f332(f332(f22(f875(x127431,a862)),f196(f875(x127431,a862))),x127432),f196(f875(x127431,a862)))), % 165.36/165.12 inference(rename_variables,[],[3533])). % 165.36/165.12 cnf(12744,plain, % 165.36/165.12 (P24(f332(f62(x127441),f196(f875(x127441,a862))))), % 165.36/165.12 inference(rename_variables,[],[3334])). % 165.36/165.12 cnf(12747,plain, % 165.36/165.12 (E(f332(f332(f22(f875(x127471,a862)),f196(f875(x127471,a862))),x127472),f196(f875(x127471,a862)))), % 165.36/165.12 inference(rename_variables,[],[3533])). % 165.36/165.12 cnf(12748,plain, % 165.36/165.12 (P24(f332(f62(x127481),f196(f875(x127481,a862))))), % 165.36/165.12 inference(rename_variables,[],[3334])). % 165.36/165.12 cnf(12752,plain, % 165.36/165.12 (E(f332(f263(x127521,x127521),f264(x127521,x127522)),x127522)), % 165.36/165.12 inference(rename_variables,[],[3213])). % 165.36/165.12 cnf(12757,plain, % 165.36/165.12 (E(f332(f332(f22(f875(x127571,a862)),f196(f875(x127571,a862))),x127572),f196(f875(x127571,a862)))), % 165.36/165.12 inference(rename_variables,[],[3533])). % 165.36/165.12 cnf(12758,plain, % 165.36/165.12 (P24(f332(f62(x127581),f196(f875(x127581,a862))))), % 165.36/165.12 inference(rename_variables,[],[3334])). % 165.36/165.12 cnf(12762,plain, % 165.36/165.12 (P24(f332(f62(x127621),f196(f875(x127621,a862))))), % 165.36/165.12 inference(rename_variables,[],[3334])). % 165.36/165.12 cnf(12765,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x127651),x127651))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12769,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x127691),x127691))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(12776,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x127761),x127761))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12789,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x127891),x127891))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12792,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x127921),x127921))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(12799,plain, % 165.36/165.12 (~P24(f332(f332(f334(x127991),x127992),f196(f875(x127991,a862))))), % 165.36/165.12 inference(rename_variables,[],[4532])). % 165.36/165.12 cnf(12810,plain, % 165.36/165.12 (P24(f332(f332(f334(x128101),x128102),f255(f875(x128101,a862))))), % 165.36/165.12 inference(rename_variables,[],[3416])). % 165.36/165.12 cnf(12814,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x128141,a862)),x128142),f255(f875(x128141,a862))))), % 165.36/165.12 inference(rename_variables,[],[3646])). % 165.36/165.12 cnf(12817,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x128171,a862)),x128172),x128172))), % 165.36/165.12 inference(rename_variables,[],[3562])). % 165.36/165.12 cnf(12823,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x128231),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(12824,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x128241),x128241))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(12828,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x128281),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(12829,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x128291),x128291))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(12834,plain, % 165.36/165.12 (P24(f332(f332(f246(a868),x128341),x128341))), % 165.36/165.12 inference(rename_variables,[],[3255])). % 165.36/165.12 cnf(12841,plain, % 165.36/165.12 (E(f332(f332(f16(x128411,x128412),x128413),x128414),x128413)), % 165.36/165.12 inference(rename_variables,[],[3246])). % 165.36/165.12 cnf(12844,plain, % 165.36/165.12 (P24(f332(f332(f246(f875(x128441,a862)),f332(f174(x128441),f172(x128441,x128442,x128443))),f332(f174(x128441),x128443)))), % 165.36/165.12 inference(rename_variables,[],[3970])). % 165.36/165.12 cnf(12848,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x128481),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(12849,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x128491),x128491))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(12853,plain, % 165.36/165.12 (~P24(f332(f332(f247(a868),x128531),f2(a868)))), % 165.36/165.12 inference(rename_variables,[],[4520])). % 165.36/165.12 cnf(12854,plain, % 165.36/165.12 (P24(f332(f332(f246(a1),x128541),x128541))), % 165.36/165.12 inference(rename_variables,[],[3256])). % 165.36/165.12 cnf(12858,plain, % 165.36/165.12 (~P24(f332(f332(f246(f875(a868,a862)),f303(a868,f332(a115,x128581),f332(a115,x128581))),f303(a868,x128582,x128581)))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2904,2908,2911,2917,2918,2925,2927,2935,2938,2953,2961,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,11629,4530,10920,10990,11214,11217,3664,3363,3588,3329,12505,3144,3145,10272,10579,3421,3137,3063,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,3717,11523,3239,3338,11641,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,3856,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,12135,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,3765,3577,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,12311,12420,4052,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470])). % 165.36/165.13 cnf(12859,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),x128591),x128591))), % 165.36/165.13 inference(rename_variables,[],[3255])). % 165.36/165.13 cnf(12861,plain, % 165.36/165.13 (~P24(f332(f332(f247(f875(a868,a862)),f303(a868,f332(a115,x128611),f332(a115,x128611))),f303(a868,x128612,x128611)))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2904,2908,2911,2917,2918,2925,2927,2935,2938,2953,2961,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,11629,4530,10920,10990,11214,11217,3664,3363,3588,3329,12505,3144,3145,10272,10579,3421,3137,3063,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,3717,11523,3239,3338,11641,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,3856,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,12859,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,3277,10609,10760,10831,11555,11710,11902,12113,12135,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,3765,3577,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,12311,12420,4052,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470,8471])). % 165.36/165.13 cnf(12862,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),x128621),x128621))), % 165.36/165.13 inference(rename_variables,[],[3255])). % 165.36/165.13 cnf(12865,plain, % 165.36/165.13 (~P24(f332(f332(f246(a868),f332(a115,x128651)),x128651))), % 165.36/165.13 inference(rename_variables,[],[4529])). % 165.36/165.13 cnf(12870,plain, % 165.36/165.13 (E(x128701,f826(f332(f5(x128702),f332(f5(x128702),x128701)),f5(x128702),x128702,x128702))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,12466,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2904,2908,2911,2917,2918,2925,2927,2935,2938,2953,2961,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3083,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,4481,12247,3246,11626,11629,4530,10920,10990,11214,11217,3664,3363,3588,3329,12505,3144,3145,10272,10579,3421,3137,3063,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,3717,11523,3239,3338,11641,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,3856,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,4542,10700,11068,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,12859,12862,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,12865,3277,10609,10760,10831,11555,11710,11902,12113,12135,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,3765,3577,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,12617,3711,10871,10877,10892,11826,11955,12041,3562,11091,12067,12176,12186,12255,12303,12311,12420,4052,3713,10612,10948,11097,11127,11138,12254,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470,8471,8472,8473,8615])). % 165.36/165.13 cnf(12871,plain, % 165.36/165.13 (P24(f332(f332(f334(x128711),f332(x128712,x128713)),f332(f311(x128714,x128711,x128712),f255(f875(x128714,a862)))))), % 165.36/165.13 inference(rename_variables,[],[3873])). % 165.36/165.13 cnf(12872,plain, % 165.36/165.13 (P21(x128721,x128721,f5(x128721),x128722)), % 165.36/165.13 inference(rename_variables,[],[3502])). % 165.36/165.13 cnf(12877,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x128771,a862)),x128772),f255(f875(x128771,a862))))), % 165.36/165.13 inference(rename_variables,[],[3646])). % 165.36/165.13 cnf(12878,plain, % 165.36/165.13 (P21(x128781,x128781,f5(x128781),x128782)), % 165.36/165.13 inference(rename_variables,[],[3502])). % 165.36/165.13 cnf(12882,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x128821,a862)),x128822),f255(f875(x128821,a862))))), % 165.36/165.13 inference(rename_variables,[],[3646])). % 165.36/165.13 cnf(12883,plain, % 165.36/165.13 (P21(x128831,x128831,f5(x128831),x128832)), % 165.36/165.13 inference(rename_variables,[],[3502])). % 165.36/165.13 cnf(12887,plain, % 165.36/165.13 (P21(x128871,x128871,f5(x128871),x128872)), % 165.36/165.13 inference(rename_variables,[],[3502])). % 165.36/165.13 cnf(12890,plain, % 165.36/165.13 (~P24(f332(f332(f247(f875(x128901,a862)),x128902),f196(f875(x128901,a862))))), % 165.36/165.13 inference(rename_variables,[],[4542])). % 165.36/165.13 cnf(12893,plain, % 165.36/165.13 (P21(x128931,x128931,f5(x128931),x128932)), % 165.36/165.13 inference(rename_variables,[],[3502])). % 165.36/165.13 cnf(12896,plain, % 165.36/165.13 (P21(x128961,x128961,f5(x128961),x128962)), % 165.36/165.13 inference(rename_variables,[],[3502])). % 165.36/165.13 cnf(12907,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x129071,a862)),f196(f875(x129071,a862))),x129072))), % 165.36/165.13 inference(rename_variables,[],[3713])). % 165.36/165.13 cnf(12911,plain, % 165.36/165.13 (E(f332(f263(x129111,x129111),f264(x129111,x129112)),x129112)), % 165.36/165.13 inference(rename_variables,[],[3213])). % 165.36/165.13 cnf(12915,plain, % 165.36/165.13 (~P24(f332(f332(f334(x129151),x129152),f196(f875(x129151,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(12919,plain, % 165.36/165.13 (P24(f332(f332(f334(x129191),f332(x129192,x129193)),f332(f311(x129194,x129191,x129192),f255(f875(x129194,a862)))))), % 165.36/165.13 inference(rename_variables,[],[3873])). % 165.36/165.13 cnf(12920,plain, % 165.36/165.13 (P21(x129201,x129201,f5(x129201),x129202)), % 165.36/165.13 inference(rename_variables,[],[3502])). % 165.36/165.13 cnf(12923,plain, % 165.36/165.13 (P24(f332(f332(f334(x129231),x129232),f255(f875(x129231,a862))))), % 165.36/165.13 inference(rename_variables,[],[3416])). % 165.36/165.13 cnf(12927,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x129271,a862)),x129272),x129272))), % 165.36/165.13 inference(rename_variables,[],[3562])). % 165.36/165.13 cnf(12933,plain, % 165.36/165.13 (~P24(f332(f332(f334(x129331),x129332),f196(f875(x129331,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(12936,plain, % 165.36/165.13 (~P24(f332(f332(f334(x129361),x129362),f196(f875(x129361,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(12940,plain, % 165.36/165.13 (E(f332(f332(f16(x129401,x129402),x129403),x129404),x129403)), % 165.36/165.13 inference(rename_variables,[],[3246])). % 165.36/165.13 cnf(12943,plain, % 165.36/165.13 (P24(f332(f332(f247(a868),x129431),f332(a115,x129431)))), % 165.36/165.13 inference(rename_variables,[],[3326])). % 165.36/165.13 cnf(12944,plain, % 165.36/165.13 (~E(f332(a115,x129441),x129441)), % 165.36/165.13 inference(rename_variables,[],[4447])). % 165.36/165.13 cnf(12947,plain, % 165.36/165.13 (P24(f332(f332(f247(a868),x129471),f332(a115,f332(f332(f81(a868),x129472),x129471))))), % 165.36/165.13 inference(rename_variables,[],[3715])). % 165.36/165.13 cnf(12948,plain, % 165.36/165.13 (P24(f332(f332(f247(a868),x129481),f332(a115,x129481)))), % 165.36/165.13 inference(rename_variables,[],[3326])). % 165.36/165.13 cnf(12950,plain, % 165.36/165.13 (~E(f332(f332(f82(a868),f332(a115,f2(a868))),f34(x129501,x129502)),f332(f332(f82(a868),f332(a115,f2(a868))),f33(x129503,x129504)))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,12466,12872,12878,12883,12887,12893,12896,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,12701,12944,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,2838,2839,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2904,2908,2911,2914,2917,2918,2925,2927,2935,2938,2953,2961,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,12752,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3083,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3130,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,12277,4481,12247,3246,11626,11629,12841,4530,10920,10990,11214,11217,3664,3241,3363,3588,3329,12505,3144,3145,10272,10579,4514,3421,3137,3063,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,11111,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,12943,3717,11523,3239,3338,11641,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,3856,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,3970,10932,12020,12093,12147,12194,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,12814,12877,12882,4542,10700,11068,12151,12890,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,12859,12862,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,12810,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,12799,12915,12933,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,12865,3277,10609,10760,10831,11555,11710,11902,12113,12135,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,3765,3577,11519,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,12617,12871,12919,3711,10871,10877,10892,11826,11955,12041,12308,3562,11091,12067,12176,12186,12255,12303,12311,12420,12817,4052,3713,10612,10948,11097,11127,11138,12254,12297,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,12185,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,10793,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470,8471,8472,8473,8615,8851,8852,8923,8938,8992,8993,9108,9142,9165,9193,9232,9418,9675,9806,9868,9924,9926,6028,6404,6405,6492])). % 165.36/165.13 cnf(12957,plain, % 165.36/165.13 (P24(f332(f332(f246(a1),f2(a1)),f332(f103(a1),x129571)))), % 165.36/165.13 inference(rename_variables,[],[3358])). % 165.36/165.13 cnf(12960,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),f2(a868)),x129601))), % 165.36/165.13 inference(rename_variables,[],[3277])). % 165.36/165.13 cnf(12964,plain, % 165.36/165.13 (~E(f332(a115,x129641),f2(a868))), % 165.36/165.13 inference(rename_variables,[],[4457])). % 165.36/165.13 cnf(12973,plain, % 165.36/165.13 (~P24(f332(f332(f334(x129731),x129732),f196(f875(x129731,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(12976,plain, % 165.36/165.13 (P24(f332(f62(a868),f305(a868,x129761,x129762)))), % 165.36/165.13 inference(rename_variables,[],[3473])). % 165.36/165.13 cnf(12977,plain, % 165.36/165.13 (E(f332(f332(f245(a868),f332(a115,x129771)),f332(a115,x129772)),f332(a115,f332(f332(f245(a868),x129771),x129772)))), % 165.36/165.13 inference(rename_variables,[],[3434])). % 165.36/165.13 cnf(12980,plain, % 165.36/165.13 (P24(f332(f62(a868),f305(a868,x129801,x129802)))), % 165.36/165.13 inference(rename_variables,[],[3473])). % 165.36/165.13 cnf(12981,plain, % 165.36/165.13 (E(f332(f332(f244(a868),f332(a115,x129811)),f332(a115,x129812)),f332(a115,f332(f332(f244(a868),x129811),x129812)))), % 165.36/165.13 inference(rename_variables,[],[3433])). % 165.36/165.13 cnf(12984,plain, % 165.36/165.13 (P24(f332(f62(a868),f305(a868,x129841,x129842)))), % 165.36/165.13 inference(rename_variables,[],[3473])). % 165.36/165.13 cnf(12992,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x129921,a862)),f332(f174(x129921),f332(f137(x129921,x129922),x129923))),f332(f174(x129921),x129923)))), % 165.36/165.13 inference(rename_variables,[],[3919])). % 165.36/165.13 cnf(12993,plain, % 165.36/165.13 (E(f332(f332(f16(x129931,x129932),x129933),x129934),x129933)), % 165.36/165.13 inference(rename_variables,[],[3246])). % 165.36/165.13 cnf(12996,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x129961,a862)),f332(f174(x129961),f332(f332(f177(x129961),x129962),x129963))),f332(f174(x129961),x129963)))), % 165.36/165.13 inference(rename_variables,[],[3964])). % 165.36/165.13 cnf(12997,plain, % 165.36/165.13 (E(f332(f332(f16(x129971,x129972),x129973),x129974),x129973)), % 165.36/165.13 inference(rename_variables,[],[3246])). % 165.36/165.13 cnf(13001,plain, % 165.36/165.13 (E(f332(f332(f16(x130011,x130012),x130013),x130014),x130013)), % 165.36/165.13 inference(rename_variables,[],[3246])). % 165.36/165.13 cnf(13014,plain, % 165.36/165.13 (P24(f332(f332(f246(a1),f2(a1)),f332(f103(a1),x130141)))), % 165.36/165.13 inference(rename_variables,[],[3358])). % 165.36/165.13 cnf(13017,plain, % 165.36/165.13 (~P24(f332(f332(f334(x130171),x130172),f196(f875(x130171,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(13020,plain, % 165.36/165.13 (~P24(f332(f332(f334(x130201),x130202),f196(f875(x130201,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(13021,plain, % 165.36/165.13 (E(f332(f263(x130211,x130211),f264(x130211,x130212)),x130212)), % 165.36/165.13 inference(rename_variables,[],[3213])). % 165.36/165.13 cnf(13022,plain, % 165.36/165.13 (P21(x130221,x130221,f5(x130221),x130222)), % 165.36/165.13 inference(rename_variables,[],[3502])). % 165.36/165.13 cnf(13026,plain, % 165.36/165.13 (E(f332(f263(x130261,x130261),f264(x130261,x130262)),x130262)), % 165.36/165.13 inference(rename_variables,[],[3213])). % 165.36/165.13 cnf(13031,plain, % 165.36/165.13 (P24(f332(f332(f247(f875(a1,a862)),f303(a1,f79(a1),f2(a1))),f303(a1,f2(a1),f79(a1))))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,12466,12872,12878,12883,12887,12893,12896,12920,13022,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,12701,12944,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,12633,2838,2839,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2904,2908,2911,2914,2917,2918,2925,2927,2935,2938,2944,2953,2961,2962,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,12752,12911,13021,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3083,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3130,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,12277,4481,12247,3246,11626,11629,12841,12940,12993,12997,13001,4530,10920,10990,11214,11217,3664,3241,3363,3588,3355,3329,12505,3144,3145,10272,10579,4514,3421,3137,3063,3251,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,11111,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,12943,3717,11523,3239,3338,11641,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,12629,12976,12980,12984,3856,3433,12981,3434,12977,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,12371,12992,3964,12996,3970,10932,12020,12093,12147,12194,12844,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,12814,12877,12882,4542,10700,11068,12151,12890,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,12859,12862,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,12810,12923,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,12799,12915,12933,12936,12973,13017,13020,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,12957,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,12865,3277,10609,10760,10831,11555,11710,11902,12113,12135,12697,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,4275,3765,3577,11519,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,12617,12871,12919,3711,10871,10877,10892,11826,11955,12041,12308,3562,11091,12067,12176,12186,12255,12303,12311,12420,12817,12927,4052,3713,10612,10948,11097,11127,11138,12254,12297,12907,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,12185,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,10793,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470,8471,8472,8473,8615,8851,8852,8923,8938,8992,8993,9108,9142,9165,9193,9232,9418,9675,9806,9868,9924,9926,6028,6404,6405,6492,6513,6514,6927,7143,8541,8574,8768,8949,8950,9019,9020,9278,9279,9280,9281,9473,9747,10046,10097,10098,6474,8378])). % 165.36/165.13 cnf(13033,plain, % 165.36/165.13 (P24(f332(f332(f247(f875(a1,a862)),f303(a1,f2(a1),f2(a1))),f303(a1,f332(f80(a1),f332(f103(a1),f332(a115,x130331))),f2(a1))))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,12466,12872,12878,12883,12887,12893,12896,12920,13022,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,12701,12944,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,12633,2838,2839,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2904,2908,2911,2914,2917,2918,2925,2927,2935,2938,2944,2953,2961,2962,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,12752,12911,13021,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3083,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3130,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,12277,4481,12247,3246,11626,11629,12841,12940,12993,12997,13001,4530,10920,10990,11214,11217,3664,3241,3363,3588,3355,3329,12505,3144,3145,10272,10579,4514,3421,3137,3063,3251,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,11111,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,12943,3717,11523,3239,3338,11641,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,12629,12976,12980,12984,3856,3433,12981,3434,12977,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,12371,12992,3964,12996,3970,10932,12020,12093,12147,12194,12844,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,12814,12877,12882,4542,10700,11068,12151,12890,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,12859,12862,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,12854,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,12810,12923,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,12799,12915,12933,12936,12973,13017,13020,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,12957,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,12865,3277,10609,10760,10831,11555,11710,11902,12113,12135,12697,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,4275,3765,3577,11519,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,12617,12871,12919,3711,10871,10877,10892,11826,11955,12041,12308,3562,11091,12067,12176,12186,12255,12303,12311,12420,12817,12927,4052,3713,10612,10948,11097,11127,11138,12254,12297,12907,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,12185,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,10793,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470,8471,8472,8473,8615,8851,8852,8923,8938,8992,8993,9108,9142,9165,9193,9232,9418,9675,9806,9868,9924,9926,6028,6404,6405,6492,6513,6514,6927,7143,8541,8574,8768,8949,8950,9019,9020,9278,9279,9280,9281,9473,9747,10046,10097,10098,6474,8378,8379])). % 165.36/165.13 cnf(13040,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),f2(a868)),x130401))), % 165.36/165.13 inference(rename_variables,[],[3277])). % 165.36/165.13 cnf(13041,plain, % 165.36/165.13 (P24(f332(f332(f247(a868),f2(a868)),f332(a115,x130411)))), % 165.36/165.13 inference(rename_variables,[],[3338])). % 165.36/165.13 cnf(13042,plain, % 165.36/165.13 (E(f332(f263(x130421,x130421),f264(x130421,x130422)),x130422)), % 165.36/165.13 inference(rename_variables,[],[3213])). % 165.36/165.13 cnf(13045,plain, % 165.36/165.13 (P24(f332(f48(f332(f263(x130451,x130451),f264(x130451,f332(f332(f81(a868),f332(f332(f82(a868),f332(f266(a868,a868),f332(f332(f267(a868,a868),f2(a868)),x130452))),f332(a115,f332(f332(f81(a868),x130453),f332(f270(a868,a868),f332(f332(f267(a868,a868),f2(a868)),x130452)))))),f332(f270(a868,a868),f332(f332(f267(a868,a868),f2(a868)),x130452))))),f332(a115,f332(f332(f81(a868),x130453),f332(f270(a868,a868),f332(f332(f267(a868,a868),f2(a868)),x130452))))),f332(f332(f267(a868,a868),f2(a868)),x130452)))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,12466,12872,12878,12883,12887,12893,12896,12920,13022,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,12701,12944,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,12633,12964,2838,2839,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2904,2908,2911,2914,2917,2918,2925,2927,2935,2938,2944,2953,2961,2962,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,12752,12911,13021,13026,13042,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3083,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3130,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,12277,4481,12247,3246,11626,11629,12841,12940,12993,12997,13001,4530,10920,10990,11214,11217,3664,3241,3363,3588,3355,3329,12505,3144,3145,10272,10579,4514,3421,3137,3063,3251,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,11111,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,3444,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,12943,12948,3717,11523,3239,3338,11641,12546,13041,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,12629,12976,12980,12984,3856,3433,12981,3434,12977,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,12371,12992,3964,12996,3970,10932,12020,12093,12147,12194,12844,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,12814,12877,12882,4542,10700,11068,12151,12890,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,12859,12862,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,12854,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,12810,12923,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,12799,12915,12933,12936,12973,13017,13020,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,12957,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,12865,3277,10609,10760,10831,11555,11710,11902,12113,12135,12697,12960,13040,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,4275,3765,3577,11519,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,12617,12871,12919,3711,10871,10877,10892,11826,11955,12041,12308,3562,11091,12067,12176,12186,12255,12303,12311,12420,12817,12927,4052,3713,10612,10948,11097,11127,11138,12254,12297,12907,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,12185,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,10793,12947,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470,8471,8472,8473,8615,8851,8852,8923,8938,8992,8993,9108,9142,9165,9193,9232,9418,9675,9806,9868,9924,9926,6028,6404,6405,6492,6513,6514,6927,7143,8541,8574,8768,8949,8950,9019,9020,9278,9279,9280,9281,9473,9747,10046,10097,10098,6474,8378,8379,8817,8835])). % 165.36/165.13 cnf(13061,plain, % 165.36/165.13 (E(f332(f332(f81(a868),f2(a868)),f816(f332(a115,f2(a868)),f2(a868))),f2(a868))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,12466,12872,12878,12883,12887,12893,12896,12920,13022,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,12701,12944,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,12633,12964,2838,2839,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2902,2904,2908,2911,2914,2917,2918,2925,2927,2935,2938,2939,2944,2953,2961,2962,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,12752,12911,13021,13026,13042,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3083,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3130,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,12277,4481,12247,3246,11626,11629,12841,12940,12993,12997,13001,4530,10920,10990,11214,11217,3664,3241,3363,3588,3355,3329,12505,3144,3145,10272,10579,4514,3421,3137,3063,3251,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,11111,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,3444,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,12943,12948,3717,11523,3239,3338,11641,12546,13041,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,12853,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,12629,12976,12980,12984,3856,3433,12981,3434,12977,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,12371,12992,3964,12996,3970,10932,12020,12093,12147,12194,12844,3971,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,12814,12877,12882,4542,10700,11068,12151,12890,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,12859,12862,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,12854,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,12810,12923,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,12799,12915,12933,12936,12973,13017,13020,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,12957,13014,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,12865,3277,10609,10760,10831,11555,11710,11902,12113,12135,12697,12960,13040,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,4275,3765,3577,11519,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,12617,12871,12919,3711,10871,10877,10892,11826,11955,12041,12308,3562,11091,12067,12176,12186,12255,12303,12311,12420,12817,12927,4052,3713,10612,10948,11097,11127,11138,12254,12297,12907,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,12185,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,10793,12947,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470,8471,8472,8473,8615,8851,8852,8923,8938,8992,8993,9108,9142,9165,9193,9232,9418,9675,9806,9868,9924,9926,6028,6404,6405,6492,6513,6514,6927,7143,8541,8574,8768,8949,8950,9019,9020,9278,9279,9280,9281,9473,9747,10046,10097,10098,6474,8378,8379,8817,8835,9748,10096,4636,4638])). % 165.36/165.13 cnf(13109,plain, % 165.36/165.13 (~P24(f332(f332(f247(a1),f2(a1)),f2(a1)))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,12466,12872,12878,12883,12887,12893,12896,12920,13022,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,12701,12944,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,12633,12964,2838,2839,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2902,2904,2908,2911,2914,2917,2918,2925,2927,2935,2938,2939,2944,2953,2961,2962,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,12752,12911,13021,13026,13042,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3083,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3130,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,12277,4481,12247,3246,11626,11629,12841,12940,12993,12997,13001,4530,10920,10990,11214,11217,3664,3241,3363,3588,3355,3329,12505,3144,3145,10272,10579,4514,3421,3137,3063,3251,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,11111,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,3444,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,12943,12948,3717,11523,3239,3338,11641,12546,13041,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,12853,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,12629,12976,12980,12984,3856,3433,12981,3434,12977,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,12371,12992,3964,12996,3970,10932,12020,12093,12147,12194,12844,3971,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,12814,12877,12882,4542,10700,11068,12151,12890,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,12859,12862,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,12854,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,12810,12923,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,12799,12915,12933,12936,12973,13017,13020,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,12957,13014,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,12865,3277,10609,10760,10831,11555,11710,11902,12113,12135,12697,12960,13040,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,4275,3765,3577,11519,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,12617,12871,12919,3711,10871,10877,10892,11826,11955,12041,12308,3562,11091,12067,12176,12186,12255,12303,12311,12420,12817,12927,4052,3713,10612,10948,11097,11127,11138,12254,12297,12907,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,12185,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,10793,12947,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470,8471,8472,8473,8615,8851,8852,8923,8938,8992,8993,9108,9142,9165,9193,9232,9418,9675,9806,9868,9924,9926,6028,6404,6405,6492,6513,6514,6927,7143,8541,8574,8768,8949,8950,9019,9020,9278,9279,9280,9281,9473,9747,10046,10097,10098,6474,8378,8379,8817,8835,9748,10096,4636,4638,4639,4695,4703,4841,4857,4858,4886,4887,4918,4973,5036,5172,5208,5211,5219,5220,5246,5324,5345,5479,5547,5548,5549,5666])). % 165.36/165.13 cnf(13111,plain, % 165.36/165.13 (P24(f332(f332(f247(a1),f2(a1)),f332(f76(a1),f79(a1))))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,12466,12872,12878,12883,12887,12893,12896,12920,13022,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,12701,12944,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,12633,12964,2838,2839,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2902,2904,2908,2911,2914,2917,2918,2925,2927,2935,2938,2939,2944,2953,2961,2962,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,12752,12911,13021,13026,13042,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3083,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3130,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,12277,4481,12247,3246,11626,11629,12841,12940,12993,12997,13001,4530,10920,10990,11214,11217,3664,3241,3363,3588,3355,3329,12505,3144,3145,10272,10579,4514,3421,3137,3063,3251,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,11111,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,3444,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,12943,12948,3717,11523,3239,3338,11641,12546,13041,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,12853,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,12629,12976,12980,12984,3856,3433,12981,3434,12977,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,12371,12992,3964,12996,3970,10932,12020,12093,12147,12194,12844,3971,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,12814,12877,12882,4542,10700,11068,12151,12890,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,12859,12862,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,12854,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,12810,12923,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,12799,12915,12933,12936,12973,13017,13020,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,12957,13014,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,12865,3277,10609,10760,10831,11555,11710,11902,12113,12135,12697,12960,13040,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,4275,3765,3577,11519,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,12617,12871,12919,3711,10871,10877,10892,11826,11955,12041,12308,3562,11091,12067,12176,12186,12255,12303,12311,12420,12817,12927,4052,3713,10612,10948,11097,11127,11138,12254,12297,12907,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,12185,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,10793,12947,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470,8471,8472,8473,8615,8851,8852,8923,8938,8992,8993,9108,9142,9165,9193,9232,9418,9675,9806,9868,9924,9926,6028,6404,6405,6492,6513,6514,6927,7143,8541,8574,8768,8949,8950,9019,9020,9278,9279,9280,9281,9473,9747,10046,10097,10098,6474,8378,8379,8817,8835,9748,10096,4636,4638,4639,4695,4703,4841,4857,4858,4886,4887,4918,4973,5036,5172,5208,5211,5219,5220,5246,5324,5345,5479,5547,5548,5549,5666,5667])). % 165.36/165.13 cnf(13125,plain, % 165.36/165.13 (~P24(f332(f332(f247(a868),f332(a115,f332(f332(f81(a868),x131251),x131252))),f332(a115,x131251)))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,12466,12872,12878,12883,12887,12893,12896,12920,13022,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,12701,12944,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,12633,12964,2838,2839,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2902,2904,2908,2911,2914,2917,2918,2925,2927,2935,2938,2939,2944,2953,2961,2962,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,12752,12911,13021,13026,13042,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3083,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3130,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,12277,4481,12247,3246,11626,11629,12841,12940,12993,12997,13001,4530,10920,10990,11214,11217,3664,3241,3363,3588,3355,3329,12505,3144,3145,10272,10579,4514,3421,3137,3063,3251,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,11111,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,3444,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,12943,12948,3717,11523,3239,3338,11641,12546,13041,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,12853,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,12629,12976,12980,12984,3856,3433,12981,3434,12977,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,12371,12992,3964,12996,3970,10932,12020,12093,12147,12194,12844,3971,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,12814,12877,12882,4542,10700,11068,12151,12890,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,12859,12862,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,12854,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,12810,12923,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,12799,12915,12933,12936,12973,13017,13020,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,12957,13014,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,12865,3277,10609,10760,10831,11555,11710,11902,12113,12135,12697,12960,13040,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,4275,3765,3577,11519,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,12617,12871,12919,3711,10871,10877,10892,11826,11955,12041,12308,3562,11091,12067,12176,12186,12255,12303,12311,12420,12817,12927,4052,3713,10612,10948,11097,11127,11138,12254,12297,12907,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,12185,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,10793,12947,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470,8471,8472,8473,8615,8851,8852,8923,8938,8992,8993,9108,9142,9165,9193,9232,9418,9675,9806,9868,9924,9926,6028,6404,6405,6492,6513,6514,6927,7143,8541,8574,8768,8949,8950,9019,9020,9278,9279,9280,9281,9473,9747,10046,10097,10098,6474,8378,8379,8817,8835,9748,10096,4636,4638,4639,4695,4703,4841,4857,4858,4886,4887,4918,4973,5036,5172,5208,5211,5219,5220,5246,5324,5345,5479,5547,5548,5549,5666,5667,5693,5697,5757,5759,5768,5774,5846])). % 165.36/165.13 cnf(13129,plain, % 165.36/165.13 (~E(f332(f190(x131291,f875(x131292,a862),x131293,f196(f875(x131291,a862))),x131294),f332(f208(f875(x131292,a862)),f332(f332(f42(f45(a1,x131295,x131295),f875(x131292,a862)),x131296),a115)))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,12466,12872,12878,12883,12887,12893,12896,12920,13022,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,12701,12944,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,12633,12964,2838,2839,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2902,2904,2908,2911,2914,2917,2918,2925,2927,2935,2938,2939,2944,2953,2961,2962,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,12752,12911,13021,13026,13042,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3083,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3130,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,12277,4481,12247,3246,11626,11629,12841,12940,12993,12997,13001,4530,10920,10990,11214,11217,3664,3241,3363,3588,3355,3329,12505,3144,3145,10272,10579,4514,3421,3137,3063,3251,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,11111,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,3444,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,12943,12948,3717,11523,3239,3338,11641,12546,13041,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,12853,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,12629,12976,12980,12984,3856,3433,12981,3434,12977,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,12371,12992,3964,12996,3970,10932,12020,12093,12147,12194,12844,3971,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,12814,12877,12882,4542,10700,11068,12151,12890,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,12859,12862,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,12854,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,12810,12923,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,12799,12915,12933,12936,12973,13017,13020,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,12957,13014,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,12865,3277,10609,10760,10831,11555,11710,11902,12113,12135,12697,12960,13040,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,4275,3765,3577,11519,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,12617,12871,12919,3711,10871,10877,10892,11826,11955,12041,12308,3562,11091,12067,12176,12186,12255,12303,12311,12420,12817,12927,4052,3713,10612,10948,11097,11127,11138,12254,12297,12907,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,12185,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,10793,12947,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470,8471,8472,8473,8615,8851,8852,8923,8938,8992,8993,9108,9142,9165,9193,9232,9418,9675,9806,9868,9924,9926,6028,6404,6405,6492,6513,6514,6927,7143,8541,8574,8768,8949,8950,9019,9020,9278,9279,9280,9281,9473,9747,10046,10097,10098,6474,8378,8379,8817,8835,9748,10096,4636,4638,4639,4695,4703,4841,4857,4858,4886,4887,4918,4973,5036,5172,5208,5211,5219,5220,5246,5324,5345,5479,5547,5548,5549,5666,5667,5693,5697,5757,5759,5768,5774,5846,5924,6051])). % 165.36/165.13 cnf(13133,plain, % 165.36/165.13 (~P24(f332(f62(x131331),f40(f875(x131331,a862),f255(f875(f875(x131331,a862),a862)))))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,12466,12872,12878,12883,12887,12893,12896,12920,13022,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,12701,12944,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,12633,12964,2838,2839,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2902,2904,2908,2911,2914,2917,2918,2925,2927,2935,2938,2939,2944,2953,2961,2962,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,12752,12911,13021,13026,13042,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3083,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3130,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,12277,4481,12247,3246,11626,11629,12841,12940,12993,12997,13001,4530,10920,10990,11214,11217,3664,3241,3363,3588,3355,3329,12505,3144,3145,10272,10579,4514,3421,3137,3063,3251,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,11111,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,3444,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,12943,12948,3717,11523,3239,3338,11641,12546,13041,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,12853,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,12629,12976,12980,12984,3856,3433,12981,3434,12977,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,12371,12992,3964,12996,3970,10932,12020,12093,12147,12194,12844,3971,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,12814,12877,12882,4542,10700,11068,12151,12890,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,12859,12862,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,12854,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,12810,12923,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,12799,12915,12933,12936,12973,13017,13020,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,12957,13014,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,12865,3277,10609,10760,10831,11555,11710,11902,12113,12135,12697,12960,13040,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,4275,3765,3577,11519,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,12617,12871,12919,3711,10871,10877,10892,11826,11955,12041,12308,3562,11091,12067,12176,12186,12255,12303,12311,12420,12817,12927,4052,3713,10612,10948,11097,11127,11138,12254,12297,12907,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,12185,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,10793,12947,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470,8471,8472,8473,8615,8851,8852,8923,8938,8992,8993,9108,9142,9165,9193,9232,9418,9675,9806,9868,9924,9926,6028,6404,6405,6492,6513,6514,6927,7143,8541,8574,8768,8949,8950,9019,9020,9278,9279,9280,9281,9473,9747,10046,10097,10098,6474,8378,8379,8817,8835,9748,10096,4636,4638,4639,4695,4703,4841,4857,4858,4886,4887,4918,4973,5036,5172,5208,5211,5219,5220,5246,5324,5345,5479,5547,5548,5549,5666,5667,5693,5697,5757,5759,5768,5774,5846,5924,6051,6077,6246])). % 165.36/165.13 cnf(13145,plain, % 165.36/165.13 (~P24(f332(f332(f247(a868),f2(a868)),f196(a868)))), % 165.36/165.13 inference(scs_inference,[],[4560,3502,10985,12023,12123,12215,12251,12259,12324,12464,12466,12872,12878,12883,12887,12893,12896,12920,13022,3511,12087,12526,12528,3512,12154,3223,12491,12493,3224,12507,3189,12397,4482,4483,11603,4222,12518,12521,3227,12534,3062,3123,12433,4465,3564,4447,10140,10150,10163,10174,10177,10280,10283,10286,10389,10500,10806,10970,10973,11168,11258,11265,11279,11331,11334,11378,11444,11490,11506,11805,11830,11842,11871,11877,11972,12083,12090,12243,12294,12429,12547,12701,12944,4462,10373,10464,3314,3275,12487,3471,3170,4457,12618,12633,12964,2838,2839,2847,2848,2850,2851,2854,2855,2857,2858,2859,2861,2862,2867,2868,2874,2875,2876,2881,2882,2889,2898,2902,2904,2908,2911,2914,2917,2918,2925,2927,2935,2938,2939,2944,2953,2961,2962,2965,2966,2967,2976,2989,2993,2994,3001,3002,3003,3004,3008,3009,3010,3018,3025,4442,3041,3122,4443,3601,3834,11537,3094,11255,3237,3210,3213,10143,10212,10215,10307,10310,10603,11270,11273,11389,11431,11436,11532,11993,12191,12377,12431,12437,12442,12444,12452,12454,12456,12485,12532,12538,12752,12911,13021,13026,13042,3847,3184,12272,12276,12280,3190,3198,3725,3325,12327,12400,3967,3083,3084,4459,3465,3819,11305,3313,12479,3149,3114,3639,12458,3109,3941,3130,3644,4426,3092,3093,3072,3098,3737,3129,3315,10755,12084,3182,3183,3362,4541,10343,3906,4472,10203,10370,11165,12239,12273,12277,4481,12247,3246,11626,11629,12841,12940,12993,12997,13001,4530,10920,10990,11214,11217,3664,3241,3363,3588,3355,3329,12505,3144,3145,10272,10579,4514,3421,3137,3063,3251,3166,11295,4054,12262,12389,3908,10926,11052,11100,12223,12229,12338,12341,12364,4553,10858,10959,11057,11159,11184,11222,11228,12170,4554,11060,11162,4555,11063,11111,4556,11114,4557,3165,3462,12126,12167,12246,3627,4338,4339,3444,4470,11286,3566,3604,3782,3533,12735,12739,12743,12747,12757,3829,12120,3447,3706,3326,10291,10409,10478,10539,10542,10582,10676,10910,11801,11864,11943,11984,12061,12064,12368,12553,12612,12655,12658,12700,12718,12943,12948,3717,11523,3239,3338,11641,12546,13041,3527,4520,10180,10183,10209,10684,10697,10816,11206,11298,11693,11698,11919,11922,12005,12014,12173,12266,12558,12577,12580,12604,12659,12823,12828,12848,12853,4536,11408,11439,11474,11503,12668,12672,3704,3472,3473,12583,12586,12589,12592,12626,12629,12976,12980,12984,3856,3433,12981,3434,12977,3283,3285,3258,4517,3143,4467,3655,4192,3976,3454,4537,4048,11179,3587,3297,11650,11653,12094,12195,12348,4017,3975,11794,12141,3919,10752,11978,12148,12371,12992,3964,12996,3970,10932,12020,12093,12147,12194,12844,3971,3628,11804,11950,12028,12074,4006,3646,10929,10995,11076,11133,11971,12042,12289,12361,12374,12814,12877,12882,4542,10700,11068,12151,12890,3255,10300,10396,10525,10589,10658,10703,10706,10739,10763,10800,10838,10874,11597,11644,11774,11829,11845,11848,11851,11854,12035,12049,12052,12055,12058,12134,12198,12300,12344,12605,12632,12710,12721,12726,12729,12732,12765,12776,12789,12834,12859,12862,3256,10329,10384,10594,10679,10803,11381,11678,11681,11690,11780,11791,11810,11815,11857,11880,11897,12623,12769,12792,12824,12829,12849,12854,3257,3334,12008,12688,12736,12740,12744,12748,12758,12762,4516,10246,10338,10449,10473,10721,10766,10776,11453,11551,11572,11575,11578,11594,11748,11751,11754,11757,11841,11860,11863,11876,11931,11934,11937,11940,12015,12105,12108,12201,12204,12265,12293,12330,12409,3416,10545,10811,10855,11122,11203,11366,11606,12242,12412,12810,12923,4532,10730,10742,10847,10865,10868,10923,11009,11017,11033,11071,11085,11094,11130,11171,11176,11194,11197,11200,11231,11238,11241,11623,11659,11925,11928,11962,12009,12038,12179,12220,12226,12312,12315,12334,12388,12394,12403,12423,12687,12704,12707,12799,12915,12933,12936,12973,13017,13020,3319,10576,10606,10615,11151,11705,12331,12345,12669,12673,12676,3358,12957,13014,3352,3786,3722,10249,11526,11554,12650,4529,10200,10564,10567,11012,11030,11489,11542,11582,11607,11711,11736,11739,11742,11745,12004,12865,3277,10609,10760,10831,11555,11710,11902,12113,12135,12697,12960,13040,3747,11656,12599,4098,3478,4527,3758,3794,4506,4509,4510,3230,3234,4508,4507,4511,4275,3765,3577,11519,4198,11388,4544,10168,10171,10430,10481,10484,10489,10897,11360,11610,11714,4551,11088,11211,11247,3983,12162,3873,11244,11581,11585,11647,12250,12258,12337,12617,12871,12919,3711,10871,10877,10892,11826,11955,12041,12308,3562,11091,12067,12176,12186,12255,12303,12311,12420,12817,12927,4052,3713,10612,10948,11097,11127,11138,12254,12297,12907,3530,10528,10531,10618,10787,3529,4548,11520,4538,4543,12567,4549,10669,10769,11363,11394,12129,12138,12182,12358,4158,10745,11975,12159,12185,4059,3746,12426,3690,3691,4546,10222,10225,10570,10573,11405,11586,12367,4547,11500,11591,3715,10534,10793,12947,3990,4569,4595,4644,4646,4677,4694,4701,4702,4738,4743,4773,4779,4863,4888,4889,4904,4926,4951,4952,4974,4975,4988,4992,5015,5022,5040,5043,5044,5045,5050,5051,5073,5098,5099,5109,5114,5120,5164,5165,5173,5183,5187,5189,5199,5201,5207,5210,5212,5227,5234,5237,5238,5239,5243,5282,5295,5303,5305,5306,5310,5311,5312,5320,5323,5327,5328,5329,5336,5340,5341,5342,5350,5354,5355,5356,5361,5374,5383,5395,5397,5405,5406,5410,5414,5439,5445,5455,5456,5471,5483,5505,5511,5529,5530,5533,5552,5560,5561,5566,5567,5577,5579,5591,5595,5604,5605,5607,5622,5627,5637,5638,5650,5657,5671,5675,5678,5684,5685,5686,5689,5694,5732,5733,5736,5738,5741,5742,5743,5745,5747,5749,5754,5761,5776,5790,5795,5796,5809,5810,5815,5819,5821,5826,5867,5879,5888,5892,5903,5907,5908,5916,5929,5935,5953,5956,5965,5995,6009,6034,6054,6055,6058,6072,6074,6076,6078,6091,6092,6095,6097,6100,6101,6113,6121,6122,6123,6125,6127,6170,6171,6176,6179,6185,6189,6225,6227,6229,6231,6240,6242,6244,6250,6252,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6355,6356,6359,6360,6361,6363,6364,6365,6366,6373,6406,6407,6416,6437,6438,6458,6461,6472,6473,6479,6510,6512,6526,6563,6565,6566,6619,6643,6685,6705,6714,6715,6716,6717,6736,6737,6743,6756,6759,6761,6763,6764,6765,6767,6781,6792,6794,6795,6808,6812,6863,6874,6876,6880,6897,6898,6932,6944,6975,7007,7061,7089,7144,7165,7174,7177,7232,7240,7298,7300,7315,7325,7326,7327,7343,7349,7351,7401,7411,7414,7430,7481,7483,7486,7530,7531,7549,7616,7635,7658,7681,7696,7710,7721,7730,7731,7758,7761,7763,7772,7808,7819,7844,7901,7935,7968,8007,8023,8039,8040,8113,8166,8185,8209,8229,8253,8349,8351,8357,8371,8375,8390,8412,8420,8422,8433,8439,8443,8463,8477,8478,8494,8495,8500,8501,8502,8503,8504,8522,8523,8524,8532,8546,8548,8560,8564,8566,8567,8568,8576,8581,8607,8608,8640,8653,8657,8675,8697,8698,8699,8700,8712,8713,8735,8745,8755,8756,8757,8758,8760,8781,8782,8793,8837,8843,8849,8861,8866,8868,8870,8871,8875,8885,8958,8989,8990,8991,9005,9023,9028,9056,9057,9101,9125,9170,9171,9172,9181,9207,9221,9224,9227,9247,9248,9276,9335,9370,9371,9372,9396,9397,9415,9432,9438,9449,9472,9494,9502,9503,9504,9505,9520,9522,9527,9558,9559,9565,9566,9610,9611,9620,9643,9652,9662,9664,9665,9674,9688,9691,9719,9753,9755,9759,9815,9856,9857,9859,9869,9870,9890,9895,9936,9987,10058,10059,10112,10126,2,8,9,4582,4583,4601,4632,4633,4635,4663,4669,4670,4681,4730,4732,4764,4778,4807,4905,4906,4919,4939,4995,4996,4999,5000,5002,5004,5005,5014,5018,5019,5029,5041,5042,5048,5068,5069,5086,5091,5092,5093,5094,5097,5105,5108,5115,5179,5185,5186,5193,5224,5235,5241,5260,5280,5281,5288,5289,5290,5299,5309,5316,5318,5319,5325,5332,5333,5346,5347,5348,5349,5351,5352,5357,5358,5359,5360,5391,5392,5393,5401,5402,5403,5404,5447,5452,5454,5490,5492,5493,5495,5496,5498,5499,5501,5510,5515,5517,5518,5519,5520,5521,5522,5531,5541,5544,5555,5571,5572,5575,5585,5587,5588,5589,5614,5624,5640,5641,5651,5652,5654,5656,5661,5696,5701,5703,5763,5797,5798,5802,5808,5811,5812,5813,5814,5820,5831,5832,5834,5835,5843,5864,5895,5911,5914,5915,5917,5926,5943,5947,5950,5951,5952,5967,5977,5978,6011,6012,6016,6036,6039,6043,6062,6067,6068,6093,6096,6104,6112,6120,6124,6131,6132,6133,6134,6173,6190,6243,6278,6280,6301,6302,6307,6311,6312,6315,6321,6330,6347,6368,6369,6374,6384,6399,6419,6425,6427,6442,6443,6446,6447,6449,6451,6452,6453,6455,6457,6460,6465,6466,6468,6469,6475,6477,6520,6525,6539,6541,6542,6543,6577,6582,6584,6589,6590,6598,6602,6614,6638,6639,6641,6642,6653,6658,6676,6679,6698,6731,6732,6733,6738,6752,6771,6773,6775,6777,6782,6788,6790,6805,6810,6813,6849,6850,6851,6865,6866,6868,6869,6888,6890,6904,6930,6952,6963,6965,6967,6969,6970,6971,7004,7005,7010,7011,7018,7019,7021,7023,7042,7051,7052,7064,7074,7113,7123,7127,7134,7145,7151,7153,7159,7167,7168,7181,7198,7216,7218,7235,7284,7285,7286,7288,7290,7294,7299,7322,7364,7397,7412,7429,7461,7464,7490,7514,7532,7535,7536,7546,7565,7567,7569,7571,7572,7573,7598,7624,7625,7657,7659,7660,7661,7666,7688,7697,7707,7712,7718,7720,7726,7738,7739,7741,7764,7770,7791,7857,7858,7904,7912,7913,7937,7938,7955,7956,8014,8015,8042,8070,8081,8083,8092,8104,8135,8141,8148,8161,8180,8186,8208,8251,8279,8291,8309,8312,8342,8365,8423,8424,8427,8428,8526,8527,8528,8529,8555,8584,8611,8656,8674,8729,8774,8777,8790,8797,8834,8881,8882,8897,8898,9030,9034,9054,9065,9088,9090,9093,9097,9099,9100,9111,9112,9132,9138,9150,9192,9211,9260,9261,9268,9328,9332,9367,9374,9377,9380,9381,9395,9411,9420,9431,9439,9440,9442,9444,9470,9593,9638,9639,9681,9726,9842,9899,9963,10037,10050,10055,3,2585,2587,2588,2591,2594,2595,2596,2597,2609,2611,2614,2615,2616,2625,2626,2627,2631,2632,2633,2634,2635,2636,2637,2639,2640,2642,2643,2646,2647,2648,2653,2654,2655,2659,2660,2661,2665,2666,2667,2672,2673,2677,2678,2679,2684,2685,2686,2690,2691,2692,2695,2697,2698,2699,2702,2703,2704,2717,2740,2742,2743,2752,2754,2756,2757,2759,2779,2781,2788,2813,5216,5279,5377,5463,5464,5465,5542,5639,5670,5704,5720,5722,5728,5791,5792,5793,5794,5800,5833,5962,6001,6010,6033,6070,6105,6110,6259,6264,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6421,6489,6490,6576,6609,6610,6650,6651,6789,6804,6877,6878,6885,6905,6928,6936,6938,6985,7008,7009,7027,7028,7063,7107,7108,7205,7266,7267,7268,7269,7283,7316,7369,7370,7379,7387,7388,7400,7432,7433,7434,7435,7579,7580,7582,7584,7590,7591,7799,7805,7806,7816,7855,7933,7973,8026,8047,8048,8120,8222,8289,8290,8292,8327,8386,8387,8452,8470,8471,8472,8473,8615,8851,8852,8923,8938,8992,8993,9108,9142,9165,9193,9232,9418,9675,9806,9868,9924,9926,6028,6404,6405,6492,6513,6514,6927,7143,8541,8574,8768,8949,8950,9019,9020,9278,9279,9280,9281,9473,9747,10046,10097,10098,6474,8378,8379,8817,8835,9748,10096,4636,4638,4639,4695,4703,4841,4857,4858,4886,4887,4918,4973,5036,5172,5208,5211,5219,5220,5246,5324,5345,5479,5547,5548,5549,5666,5667,5693,5697,5757,5759,5768,5774,5846,5924,6051,6077,6246,6367,6523,6723,6724,6939,6980])). % 165.36/165.13 cnf(13253,plain, % 165.36/165.13 (~P24(f332(f332(f334(a868),x132531),f332(f253(a868),f2(a868))))), % 165.36/165.13 inference(rename_variables,[],[11675])). % 165.36/165.13 cnf(13256,plain, % 165.36/165.13 (~P24(f332(f332(f334(f874(x132561,x132561)),x132562),f264(x132561,f196(f875(x132561,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10864])). % 165.36/165.13 cnf(13259,plain, % 165.36/165.13 (P24(f332(f332(f334(x132591),f332(x132592,x132593)),f332(f311(x132594,x132591,x132592),f255(f875(x132594,a862)))))), % 165.36/165.13 inference(rename_variables,[],[3873])). % 165.36/165.13 cnf(13262,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),x132621),f332(f332(f81(a868),x132621),x132622)))), % 165.36/165.13 inference(rename_variables,[],[3529])). % 165.36/165.13 cnf(13265,plain, % 165.36/165.13 (~P24(f332(f332(f334(x132651),x132652),f196(f875(x132651,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(13270,plain, % 165.36/165.13 (~P24(f332(f332(f334(x132701),x132702),f196(f875(x132701,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(13273,plain, % 165.36/165.13 (~P24(f332(f332(f334(x132731),x132732),f196(f875(x132731,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(13278,plain, % 165.36/165.13 (~E(f332(a115,x132781),f2(a868))), % 165.36/165.13 inference(rename_variables,[],[4457])). % 165.36/165.13 cnf(13281,plain, % 165.36/165.13 (~E(f332(f332(f104(a868),f332(a115,x132811)),x132811),f332(a115,x132811))), % 165.36/165.13 inference(rename_variables,[],[11424])). % 165.36/165.13 cnf(13290,plain, % 165.36/165.13 (~E(f332(f332(f152(x132901),x132902),x132903),x132903)), % 165.36/165.13 inference(rename_variables,[],[4472])). % 165.36/165.13 cnf(13293,plain, % 165.36/165.13 (P24(f332(f332(f334(x132931),f332(x132932,x132933)),f332(f311(x132934,x132931,x132932),f255(f875(x132934,a862)))))), % 165.36/165.13 inference(rename_variables,[],[3873])). % 165.36/165.13 cnf(13298,plain, % 165.36/165.13 (P38(x132981,x132982,x132983,f332(f332(f155(x132984,x132981),x132985),f117(x132984,f116(x132984))),f116(x132982))), % 165.36/165.13 inference(rename_variables,[],[11106])). % 165.36/165.13 cnf(13304,plain, % 165.36/165.13 (~P24(f332(f332(f334(f874(x133041,x133041)),x133042),f264(x133041,f196(f875(x133041,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10864])). % 165.36/165.13 cnf(13309,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x133091,a862)),x133092),x133092))), % 165.36/165.13 inference(rename_variables,[],[3562])). % 165.36/165.13 cnf(13314,plain, % 165.36/165.13 (~P24(f332(f332(f334(f874(x133141,x133141)),x133142),f264(x133141,f196(f875(x133141,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10864])). % 165.36/165.13 cnf(13325,plain, % 165.36/165.13 (P24(f332(f332(f247(a868),x133251),f332(f332(f82(a868),f332(a115,x133251)),f332(a115,x133251))))), % 165.36/165.13 inference(rename_variables,[],[10530])). % 165.36/165.13 cnf(13330,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x133301,a862)),x133302),f332(f332(f310(x133301),x133303),x133302)))), % 165.36/165.13 inference(rename_variables,[],[3711])). % 165.36/165.13 cnf(13338,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x133381,a862)),x133382),x133382))), % 165.36/165.13 inference(rename_variables,[],[3562])). % 165.36/165.13 cnf(13344,plain, % 165.36/165.13 (~P24(f332(f332(f196(f875(x133441,f875(x133442,a862))),x133443),x133444))), % 165.36/165.13 inference(rename_variables,[],[4549])). % 165.36/165.13 cnf(13350,plain, % 165.36/165.13 (~P24(f332(f332(f334(a868),x133501),f332(f253(a868),f2(a868))))), % 165.36/165.13 inference(rename_variables,[],[11675])). % 165.36/165.13 cnf(13355,plain, % 165.36/165.13 (P24(f332(f332(f247(a1),f332(f332(f22(a1),x133551),f79(a1))),x133551))), % 165.36/165.13 inference(rename_variables,[],[10678])). % 165.36/165.13 cnf(13358,plain, % 165.36/165.13 (P24(f332(f332(f247(a1),f332(f332(f22(a1),x133581),f79(a1))),x133581))), % 165.36/165.13 inference(rename_variables,[],[10678])). % 165.36/165.13 cnf(13363,plain, % 165.36/165.13 (E(f332(x133631,f827(f332(x133631,x133632),f332(f208(x133633),x133632),x133631,x133634,x133633)),f332(x133631,x133632))), % 165.36/165.13 inference(rename_variables,[],[11043])). % 165.36/165.13 cnf(13366,plain, % 165.36/165.13 (~P38(x133661,x133662,x133663,f332(f332(f155(x133664,x133661),x133665),f332(a115,f116(x133664))),f116(x133662))), % 165.36/165.13 inference(rename_variables,[],[11102])). % 165.36/165.13 cnf(13369,plain, % 165.36/165.13 (~P24(f332(f332(f334(a868),x133691),f332(f253(a868),f2(a868))))), % 165.36/165.13 inference(rename_variables,[],[11675])). % 165.36/165.13 cnf(13372,plain, % 165.36/165.13 (~P24(f332(f332(f334(f874(x133721,x133721)),x133722),f264(x133721,f196(f875(x133721,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10864])). % 165.36/165.13 cnf(13383,plain, % 165.36/165.13 (~P24(f332(f332(f334(f874(x133831,x133831)),x133832),f264(x133831,f196(f875(x133831,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10864])). % 165.36/165.13 cnf(13386,plain, % 165.36/165.13 (~P24(f332(f332(f334(a868),x133861),f332(f253(a868),f2(a868))))), % 165.36/165.13 inference(rename_variables,[],[11675])). % 165.36/165.13 cnf(13389,plain, % 165.36/165.13 (~P24(f332(f332(f334(x133891),x133892),f196(f875(x133891,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(13394,plain, % 165.36/165.13 (~E(f332(f332(f81(a1),x133941),x133941),a100)), % 165.36/165.13 inference(rename_variables,[],[4470])). % 165.36/165.13 cnf(13401,plain, % 165.36/165.13 (E(f332(f332(f135(x134011),x134012),f116(x134011)),x134012)), % 165.36/165.13 inference(rename_variables,[],[3184])). % 165.36/165.13 cnf(13410,plain, % 165.36/165.13 (~E(f332(f332(f152(x134101),x134102),x134103),x134103)), % 165.36/165.13 inference(rename_variables,[],[4472])). % 165.36/165.13 cnf(13424,plain, % 165.36/165.13 (P24(f332(f332(f246(a1),x134241),x134241))), % 165.36/165.13 inference(rename_variables,[],[3256])). % 165.36/165.13 cnf(13427,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),x134271),f332(f332(f82(a868),x134271),x134271)))), % 165.36/165.13 inference(rename_variables,[],[3530])). % 165.36/165.13 cnf(13458,plain, % 165.36/165.13 (E(f332(x134581,f827(f332(x134581,x134582),f332(f208(x134583),x134582),x134581,x134584,x134583)),f332(x134581,x134582))), % 165.36/165.13 inference(rename_variables,[],[11043])). % 165.36/165.13 cnf(13461,plain, % 165.36/165.13 (~P24(f332(f332(f246(a868),f332(f332(f82(a868),f332(a115,x134611)),f332(a115,x134611))),x134611))), % 165.36/165.13 inference(rename_variables,[],[10617])). % 165.36/165.13 cnf(13480,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),x134801),f332(f332(f82(a868),x134801),x134801)))), % 165.36/165.13 inference(rename_variables,[],[3530])). % 165.36/165.13 cnf(13483,plain, % 165.36/165.13 (E(f332(x134831,f827(f332(x134831,x134832),f332(f208(x134833),x134832),x134831,x134834,x134833)),f332(x134831,x134832))), % 165.36/165.13 inference(rename_variables,[],[11043])). % 165.36/165.13 cnf(13490,plain, % 165.36/165.13 (~P24(f332(f332(f334(a868),x134901),f332(f253(a868),f2(a868))))), % 165.36/165.13 inference(rename_variables,[],[11675])). % 165.36/165.13 cnf(13495,plain, % 165.36/165.13 (~P24(f332(f332(f246(a868),f332(f332(f82(a868),f332(a115,x134951)),f332(a115,x134951))),x134951))), % 165.36/165.13 inference(rename_variables,[],[10617])). % 165.36/165.13 cnf(13498,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),x134981),f332(f332(f81(a868),x134981),x134982)))), % 165.36/165.13 inference(rename_variables,[],[3529])). % 165.36/165.13 cnf(13504,plain, % 165.36/165.13 (~P24(f332(f332(f334(x135041),x135042),f196(f875(x135041,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(13507,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x135071,a862)),x135072),x135072))), % 165.36/165.13 inference(rename_variables,[],[3562])). % 165.36/165.13 cnf(13512,plain, % 165.36/165.13 (~P24(f332(f332(f334(f874(f869(x135121),f869(x135121))),f332(f332(f267(f869(x135121),f869(x135121)),x135122),f116(x135121))),f158(x135121,x135123)))), % 165.36/165.13 inference(rename_variables,[],[4555])). % 165.36/165.13 cnf(13515,plain, % 165.36/165.13 (~P24(f332(f332(f334(x135151),x135152),f332(f312(x135151,x135153,x135154),f196(f875(x135153,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10867])). % 165.36/165.13 cnf(13518,plain, % 165.36/165.13 (E(f332(f332(f135(x135181),x135182),f116(x135181)),x135182)), % 165.36/165.13 inference(rename_variables,[],[3184])). % 165.36/165.13 cnf(13521,plain, % 165.36/165.13 (~P24(f332(f332(f246(a868),f332(a115,x135211)),x135211))), % 165.36/165.13 inference(rename_variables,[],[4529])). % 165.36/165.13 cnf(13524,plain, % 165.36/165.13 (P24(f332(f332(f247(a1),f332(f332(f22(a1),x135241),f79(a1))),x135241))), % 165.36/165.13 inference(rename_variables,[],[10678])). % 165.36/165.13 cnf(13529,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x135291,a862)),f332(f174(x135291),f172(x135291,x135292,x135293))),f332(f174(x135291),x135293)))), % 165.36/165.13 inference(rename_variables,[],[3970])). % 165.36/165.13 cnf(13543,plain, % 165.36/165.13 (~P24(f332(f332(f246(a868),f332(f332(f82(a868),f332(a115,x135431)),f332(a115,x135431))),x135431))), % 165.36/165.13 inference(rename_variables,[],[10617])). % 165.36/165.13 cnf(13560,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),x135601),f332(f332(f82(a868),x135601),x135601)))), % 165.36/165.13 inference(rename_variables,[],[3530])). % 165.36/165.13 cnf(13563,plain, % 165.36/165.13 (E(f332(f263(x135631,x135631),f264(x135631,x135632)),x135632)), % 165.36/165.13 inference(rename_variables,[],[3213])). % 165.36/165.13 cnf(13579,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x135791,a862)),f332(f174(x135791),f172(x135791,x135792,x135793))),f332(f174(x135791),x135793)))), % 165.36/165.13 inference(rename_variables,[],[3970])). % 165.36/165.13 cnf(13584,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),x135841),f332(f332(f82(a868),x135841),x135841)))), % 165.36/165.13 inference(rename_variables,[],[3530])). % 165.36/165.13 cnf(13592,plain, % 165.36/165.13 (P24(f332(f332(f246(a1),x135921),x135921))), % 165.36/165.13 inference(rename_variables,[],[3256])). % 165.36/165.13 cnf(13595,plain, % 165.36/165.13 (~P24(f332(f332(f247(a868),f332(f332(f81(a868),x135951),x135952)),x135951))), % 165.36/165.13 inference(rename_variables,[],[4547])). % 165.36/165.13 cnf(13598,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x135981,a862)),x135982),f332(f332(f113(f875(x135981,a862)),x135983),f255(f875(x135981,a862)))))), % 165.36/165.13 inference(rename_variables,[],[11075])). % 165.36/165.13 cnf(13605,plain, % 165.36/165.13 (~P24(f332(f332(f196(f875(x136051,f875(x136052,a862))),x136053),x136054))), % 165.36/165.13 inference(rename_variables,[],[4549])). % 165.36/165.13 cnf(13608,plain, % 165.36/165.13 (~P24(f332(f332(f334(f874(x136081,x136081)),x136082),f264(x136081,f196(f875(x136081,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10864])). % 165.36/165.13 cnf(13613,plain, % 165.36/165.13 (~P24(f332(f332(f334(a868),x136131),f332(f253(a868),f2(a868))))), % 165.36/165.13 inference(rename_variables,[],[11675])). % 165.36/165.13 cnf(13618,plain, % 165.36/165.13 (P24(f332(f332(f334(f874(x136181,x136181)),f332(f332(f267(x136181,x136181),x136182),x136182)),f308(x136181,x136183)))), % 165.36/165.13 inference(rename_variables,[],[3908])). % 165.36/165.13 cnf(13623,plain, % 165.36/165.13 (E(f332(f332(f135(x136231),x136232),f116(x136231)),x136232)), % 165.36/165.13 inference(rename_variables,[],[3184])). % 165.36/165.13 cnf(13646,plain, % 165.36/165.13 (~P24(f332(f332(f247(a868),f332(f332(f81(a868),x136461),x136462)),x136462))), % 165.36/165.13 inference(rename_variables,[],[4546])). % 165.36/165.13 cnf(13663,plain, % 165.36/165.13 (~P24(f332(f332(f246(a868),f332(a115,x136631)),x136631))), % 165.36/165.13 inference(rename_variables,[],[4529])). % 165.36/165.13 cnf(13668,plain, % 165.36/165.13 (~P24(f332(f332(f334(x136681),x136682),f196(f875(x136681,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(13686,plain, % 165.36/165.13 (~P24(f332(f332(f334(x136861),x136862),f332(f312(x136861,x136863,x136864),f196(f875(x136863,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10867])). % 165.36/165.13 cnf(13689,plain, % 165.36/165.13 (~P24(f332(f332(f334(x136891),x136892),f196(f875(x136891,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(13696,plain, % 165.36/165.13 (~P24(f332(f332(f334(x136961),x136962),f196(f875(x136961,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(13699,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),x136991),f332(f332(f82(a868),x136991),x136991)))), % 165.36/165.13 inference(rename_variables,[],[3530])). % 165.36/165.13 cnf(13702,plain, % 165.36/165.13 (~E(f332(f332(f152(x137021),x137022),x137023),x137023)), % 165.36/165.13 inference(rename_variables,[],[4472])). % 165.36/165.13 cnf(13707,plain, % 165.36/165.13 (~P24(f332(f332(f196(f875(x137071,f875(x137072,a862))),x137073),x137074))), % 165.36/165.13 inference(rename_variables,[],[4549])). % 165.36/165.13 cnf(13710,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x137101,a862)),x137102),x137102))), % 165.36/165.13 inference(rename_variables,[],[3562])). % 165.36/165.13 cnf(13722,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),f2(a868)),x137221))), % 165.36/165.13 inference(rename_variables,[],[3277])). % 165.36/165.13 cnf(13725,plain, % 165.36/165.13 (~P24(f332(f332(f334(f874(x137251,x137251)),x137252),f264(x137251,f196(f875(x137251,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10864])). % 165.36/165.13 cnf(13728,plain, % 165.36/165.13 (~P24(f332(f332(f196(f875(x137281,f875(x137282,a862))),x137283),x137284))), % 165.36/165.13 inference(rename_variables,[],[4549])). % 165.36/165.13 cnf(13731,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x137311,a862)),f332(f174(x137311),f172(x137311,x137312,x137313))),f332(f174(x137311),x137313)))), % 165.36/165.13 inference(rename_variables,[],[3970])). % 165.36/165.13 cnf(13748,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x137481,a862)),f332(f174(x137481),f172(x137481,x137482,x137483))),f332(f174(x137481),x137483)))), % 165.36/165.13 inference(rename_variables,[],[3970])). % 165.36/165.13 cnf(13762,plain, % 165.36/165.13 (~E(f332(f332(f152(x137621),x137622),x137623),x137623)), % 165.36/165.13 inference(rename_variables,[],[4472])). % 165.36/165.13 cnf(13772,plain, % 165.36/165.13 (~E(f332(f332(f152(x137721),x137722),x137723),x137723)), % 165.36/165.13 inference(rename_variables,[],[4472])). % 165.36/165.13 cnf(13781,plain, % 165.36/165.13 (P24(f332(f332(f334(x137811),f332(x137812,x137813)),f332(f311(x137814,x137811,x137812),f255(f875(x137814,a862)))))), % 165.36/165.13 inference(rename_variables,[],[3873])). % 165.36/165.13 cnf(13786,plain, % 165.36/165.13 (~P24(f332(f332(f196(f875(x137861,f875(x137862,a862))),x137863),x137864))), % 165.36/165.13 inference(rename_variables,[],[4549])). % 165.36/165.13 cnf(13793,plain, % 165.36/165.13 (~P24(f332(f332(f334(a868),x137931),f332(f253(a868),f2(a868))))), % 165.36/165.13 inference(rename_variables,[],[11675])). % 165.36/165.13 cnf(13802,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),f45(a868,x138021,x138022)),x138021))), % 165.36/165.13 inference(rename_variables,[],[3722])). % 165.36/165.13 cnf(13812,plain, % 165.36/165.13 (~P24(f332(f332(f334(x138121),x138122),f196(f875(x138121,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(13815,plain, % 165.36/165.13 (E(f332(f332(f135(x138151),f116(x138151)),x138152),x138152)), % 165.36/165.13 inference(rename_variables,[],[3208])). % 165.36/165.13 cnf(13822,plain, % 165.36/165.13 (~P38(x138221,x138222,x138223,f332(f332(f155(x138224,x138221),x138225),f332(a115,f116(x138224))),f116(x138222))), % 165.36/165.13 inference(rename_variables,[],[11102])). % 165.36/165.13 cnf(13829,plain, % 165.36/165.13 (P24(f332(f332(f246(a1),x138291),x138291))), % 165.36/165.13 inference(rename_variables,[],[3256])). % 165.36/165.13 cnf(13832,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),f2(a868)),x138321))), % 165.36/165.13 inference(rename_variables,[],[3277])). % 165.36/165.13 cnf(13850,plain, % 165.36/165.13 (~P24(f332(f332(f334(f874(x138501,x138501)),x138502),f264(x138501,f196(f875(x138501,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10864])). % 165.36/165.13 cnf(13864,plain, % 165.36/165.13 (P24(f332(f332(f247(a1),f332(f332(f22(a1),x138641),f79(a1))),x138641))), % 165.36/165.13 inference(rename_variables,[],[10678])). % 165.36/165.13 cnf(13880,plain, % 165.36/165.13 (~P24(f332(f332(f246(a868),f332(a115,x138801)),x138801))), % 165.36/165.13 inference(rename_variables,[],[4529])). % 165.36/165.13 cnf(13897,plain, % 165.36/165.13 (E(f332(f263(x138971,x138971),f264(x138971,x138972)),x138972)), % 165.36/165.13 inference(rename_variables,[],[3213])). % 165.36/165.13 cnf(13900,plain, % 165.36/165.13 (~E(f332(f332(f152(x139001),x139002),x139003),x139003)), % 165.36/165.13 inference(rename_variables,[],[4472])). % 165.36/165.13 cnf(13903,plain, % 165.36/165.13 (~P24(f332(f332(f334(x139031),x139032),f196(f875(x139031,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(13922,plain, % 165.36/165.13 (P24(f332(f332(f247(a1),f332(f332(f22(a1),x139221),f79(a1))),x139221))), % 165.36/165.13 inference(rename_variables,[],[10678])). % 165.36/165.13 cnf(13927,plain, % 165.36/165.13 (~P24(f332(f332(f334(f874(f869(x139271),f869(x139271))),f332(f332(f267(f869(x139271),f869(x139271)),f116(x139271)),x139272)),f158(x139271,x139273)))), % 165.36/165.13 inference(rename_variables,[],[4557])). % 165.36/165.13 cnf(13950,plain, % 165.36/165.13 (~P24(f332(f332(f334(f874(x139501,x139501)),x139502),f264(x139501,f196(f875(x139501,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10864])). % 165.36/165.13 cnf(13957,plain, % 165.36/165.13 (~P24(f332(f332(f334(f874(x139571,x139571)),x139572),f264(x139571,f196(f875(x139571,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10864])). % 165.36/165.13 cnf(13960,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),f2(a868)),x139601))), % 165.36/165.13 inference(rename_variables,[],[3277])). % 165.36/165.13 cnf(13980,plain, % 165.36/165.13 (P24(f332(f332(f246(a1),x139801),x139801))), % 165.36/165.13 inference(rename_variables,[],[3256])). % 165.36/165.13 cnf(13983,plain, % 165.36/165.13 (P24(f332(f332(f334(x139831),f332(x139832,x139833)),f332(f311(x139834,x139831,x139832),f255(f875(x139834,a862)))))), % 165.36/165.13 inference(rename_variables,[],[3873])). % 165.36/165.13 cnf(13999,plain, % 165.36/165.13 (~E(f332(f332(f152(x139991),x139992),x139993),x139993)), % 165.36/165.13 inference(rename_variables,[],[4472])). % 165.36/165.13 cnf(14012,plain, % 165.36/165.13 (E(f332(f263(x140121,x140121),f264(x140121,x140122)),x140122)), % 165.36/165.13 inference(rename_variables,[],[3213])). % 165.36/165.13 cnf(14028,plain, % 165.36/165.13 (~E(f332(f332(f152(x140281),x140282),x140283),x140283)), % 165.36/165.13 inference(rename_variables,[],[4472])). % 165.36/165.13 cnf(14031,plain, % 165.36/165.13 (E(f332(f332(f135(x140311),x140312),f116(x140311)),x140312)), % 165.36/165.13 inference(rename_variables,[],[3184])). % 165.36/165.13 cnf(14044,plain, % 165.36/165.13 (E(f332(x140441,f827(f332(x140441,x140442),f332(f208(x140443),x140442),x140441,x140444,x140443)),f332(x140441,x140442))), % 165.36/165.13 inference(rename_variables,[],[11043])). % 165.36/165.13 cnf(14049,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),x140491),f332(f332(f81(a868),x140491),x140492)))), % 165.36/165.13 inference(rename_variables,[],[3529])). % 165.36/165.13 cnf(14052,plain, % 165.36/165.13 (~E(f332(f332(f152(x140521),x140522),x140523),x140523)), % 165.36/165.13 inference(rename_variables,[],[4472])). % 165.36/165.13 cnf(14066,plain, % 165.36/165.13 (P24(f332(f332(f246(a868),x140661),f332(f332(f81(a868),x140661),x140662)))), % 165.36/165.13 inference(rename_variables,[],[3529])). % 165.36/165.13 cnf(14069,plain, % 165.36/165.13 (~E(f332(f332(f104(a868),f332(a115,x140691)),x140691),f332(a115,x140691))), % 165.36/165.13 inference(rename_variables,[],[11424])). % 165.36/165.13 cnf(14080,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x140801,a862)),f332(f174(x140801),f172(x140801,x140802,x140803))),f332(f174(x140801),x140803)))), % 165.36/165.13 inference(rename_variables,[],[3970])). % 165.36/165.13 cnf(14093,plain, % 165.36/165.13 (~P24(f332(f332(f334(x140931),x140932),f196(f875(x140931,a862))))), % 165.36/165.13 inference(rename_variables,[],[4532])). % 165.36/165.13 cnf(14100,plain, % 165.36/165.13 (~P24(f332(f332(f334(f874(x141001,x141001)),x141002),f264(x141001,f196(f875(x141001,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10864])). % 165.36/165.13 cnf(14107,plain, % 165.36/165.13 (~P24(f332(f332(f334(a868),x141071),f332(f253(a868),f2(a868))))), % 165.36/165.13 inference(rename_variables,[],[11675])). % 165.36/165.13 cnf(14113,plain, % 165.36/165.13 (~E(f332(f332(f152(x141131),x141132),x141133),x141133)), % 165.36/165.13 inference(rename_variables,[],[4472])). % 165.36/165.13 cnf(14131,plain, % 165.36/165.13 (E(f332(f263(x141311,x141311),f264(x141311,x141312)),x141312)), % 165.36/165.13 inference(rename_variables,[],[3213])). % 165.36/165.13 cnf(14145,plain, % 165.36/165.13 (~P24(f332(f332(f247(a868),x141451),x141451))), % 165.36/165.13 inference(rename_variables,[],[4516])). % 165.36/165.13 cnf(14152,plain, % 165.36/165.13 (E(f332(x141521,f827(f332(x141521,x141522),f332(f208(x141523),x141522),x141521,x141524,x141523)),f332(x141521,x141522))), % 165.36/165.13 inference(rename_variables,[],[11043])). % 165.36/165.13 cnf(14161,plain, % 165.36/165.13 (~P24(f332(f332(f247(a868),f332(f332(f81(a868),x141611),x141612)),x141611))), % 165.36/165.13 inference(rename_variables,[],[4547])). % 165.36/165.13 cnf(14181,plain, % 165.36/165.13 (E(f332(f263(x141811,x141811),f264(x141811,x141812)),x141812)), % 165.36/165.13 inference(rename_variables,[],[3213])). % 165.36/165.13 cnf(14186,plain, % 165.36/165.13 (~P24(f332(f332(f246(a868),f332(a115,x141861)),x141861))), % 165.36/165.13 inference(rename_variables,[],[4529])). % 165.36/165.13 cnf(14208,plain, % 165.36/165.13 (~P24(f332(f332(f334(x142081),x142082),f332(f312(x142081,x142083,x142084),f196(f875(x142083,a862)))))), % 165.36/165.13 inference(rename_variables,[],[10867])). % 165.36/165.13 cnf(14241,plain, % 165.36/165.13 (~P24(f332(f332(f334(a868),x142411),f332(f253(a868),f2(a868))))), % 165.36/165.13 inference(rename_variables,[],[11675])). % 165.36/165.13 cnf(14261,plain, % 165.36/165.13 (P24(f332(f332(f247(a868),x142611),f332(a115,f332(f332(f81(a868),x142612),x142611))))), % 165.36/165.13 inference(rename_variables,[],[3715])). % 165.36/165.13 cnf(14269,plain, % 165.36/165.13 (P24(f332(f332(f334(x142691),f332(x142692,x142693)),f332(f311(x142694,x142691,x142692),f255(f875(x142694,a862)))))), % 165.36/165.13 inference(rename_variables,[],[3873])). % 165.36/165.13 cnf(14293,plain, % 165.36/165.13 (~P24(f332(f332(f334(a868),x142931),f332(f253(a868),f2(a868))))), % 165.36/165.13 inference(rename_variables,[],[11675])). % 165.36/165.13 cnf(14339,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x143391,a862)),f332(f174(x143391),f172(x143391,x143392,x143393))),f332(f174(x143391),x143393)))), % 165.36/165.13 inference(rename_variables,[],[3970])). % 165.36/165.13 cnf(14352,plain, % 165.36/165.13 (P24(f332(f332(f246(f875(x143521,a862)),f332(f174(x143521),f172(x143521,x143522,x143523))),f332(f174(x143521),x143523)))), % 165.36/165.13 inference(rename_variables,[],[3970])). % 165.36/165.13 cnf(14365,plain, % 165.36/165.13 ($false), % 165.36/165.13 inference(scs_inference,[],[3283,3704,3285,4017,3856,4054,3041,4548,3258,4506,4536,4517,3908,13618,3334,4553,4508,3352,3717,4532,13265,13270,13273,13389,13504,13668,13689,13696,13812,13903,14093,3970,13529,13579,13731,13748,14080,14339,14352,3358,3873,13259,13293,13781,13983,14269,3746,3362,4462,4457,13278,4541,4472,13290,13410,13702,13762,13772,13900,13999,14028,14052,14113,4470,13394,3239,3338,4048,3919,3255,3256,13424,13592,13829,13980,3722,13802,3277,13722,13832,13960,3577,3711,13330,3562,13309,13338,13507,13710,3713,3530,13427,13480,13560,13584,13699,3529,13262,13498,14049,14066,4158,3715,14261,3213,13563,13897,14012,14131,14181,3184,13401,13518,13623,14031,3093,3208,13815,4554,4555,13512,4557,13927,4516,14145,4529,13521,13663,13880,14186,4538,4543,4549,13344,13605,13707,13728,13786,4546,13646,4547,13595,14161,3471,11424,13281,14069,10232,12950,10499,13129,10288,11856,12560,11733,11773,12353,11235,13111,10470,13031,12137,10530,13325,11779,12601,13033,10518,12614,10975,12355,12384,12391,10854,13045,11075,13598,10818,10678,13355,13358,13524,13864,13922,11677,4281,3630,12411,10849,11137,11096,11043,13363,13458,13483,14044,14152,13061,10211,12870,10851,10347,11219,11188,10622,10461,3316,3289,3197,11041,11119,10901,12858,12861,13125,10627,13109,13145,11557,12080,12069,11065,11110,12175,10196,12620,11673,11729,11675,13253,13350,13369,13386,13490,13613,13793,14107,14241,14293,10635,11029,10864,13256,13304,13314,13372,13383,13608,13725,13850,13950,13957,14100,11992,10867,13515,13686,14208,11070,11140,10617,13461,13495,13543,10720,11930,11933,11193,12407,12323,13133,11102,13366,13822,10879,11106,13298,2864,3820,9,2,5282,7901,8443,8422,6100,8989,6051,8532,9869,5530,5567,8439,7149,5924,6566,8567,7761,8712,9248,4973,9432,5761,9472,8500,9719,5916,6189,7414,5354,7327,5675,9438,9936,6260,9449,8990,5929,7401,9028,9527,5605,5809,5815,8433,9227,9620,10126,5395,5456,5733,6407,5549,6723,9370,7730,5043,5201,8566,5050,6406,6759,6717,4779,8463,9125,9494,7349,5208,6095,8007,5684,6009,6076,6123,8843,5471,5953,7300,8760,9566,6122,9753,5533,4639,8793,5361,5577,8371,8755,6975,9372,4857,7089,4636,4904,5015,6808,5732,8745,7325,6306,7808,9415,5560,9870,9815,5051,5199,5810,9022,8607,9397,8653,5320,6373,8581,6225,5879,7165,5671,5892,6246,6510,6743,8040,9101,5305,6461,6794,8495,6359,8548,7371,7710,5846,6101,5595,6231,8697,8357,7819,8349,10059,6171,8758,5747,6643,6764,5341,6473,8870,5591,8523,8,8866,5324,8023,5455,7144,5303,6077,7772,5678,7298,8478,5790,8524,9890,8640,5776,7315,8522,5172,5689,9023,9172,9559,6526,5234,6736,6756,5310,5738,4888,7968,9181,6227,8991,9520,9691,6737,8781,5479,5736,5907,6781,6091,6716,8351,8713,5650,6356,6863,5164,5311,7681,9759,9859,5306,6319,5903,6767,8576,5604,5741,10112,6715,9611,5323,5329,6072,6472,6761,9207,5774,8675,5686,5796,6055,8024,8375,5036,6257,6308,8209,9502,5745,5638,6479,9056,9643,10058,5548,6054,7935,7174,4952,5505,6252,9171,6185,6792,9244,5410,5414,7481,8875,5238,8113,5356,5439,5547,8494,8568,6685,6367,5345,5685,6275,8501,6724,7616,6416,8608,9522,5295,9652,6304,5237,5697,4975,5220,8657,9558,9170,6765,7530,8756,6240,8885,6176,6458,7440,8503,8958,9247,7844,6127,9224,4701,6812,5243,8229,4644,9005,4595,5693,7871,4702,5165,5210,8039,5044,5239,5956,8253,8560,5607,5342,5511,5579,6276,6874,7696,5757,6365,7326,4926,5795,7007,5743,6034,6763,6314,9857,4974,5173,6125,8861,8782,5340,5405,6074,9504,7635,9755,9664,6121,8837,9503,6360,8735,6097,4694,5022,6058,6795,7343,8166,9371,5406,4569,7531,5312,6268,7763,6242,7483,7549,9505,4638,9662,6282,5109,4646,5211,6876,7061,7351,9674,5529,4738,5336,5888,4951,9565,9856,5637,5965,6364,6897,7758,6714,4773,6170,8699,4918,9335,9987,5098,4863,5483,5995,9610,9057,8775,5246,6092,8502,4889,5561,9276,5212,5374,6244,6898,7232,7486,7731,5867,6355,6880,8185,5768,5045,5327,9221,9688,5749,4743,5189,6078,9895,4841,6229,6438,6523,5759,7430,5754,6565,8757,6179,5227,8504,8849,7177,6944,8412,6437,6619,6932,8477,7411,5219,6361,8390,4677]), % 165.36/165.13 ['proof']). % 165.36/165.14 % SZS output end Proof % 165.36/165.14 % Total time :150.940000s %------------------------------------------------------------------------------